2404.19737v1

## Better & Faster Large Language Models via Multi-token Prediction Fabian Gloeckle * 1 2 Badr Youbi Idrissi * 1 3 Baptiste Rozière 1 David Lopez-Paz + 1 Gabriel Synnaeve + 1 ## Abstract Large language models such as GPT and Llama are trained with a next-token prediction loss. In this work, we suggest that training language models to predict multiple future tokens at once results in higher sample efficiency. More specifically, at each position in the training corpus, we ask the model to predict the following n tokens using n independent output heads, operating on top of a shared model trunk. Considering multi-token prediction as an auxiliary training task, we measure improved downstream capabilities with no overhead in training time for both code and natural language models. The method is increasingly useful for larger model sizes, and keeps its appeal when training for multiple epochs. Gains are especially pronounced on generative benchmarks like coding, where our models consistently outperform strong baselines by several percentage points. Our 13B parameter models solves 12 % more problems on HumanEval and 17 % more on MBPP than comparable next-token models. Experiments on small algorithmic tasks demonstrate that multi-token prediction is favorable for the development of induction heads and algorithmic reasoning capabilities. As an additional benefit, models trained with 4-token prediction are up to 3 × faster at inference, even with large batch sizes. ## 1. Introduction Humanity has condensed its most ingenious undertakings, surprising findings and beautiful productions into text. Large Language Models (LLMs) trained on all of these corpora are able to extract impressive amounts of world knowledge, as well as basic reasoning capabilities by implementing a simple-yet powerful-unsupervised learning task: next-token prediction. Despite the recent wave of impressive achievements (OpenAI, 2023), next-token pre- * Equal contribution + Last authors 1 FAIR at Meta 2 CERMICS Ecole des Ponts ParisTech 3 LISN Université Paris-Saclay. Correspondence to: Fabian Gloeckle <fgloeckle@meta.com>, Badr Youbi Idrissi <byoubi@meta.com>. diction remains an inefficient way of acquiring language, world knowledge and reasoning capabilities. More precisely, teacher forcing with next-token prediction latches on local patterns and overlooks 'hard' decisions. Consequently, it remains a fact that state-of-the-art next-token predictors call for orders of magnitude more data than human children to arrive at the same level of fluency (Frank, 2023). Figure 1: Overview of multi-token prediction. (Top) During training, the model predicts 4 future tokens at once, by means of a shared trunk and 4 dedicated output heads. During inference, we employ only the next-token output head. Optionally, the other three heads may be used to speed-up inference time. (Bottom) Multi-token prediction improves pass@1 on the MBPP code task, significantly so as model size increases. Error bars are confidence intervals of 90% computed with bootstrapping over dataset samples. <details> <summary>Image 1 Details</summary>  ### Visual Description ## Diagram: 4-Token Prediction Architecture ### Overview The diagram illustrates a multi-head architecture for 4-token prediction tasks. Inputs are processed through a shared layer, then distributed across four specialized heads (Head 1–4). Each head predicts a subset of tokens (2–8), with some tokens discarded at inference or used to accelerate the model up to 3× speed. ### Components/Axes - **Inputs**: Labeled 1–4, feeding into the shared layer. - **Shared Layer**: Central processing unit for all heads. - **Heads**: - Head 1: Predicts tokens 2–4. - Head 2: Predicts tokens 2–5. - Head 3: Predicts tokens 3–6. - Head 4: Predicts tokens 4–7. - **Tokens**: Numbered 1–8, with tokens 2–8 distributed across heads. - **Discarded Tokens**: Tokens 5–8 (Head 1), 6–8 (Head 2), 7–8 (Head 3), and 8 (Head 4) are marked as discarded or used for speedup. ### Detailed Analysis - **Token Distribution**: - Head 1: Tokens 2–4 (no discards). - Head 2: Tokens 2–5 (discards 6–8). - Head 3: Tokens 3–6 (discards 7–8). - Head 4: Tokens 4–7 (discards 8). - **Legend**: Discarded tokens (pink) or speedup tokens (green). ### Key Observations - **Token Overlap**: Heads share overlapping token ranges (e.g., token 4 is processed by all heads). - **Discard Strategy**: Later tokens (5–8) are progressively discarded across heads, suggesting prioritization of earlier tokens. ### Interpretation The architecture optimizes computational efficiency by parallelizing token predictions across heads while discarding less critical tokens. This design likely reduces inference latency by up to 3×, as noted in the legend. The shared layer ensures common features are extracted before specialization, balancing accuracy and speed. --- ## Chart: MBPP Pass@1 Gains with 4-Token Prediction ### Overview The bar chart compares performance gains (Pass@1) for models of varying sizes (0.3B–13B) using 4-token prediction versus a baseline. Larger models show significantly higher gains. ### Components/Axes - **X-Axis**: Model size (0.3B, 0.6B, 1.3B, 3B, 6.7B, 13B). - **Y-Axis**: Pass@1 gains (baseline: -1.7; 4-token prediction: +4.5). - **Legend**: - Baseline: Red bars. - 4-Token Prediction: Green bars. ### Detailed Analysis - **Model Sizes and Gains**: - **0.3B**: Baseline = -1.7; 4-Token = +1.8. - **0.6B**: Baseline = -4.7; 4-Token = +4.5. - **1.3B**: Baseline = -6.8; 4-Token = +6.8. - **3B**: Baseline = -11.1; 4-Token = +11.1. - **6.7B**: Baseline = -23.9; 4-Token = +23.9. - **13B**: Baseline = -26.0; 4-Token = +26.0. - **Trends**: - Larger models exhibit **linear scaling** in gains (e.g., 13B model gains match baseline losses). - Baseline performance worsens with model size (e.g., 13B baseline = -26.0). ### Key Observations - **4-Token Prediction Outperforms Baseline**: All model sizes show positive gains with 4-token prediction. - **Scalability**: Gains increase proportionally with model size (e.g., 13B model gains = 26.0, baseline = -26.0). ### Interpretation The 4-token prediction strategy significantly improves performance across all model sizes, with larger models achieving near-symmetry between baseline losses and prediction gains. This suggests that token prediction efficiency scales with model capacity, making 4-token prediction particularly valuable for high-capacity models. The baseline’s worsening performance with size implies that larger models may struggle more with non-predicted tokens, highlighting the importance of targeted prediction strategies. --- **Language Note**: All text in the image is in English. No non-English content detected. </details> In this study, we argue that training LLMs to predict multiple tokens at once will drive these models toward better sample efficiency. As anticipated in Figure 1, multi-token prediction instructs the LLM to predict the n future tokens from each position in the training corpora, all at once and in parallel (Qi et al., 2020). Contributions While multi-token prediction has been studied in previous literature (Qi et al., 2020), the present work offers the following contributions: 1. We propose a simple multi-token prediction architecture with no train time or memory overhead (Section 2). 2. We provide experimental evidence that this training paradigm is beneficial at scale, with models up to 13B parameters solving around 15% more code problems on average (Section 3). 3. Multi-token prediction enables self-speculative decoding, making models up to 3 times faster at inference time across a wide range of batch-sizes (Section 3.2). While cost-free and simple, multi-token prediction is an effective modification to train stronger and faster transformer models. We hope that our work spurs interest in novel auxiliary losses for LLMs well beyond next-token prediction, as to improve the performance, coherence, and reasoning abilities of these fascinating models. ## 2. Method Standard language modeling learns about a large text corpus x 1 , . . . x T by implementing a next-token prediction task. Formally, the learning objective is to minimize the crossentropy loss <!-- formula-not-decoded --> where P θ is our large language model under training, as to maximize the probability of x t +1 as the next future token, given the history of past tokens x t :1 = x t , . . . , x 1 . In this work, we generalize the above by implementing a multi-token prediction task, where at each position of the training corpus, the model is instructed to predict n future tokens at once. This translates into the cross-entropy loss <!-- formula-not-decoded --> To make matters tractable, we assume that our large language model P θ employs a shared trunk to produce a latent representation z t :1 of the observed context x t :1 , then fed into n independent heads to predict in parallel each of the n future tokens (see Figure 1). This leads to the following factorization of the multi-token prediction cross-entropy loss: <!-- formula-not-decoded --> <!-- formula-not-decoded --> In practice, our architecture consists of a shared transformer trunk f s producing the hidden representation z t :1 from the observed context x t :1 , n independent output heads implemented in terms of transformer layers f h i , and a shared unembedding matrix f u . Therefore, to predict n future tokens, we compute: <!-- formula-not-decoded --> for i = 1 , . . . n , where, in particular, P θ ( x t +1 | x t :1 ) is our next-token prediction head. See Appendix B for other variations of multi-token prediction architectures. Memory-efficient implementation One big challenge in training multi-token predictors is reducing their GPU memory utilization. To see why this is the case, recall that in current LLMs the vocabulary size V is much larger than the dimension d of the latent representation-therefore, logit vectors become the GPU memory usage bottleneck. Naive implementations of multi-token predictors that materialize all logits and their gradients, both of shape ( n, V ) , severely limit the allowable batch-size and average GPU memory utilization. Because of these reasons, in our architecture we propose to carefully adapt the sequence of forward and backward operations, as illustrated in Figure 2. In particular, after the forward pass through the shared trunk f s , we sequentially compute the forward and backward pass of each independent output head f i , accumulating gradients at the trunk. While this creates logits (and their gradients) for the output head f i , these are freed before continuing to the next output head f i +1 , requiring the long-term storage only of the d -dimensional trunk gradient ∂L n /∂f s . In sum, we have reduced the peak GPU memory utilization from O ( nV + d ) to O ( V + d ) , at no expense in runtime (Table S5). Inference During inference time, the most basic use of the proposed architecture is vanilla next-token autoregressive prediction using the next-token prediction head P θ ( x t +1 | x t :1 ) , while discarding all others. However, the additional output heads can be leveraged to speed up decoding from the next-token prediction head with self-speculative decoding methods such as blockwise parallel decoding (Stern et al., 2018)-a variant of speculative decoding (Leviathan et al., 2023) without the need for an additional draft model-and speculative decoding with Medusa-like tree attention (Cai et al., 2024). Figure 2: Order of the forward/backward in an n -token prediction model with n = 2 heads. By performing the forward/backward on the heads in sequential order, we avoid materializing all unembedding layer gradients in memory simultaneously and reduce peak GPU memory usage. <details> <summary>Image 2 Details</summary>  ### Visual Description ## Diagram: Neural Network Architecture with Forward/Backward Passes ### Overview The image depicts a neural network architecture with shared and head-specific components, illustrating forward and backward passes. Arrows indicate data/tensor flow, and code snippets on the right explain the computational logic. The diagram uses color-coded arrows (green, orange, blue) to differentiate operations. ### Components/Axes - **Left Diagram**: - **Labels**: - "Forward" (blue arrow), "Backward" (orange arrow), "Tensor" (gray circle). - Components: "Shared" (dark blue rectangle), "Head 1" (green rectangle), "Head 2" (green rectangle), "Loss 1" (yellow rectangle), "Loss 2" (yellow rectangle). - **Flow**: - Input `x` flows through the "Shared" layer to produce tensor `z`. - `z` splits into two paths: one to "Head 1" and another to "Head 2". - Each head computes a loss ("Loss 1" and "Loss 2"), with gradients (orange arrows) flowing backward to the "Shared" layer. - **Code Snippets** (right side): ```python z = model.shared(x) # Forward pass through shared layer d = z.detach() # Detach gradients from z d.requires_grad = True # Enable gradient tracking for detached tensor for i in range(n): # Loop over heads p = model.heads[i](d) # Forward pass through head i loss(p, y[i]).backward() # Compute loss and backward pass z.backward(gradient=d.grad) # Backward pass through shared layer with gradient ``` ### Detailed Analysis - **Forward Pass**: - Input `x` is processed by the "Shared" layer to generate tensor `z`. - `z` is split into two branches for "Head 1" and "Head 2", each producing outputs `p` for their respective losses. - **Backward Pass**: - Gradients from "Loss 1" and "Loss 2" (orange arrows) propagate backward through their heads and into the "Shared" layer. - The code explicitly detaches `z` from the computation graph (`z.detach()`) to prevent gradients from flowing through the shared layer during head-specific loss calculations. However, `d.requires_grad = True` re-enables gradient tracking for `d`, allowing the shared layer to be updated via `z.backward(gradient=d.grad)`. ### Key Observations 1. **Gradient Isolation**: The shared layer's gradients are isolated during head-specific loss computations but reintegrated during the final backward pass. 2. **Color-Coded Flow**: - Green arrows: Forward passes through heads. - Orange arrows: Backward passes for loss gradients. - Blue arrow: Forward pass through the shared layer. 3. **Code-Architecture Alignment**: - The code mirrors the diagram's flow, with `z.detach()` ensuring the shared layer is not updated during head-specific training but is later updated via explicit gradient assignment. ### Interpretation This architecture demonstrates **modular training** where a shared layer (e.g., feature extractor) is trained alongside task-specific heads (e.g., classifiers). By detaching the shared layer's output during head-specific loss calculations, the model prevents gradient leakage between heads, enabling independent optimization. The final backward pass through the shared layer aggregates gradients from all heads, allowing the shared parameters to adapt to the combined loss. This pattern is common in multi-task learning or ensemble methods where shared features are refined based on aggregated task-specific feedback. </details> ## 3. Experiments on real data We demonstrate the efficacy of multi-token prediction losses by seven large-scale experiments. Section 3.1 shows how multi-token prediction is increasingly useful when growing the model size. Section 3.2 shows how the additional prediction heads can speed up inference by a factor of 3 × using speculative decoding. Section 3.3 demonstrates how multi-token prediction promotes learning longer-term patterns, a fact most apparent in the extreme case of byte-level tokenization. Section 3.4 shows that 4 -token predictor leads to strong gains with a tokenizer of size 32 k. Section 3.5 illustrates that the benefits of multi-token prediction remain for training runs with multiple epochs. Section 3.6 showcases the rich representations promoted by pretraining with multi-token prediction losses by finetuning on the CodeContests dataset (Li et al., 2022). Section 3.7 shows that the benefits of multi-token prediction carry to natural language models, improving generative evaluations such as summarization, while not regressing significantly on standard benchmarks based on multiple choice questions and negative log-likelihoods. To allow fair comparisons between next-token predictors and n -token predictors, the experiments that follow always compare models with an equal amount of parameters. That is, when we add n -1 layers in future prediction heads, we remove n -1 layers from the shared model trunk. Please refer to Table S14 for the model architectures and to Table S13 for an overview of the hyperparameters we use in our experiments. ## 3.1. Benefits scale with model size To study this phenomenon, we train models of six sizes in the range 300M to 13B parameters from scratch on at least 91B tokens of code. The evaluation results in Fig- Figure 3: Results of n -token prediction models on MBPP by model size. We train models of six sizes in the range or 300M to 13B total parameters on code, and evaluate pass@1,10,100 on the MBPP (Austin et al., 2021) and HumanEval (Chen et al., 2021) benchmark with 1000 samples. Multi-token prediction models are worse than the baseline for small model sizes, but outperform the baseline at scale. Error bars are confidence intervals of 90% computed with bootstrapping over dataset samples. <details> <summary>Image 3 Details</summary>  ### Visual Description ## Bar Chart: Model Performance Comparison (MBPP vs Human Evaluation) ### Overview The image presents a comparative bar chart analyzing the performance of language models across different sizes (0.3B to 13B parameters) using two evaluation frameworks: MBPP (Math Benchmark Problems Project) and Human Evaluation. The chart uses vertical bars with positive/negative values to represent performance deviations from a baseline, with green bars indicating MBPP results and orange bars representing Human Evaluation outcomes. ### Components/Axes - **X-axis**: Model sizes (0.3B, 0.6B, 1.3B, 3B, 6.7B, 13B) - **Y-axis**: Performance metrics (Pass@1, Pass@10, Pass@100) with numerical deviations from baseline - **Legend**: - Green bars = MBPP - Orange bars = Human Evaluation - **Secondary Axis**: Numerical values above each bar (e.g., +4.5, -1.7) ### Detailed Analysis #### MBPP Section (Left) 1. **Pass@1**: - 0.3B: +4.5 - 0.6B: -1.7 - 1.3B: +3.9 - 3B: -5.4 - 6.7B: +2.2 - 13B: -9.8 2. **Pass@10**: - 0.3B: +2.5 - 0.6B: -1.7 - 1.3B: +3.9 - 3B: -5.4 - 6.7B: +2.2 - 13B: -9.8 3. **Pass@100**: - 0.3B: +4.5 - 0.6B: -1.7 - 1.3B: +3.9 - 3B: -5.4 - 6.7B: +2.2 - 13B: -9.8 #### Human Evaluation Section (Right) 1. **Pass@1**: - 0.3B: +1.7 - 0.6B: -0.6 - 1.3B: +5.0 - 3B: -1.0 - 6.7B: +7.5 - 13B: -2.3 2. **Pass@10**: - 0.3B: +1.7 - 0.6B: -0.6 - 1.3B: +5.0 - 3B: -1.0 - 6.7B: +7.5 - 13B: -2.3 3. **Pass@100**: - 0.3B: +1.7 - 0.6B: -0.6 - 1.3B: +5.0 - 3B: -1.0 - 6.7B: +7.5 - 13B: -2.3 ### Key Observations 1. **Model Size Correlation**: - MBPP shows inconsistent trends: 13B model performs worst (-9.8), while 0.3B has highest gain (+4.5) - Human Evaluation demonstrates stronger scaling: 13B model achieves +7.5 (Pass@100) vs 0.3B's +1.7 2. **Framework Differences**: - MBPP exhibits higher volatility: 6.7B model shows +2.2 (Pass@1) vs -9.8 (Pass@100) - Human Evaluation maintains more consistent performance across metrics 3. **Anomalies**: - MBPP 13B model underperforms all smaller models across all metrics - Human Evaluation 6.7B model shows strongest performance (+7.5 Pass@100) ### Interpretation The data suggests that while MBPP evaluation shows diminishing returns with larger models (potentially due to overfitting or problem-specific limitations), Human Evaluation reveals clearer benefits of model scaling. The negative values in MBPP for larger models indicate potential failure modes in complex problem-solving that aren't captured by human evaluators. The stark contrast between frameworks implies that MBPP might be measuring different aspects of model capability compared to human judgment, possibly highlighting issues with automated evaluation metrics in capturing nuanced reasoning abilities. </details> ure 3 for MBPP (Austin et al., 2021) and HumanEval (Chen et al., 2021) show that it is possible, with the exact same computational budget, to squeeze much more performance out of large language models given a fixed dataset using multi-token prediction. We believe this usefulness only at scale to be a likely reason why multi-token prediction has so far been largely overlooked as a promising training loss for large language model training. ## 3.2. Faster inference We implement greedy self-speculative decoding (Stern et al., 2018) with heterogeneous batch sizes using xFormers (Lefaudeux et al., 2022) and measure decoding speeds of our best 4-token prediction model with 7B parameters on completing prompts taken from a test dataset of code and natural language (Table S2) not seen during training. We observe a speedup of 3 . 0 × on code with an average of 2.5 accepted tokens out of 3 suggestions on code, and of Table 1: Multi-token prediction improves performance and unlocks efficient byte level training. We compare models with 7B parameters trained from scratch on 200B and on 314B bytes of code on the MBPP (Austin et al., 2021), HumanEval (Chen et al., 2021) and APPS (Hendrycks et al., 2021) benchmarks. Multi-token prediction largely outperforms next token prediction on these settings. All numbers were calculated using the estimator from Chen et al. (2021) based on 200 samples per problem. The temperatures were chosen optimally (based on test scores; i.e. these are oracle temperatures) for each model, dataset and pass@k and are reported in Table S12. | Training data | Vocabulary | n | MBPP | MBPP | MBPP | HumanEval | HumanEval | HumanEval | APPS/Intro | APPS/Intro | APPS/Intro | |----------------------|--------------|-----|--------|--------|--------|-------------|-------------|-------------|--------------|--------------|--------------| | Training data | Vocabulary | | @1 | @10 | @100 | @1 | @10 | @100 | @1 | @10 | @100 | | | | 1 | 19.3 | 42.4 | 64.7 | 18.1 | 28.2 | 47.8 | 0.1 | 0.5 | 2.4 | | | | 8 | 32.3 | 50.0 | 69.6 | 21.8 | 34.1 | 57.9 | 1.2 | 5.7 | 14.0 | | | | 16 | 28.6 | 47.1 | 68.0 | 20.4 | 32.7 | 54.3 | 1.0 | 5.0 | 12.9 | | | | 32 | 23.0 | 40.7 | 60.3 | 17.2 | 30.2 | 49.7 | 0.6 | 2.8 | 8.8 | | | | 1 | 30.0 | 53.8 | 73.7 | 22.8 | 36.4 | 62.0 | 2.8 | 7.8 | 17.4 | | | | 2 | 30.3 | 55.1 | 76.2 | 22.2 | 38.5 | 62.6 | 2.1 | 9.0 | 21.7 | | | | 4 | 33.8 | 55.9 | 76.9 | 24.0 | 40.1 | 66.1 | 1.6 | 7.1 | 19.9 | | | | 6 | 31.9 | 53.9 | 73.1 | 20.6 | 38.4 | 63.9 | 3.5 | 10.8 | 22.7 | | | | 8 | 30.7 | 52.2 | 73.4 | 20.0 | 36.6 | 59.6 | 3.5 | 10.4 | 22.1 | | 1T tokens (4 epochs) | | 1 | 40.7 | 65.4 | 83.4 | 31.7 | 57.6 | 83.0 | 5.4 | 17.8 | 34.1 | | 1T tokens (4 epochs) | | 4 | 43.1 | 65.9 | 83.7 | 31.6 | 57.3 | 86.2 | 4.3 | 15.6 | 33.7 | 2 . 7 × on text. On an 8-byte prediction model, the inference speedup is 6 . 4 × (Table S3). Pretraining with multi-token prediction allows the additional heads to be much more accurate than a simple finetuning of a next-token prediction model, thus allowing our models to unlock self-speculative decoding's full potential. ## 3.3. Learning global patterns with multi-byte prediction To show that the next-token prediction task latches to local patterns, we went to the extreme case of byte-level tokenization by training a 7B parameter byte-level transformer on 314B bytes, which is equivalent to around 116B tokens. The 8-byte prediction model achieves astounding improvements compared to next-byte prediction, solving 67% more problems on MBPP pass@1 and 20% more problems on HumanEval pass@1. Multi-byte prediction is therefore a very promising avenue to unlock efficient training of byte-level models. Selfspeculative decoding can achieve speedups of 6 times for the 8-byte prediction model, which would allow to fully compensate the cost of longer byte-level sequences at inference time and even be faster than a next-token prediction model by nearly two times. The 8-byte prediction model is a strong byte-based model, approaching the performance of token-based models despite having been trained on 1 . 7 × less data. ## 3.4. Searching for the optimal n To better understand the effect of the number of predicted tokens, we did comprehensive ablations on models of scale 7B trained on 200B tokens of code. We try n = 1 , 2 , 4 , 6 and 8 in this setting. Results in table 1 show that training with 4-future tokens outperforms all the other models consistently throughout HumanEval and MBPP for pass at 1, 10 and 100 metrics: +3.8%, +2.1% and +3.2% for MBPP and +1.2%, +3.7% and +4.1% for HumanEval. Interestingly, for APPS/Intro, n = 6 takes the lead with +0.7%, +3.0% and +5.3%. It is very likely that the optimal window size depends on input data distribution. As for the byte level models the optimal window size is more consistent (8 bytes) across these benchmarks. ## 3.5. Training for multiple epochs Multi-token training still maintains an edge on next-token prediction when trained on multiple epochs of the same data. The improvements diminish but we still have a +2.4% increase on pass@1 on MBPP and +3.2% increase on pass@100 on HumanEval, while having similar performance for the rest. As for APPS/Intro, a window size of 4 was already not optimal with 200B tokens of training. ## 3.6. Finetuning multi-token predictors Pretrained models with multi-token prediction loss also outperform next-token models for use in finetunings. We evaluate this by finetuning 7B parameter models from Section 3.3 on the CodeContests dataset (Li et al., 2022). We compare the 4-token prediction model with the next-token prediction baseline, and include a setting where the 4-token prediction model is stripped off its additional prediction heads and finetuned using the classical next-token prediction target. According to the results in Figure 4, both ways of finetuning the 4-token prediction model outperform the next-token prediction model on pass@k across k . This means the models are both better at understanding and solving the task and at generating diverse answers. Note that CodeContests is the most challenging coding benchmark we evaluate in this study. Next-token prediction finetuning on top of 4-token prediction pretraining appears to be the best method overall, in line with the classical paradigm of pretraining with auxiliary tasks followed by task-specific finetuning. Please refer to Appendix F for details. Figure 4: Comparison of finetuning performance on CodeContests. We finetune a 4 -token prediction model on CodeContests (Li et al., 2022) (train split) using n ′ -token prediction as training loss with n ′ = 4 or n ′ = 1 , and compare to a finetuning of the next-token prediction baseline model ( n = n ′ = 1 ). For evaluation, we generate 1000 samples per test problem for each temperature T ∈ { 0 . 5 , 0 . 6 , 0 . 7 , 0 . 8 , 0 . 9 } , and compute pass@k for each value of k and T . Shown is k ↦→ max T pass \_ at( k, T ) , i.e. we grant access to a temperature oracle. We observe that both ways of finetuning the 4-token prediction model outperform the next-token prediction baseline. Intriguingly, using next-token prediction finetuning on top of the 4-token prediction model appears to be the best method overall. <details> <summary>Image 4 Details</summary>  ### Visual Description ## Line Graph: pass@k (%) vs. k ### Overview The image depicts a line graph comparing the performance metric "pass@k (%)" across different values of `k` (x-axis) for three configurations of parameters `n` and `n'`. The y-axis represents the percentage of successful outcomes, while the x-axis spans a logarithmic scale from 1 to 1000. Three distinct lines represent different parameter combinations, with the legend positioned in the bottom-right corner. --- ### Components/Axes - **Y-Axis**: Labeled "pass@k (%)", ranging from 0.2 to 10.0 in increments of 1.0. - **X-Axis**: Labeled "k", spanning a logarithmic scale from 1 to 1000. - **Legend**: Located in the bottom-right corner, with three entries: - **Solid Red**: `n=1, n'=1` - **Dashed Black**: `n=4, n'=1` - **Dotted Green**: `n=4, n'=4` --- ### Detailed Analysis 1. **Solid Red Line (`n=1, n'=1`)**: - Starts near the origin (0.2% at `k=1`). - Gradually increases, reaching ~5.0% at `k=100` and ~9.5% at `k=1000`. - Exhibits the slowest growth rate among the three lines. 2. **Dashed Black Line (`n=4, n'=1`)**: - Begins slightly above the red line (0.3% at `k=1`). - Outperforms the red line, reaching ~6.5% at `k=100` and ~10.0% at `k=1000`. - Shows a steeper slope than the red line but less than the green line. 3. **Dotted Green Line (`n=4, n'=4`)**: - Starts at ~0.4% at `k=1`. - Demonstrates the steepest growth, surpassing the black line by `k=10`. - Reaches ~9.0% at `k=100` and ~10.0% at `k=1000`. --- ### Key Observations - All three lines exhibit **monotonic growth**, with no declines observed across the range of `k`. - The **green line (`n=4, n'=4`)** consistently outperforms the other two configurations, suggesting that higher values of `n` and `n'` improve performance. - The **red line (`n=1, n'=1`)** lags significantly behind, indicating that lower parameter values result in poorer outcomes. - The logarithmic scale on the x-axis emphasizes performance differences at larger `k` values (e.g., `k=1000`). --- ### Interpretation The graph demonstrates that increasing both `n` and `n'` parameters enhances the "pass@k" metric, likely reflecting improved efficiency or accuracy in a system (e.g., recommendation algorithms, search engines, or classification models). The logarithmic x-axis highlights that performance gains are more pronounced at higher `k` thresholds, where the system's ability to handle larger-scale data becomes critical. The divergence between configurations suggests that parameter tuning (specifically increasing `n` and `n'`) is crucial for optimizing outcomes in scenarios requiring high recall or precision at scale. No outliers or anomalies are present, as all lines follow predictable growth patterns. </details> ## 3.7. Multi-token prediction on natural language To evaluate multi-token prediction training on natural language, we train models of size 7B parameters on 200B tokens of natural language with a 4-token, 2-token and nexttoken prediction loss, respectively. In Figure 5, we evaluate the resulting checkpoints on 6 standard NLP benchmarks. On these benchmarks, the 2-future token prediction model performs on par with the next-token prediction baseline Figure 5: Multi-token training with 7B models doesn't improve performance on choice tasks. This figure shows the evolution of average accuracy of 6 standard NLP benchmarks. Detailed results in Appendix G for 7B models trained on 200B tokens of language data. The 2 future token model has the same performance as the baseline and the 4 future token model regresses a bit. Larger model sizes might be necessary to see improvements on these tasks. <details> <summary>Image 5 Details</summary>  ### Visual Description ## Line Graph: Average Accuracy vs Training Steps ### Overview The image depicts a line graph illustrating the relationship between training steps and average accuracy for three distinct configurations (n=1, n=2, n=4). The graph shows three data series with varying line styles and colors, plotted against a Cartesian coordinate system. ### Components/Axes - **X-axis (Horizontal)**: Labeled "Training step" with values ranging from 5,000 to 25,000 in increments of 5,000. - **Y-axis (Vertical)**: Labeled "Average accuracy" with values ranging from 35.0 to 52.5 in increments of 2.5. - **Legend**: Positioned in the top-left corner, containing three entries: - Solid red line: `n = 1` - Dashed blue line: `n = 2` - Dotted green line: `n = 4` ### Detailed Analysis 1. **Data Series Trends**: - **n = 1 (Solid Red)**: Starts at ~35.0 accuracy at 5,000 steps, rising sharply to ~52.5 accuracy by 25,000 steps. Maintains the highest accuracy throughout. - **n = 2 (Dashed Blue)**: Begins at ~35.0 accuracy, follows a similar upward trajectory but plateaus slightly below n=1 (~51.0 accuracy at 25,000 steps). - **n = 4 (Dotted Green)**: Starts at ~35.0 accuracy, exhibits the slowest growth, reaching ~50.5 accuracy at 25,000 steps. 2. **Key Data Points**: - At 10,000 steps: - n=1: ~47.5 - n=2: ~46.5 - n=4: ~45.5 - At 20,000 steps: - n=1: ~51.5 - n=2: ~50.5 - n=4: ~49.0 ### Key Observations - All configurations show a consistent upward trend in accuracy as training steps increase. - The gap between n=1 and n=4 narrows slightly over time but remains significant. - n=1 consistently outperforms other configurations across all training steps. ### Interpretation The data suggests that increasing the parameter `n` (likely representing model complexity, such as layers or neurons in a neural network) improves training accuracy. However, the diminishing returns for n=4 compared to n=1 and n=2 imply potential overfitting or diminishing benefits of excessive complexity. The convergence of n=2 and n=4 toward later training steps may indicate that beyond a certain threshold, additional complexity yields minimal gains. This aligns with common machine learning principles where optimal model complexity balances bias-variance tradeoffs. </details> throughout training. The 4-future token prediction model suffers a performance degradation. Detailed numbers are reported in Appendix G. However, we do not believe that multiple-choice and likelihood-based benchmarks are suited to effectively discern generative capabilities of language models. In order to avoid the need for human annotations of generation quality or language model judges-which comes with its own pitfalls, as pointed out by Koo et al. (2023)-we conduct evaluations on summarization and natural language mathematics benchmarks and compare pretrained models with training sets sizes of 200B and 500B tokens and with nexttoken and multi-token prediction losses, respectively. For summarization, we use eight benchmarks where ROUGE metrics (Lin, 2004) with respect to a ground-truth summary allow automatic evaluation of generated texts. We finetune each pretrained model on each benchmark's training dataset for three epochs and select the checkpoint with the highest ROUGE-L F 1 score on the validation dataset. Figure 6 shows that multi-token prediction models with both n = 2 and n = 4 improve over the next-token baseline in ROUGE-L F 1 scores for both training dataset sizes, with the performance gap shrinking with larger dataset size. All metrics can be found in Appendix H. For natural language mathematics, we evaluate the pretrained models in 8-shot mode on the GSM8K benchmark (Cobbe et al., 2021) and measure accuracy of the final answer produced after a chain-of-thought elicited by the fewshot examples. We evaluate pass@k metrics to quantify diversity and correctness of answers like in code evaluations Figure 6: Performance on abstractive text summarization. Average ROUGE-L (longest common subsequence overlap) F 1 score for 7B models trained on 200B and 500B tokens of natural language on eight summarization benchmarks. We finetune the respective models on each task's training data separately for three epochs and select the checkpoints with highest ROUGE-L F 1 validation score. Both n = 2 and n = 4 multi-token prediction models have an advantage over next-token prediction models. Individual scores per dataset and more details can be found in Appendix H. <details> <summary>Image 6 Details</summary>  ### Visual Description ## Bar Chart: Average ROUGE-L F1 Scores by Training Tokens and n Values ### Overview The chart compares average ROUGE-L F1 scores across three configurations (n=1, n=2, n=4) for two training token quantities (200B and 500B). The y-axis shows performance metrics, while the x-axis represents training token scale. Three color-coded bars per token quantity visualize performance differences. ### Components/Axes - **X-axis**: "Training tokens (B)" with categories 200 and 500 - **Y-axis**: "Avg. ROUGE-L F1" scaled from 25.0 to 27.5 - **Legend**: - Red = n=1 - Blue = n=2 - Green = n=4 - **Bar Colors**: - Red (n=1) bars are consistently shortest - Blue (n=2) bars show intermediate values - Green (n=4) bars are tallest ### Detailed Analysis - **200B Training Tokens**: - n=1: ~26.2 (red) - n=2: ~26.7 (blue) - n=4: ~26.6 (green) - **500B Training Tokens**: - n=1: ~27.1 (red) - n=2: ~27.4 (blue) - n=4: ~27.5 (green) ### Key Observations 1. **Performance Scaling**: All configurations show improved performance with increased training tokens (200B → 500B) 2. **n=4 Dominance**: Green bars (n=4) consistently outperform others by 0.3-0.4 F1 points across both token quantities 3. **n=2 Advantage**: Blue bars (n=2) outperform n=1 by 0.5-0.6 F1 points 4. **Diminishing Returns**: The performance gap between n=2 and n=4 narrows at 500B tokens (0.1 vs 0.3 at 200B) ### Interpretation The data demonstrates that: - Larger training token quantities (500B) improve model performance across all configurations - Increasing the number of training instances (n) has a stronger impact than token quantity alone - The n=4 configuration achieves near-maximum performance (27.5 F1) at 500B tokens, suggesting diminishing returns beyond this point - The performance hierarchy (n=4 > n=2 > n=1) remains consistent regardless of token quantity, indicating configuration efficiency matters more than scale in this context The chart suggests optimizing for higher n values when training token quantities are fixed, with 500B tokens providing the best balance between resource use and performance gains. </details> and use sampling temperatures between 0.2 and 1.4. The results are depicted in Figure S13 in Appendix I. For 200B training tokens, the n = 2 model clearly outperforms the next-token prediction baseline, while the pattern reverses after 500B tokens and n = 4 is worse throughout. ## 4. Ablations on synthetic data What drives the improvements in downstream performance of multi-token prediction models on all of the tasks we have considered? By conducting toy experiments on controlled training datasets and evaluation tasks, we demonstrate that multi-token prediction leads to qualitative changes in model capabilities and generalization behaviors . In particular, Section 4.1 shows that for small model sizes, induction capability -as discussed by Olsson et al. (2022)-either only forms when using multi-token prediction as training loss, or it is vastly improved by it. Moreover, Section 4.2 shows that multi-token prediction improves generalization on an arithmetic task, even more so than tripling model size. ## 4.1. Induction capability Induction describes a simple pattern of reasoning that completes partial patterns by their most recent continuation (Olsson et al., 2022). In other words, if a sentence contains 'AB' and later mentions 'A', induction is the prediction that the continuation is 'B'. We design a setup to measure induction Figure 7: Induction capability of n -token prediction models. Shown is accuracy on the second token of two token names that have already been mentioned previously. Shown are numbers for models trained with a next-token and a 2-token prediction loss, respectively, with two independent runs each. The lines denote per-loss averages. For small model sizes, next-token prediction models learn practically no or significantly worse induction capability than 2-token prediction models, with their disadvantage disappearing at the size of 100M nonembedding parameters. <details> <summary>Image 7 Details</summary>  ### Visual Description ## Line Graph: Induction Success vs. Parameters (M) ### Overview The image is a line graph comparing induction success rates across different parameter scales (M) for two models: a baseline model (n=1) and an optimized model (n=2). The graph shows how induction success improves with increasing parameters, with distinct trends for each model. ### Components/Axes - **X-axis**: "Parameters (M)" with a logarithmic scale (1, 3, 10, 30, 100, 300, 1000). - **Y-axis**: "Induction success" ranging from 0.0 to 0.5 in increments of 0.1. - **Legend**: Located in the bottom-right corner, with: - Red "x" markers for "n=1 (baseline)" - Blue "x" markers for "n=2 (ours)" - **Data Points**: Both lines use "x" symbols to denote measured values. ### Detailed Analysis 1. **Baseline Model (n=1, red)**: - Starts at ~0.02 induction success at 1M parameters. - Increases steadily, reaching ~0.48 at 1000M. - Slope is linear, with no significant inflection points. 2. **Optimized Model (n=2, blue)**: - Begins at ~0.15 induction success at 1M. - Peaks at ~0.45 at 30M, then plateaus with minor fluctuations. - At 1000M, induction success is ~0.47, slightly below its peak. ### Key Observations - Both models show improved induction success with more parameters, but the optimized model (n=2) achieves higher performance at lower parameter scales. - The baseline model (n=1) exhibits a consistent linear improvement, while the optimized model (n=2) demonstrates diminishing returns after 30M parameters. - At 1000M parameters, the optimized model outperforms the baseline by ~0.01 (0.47 vs. 0.48), but the gap narrows at higher scales. ### Interpretation The data suggests that increasing parameters generally enhances induction success, but the optimized model (n=2) achieves superior efficiency at smaller scales. The plateau in n=2’s performance after 30M implies potential architectural or algorithmic constraints, such as overfitting or computational limits. The baseline model’s linear trend indicates no such constraints but requires significantly more parameters to match the optimized model’s performance. This highlights a trade-off between parameter efficiency and scalability in model design. </details> capability in a controlled way. Training small models of sizes 1M to 1B nonembedding parameters on a dataset of children stories, we measure induction capability by means of an adapted test set: in 100 stories from the original test split, we replace the character names by randomly generated names that consist of two tokens with the tokenizer we employ. Predicting the first of these two tokens is linked to the semantics of the preceding text, while predicting the second token of each name's occurrence after it has been mentioned at least once can be seen as a pure induction task. In our experiments, we train for up to 90 epochs and perform early stopping with respect to the test metric (i.e. we allow an epoch oracle). Figure 7 reports induction capability as measured by accuracy on the names' second tokens in relation to model size for two runs with different seeds. We find that 2-token prediction loss leads to a vastly improved formation of induction capability for models of size 30M nonembedding parameters and below, with their advantage disappearing for sizes of 100M nonembedding parameters and above. 1 We interpret this finding as follows: multitoken prediction losses help models to learn transferring information across sequence positions, which lends itself to the formation of induction heads and other in-context learning mechanisms. However, once induction capability has been formed, these learned features transform induction 1 Note that a perfect score is not reachable in this benchmark as some of the tokens in the names in the evaluation dataset never appear in the training data, and in our architecture, embedding and unembedding parameters are not linked. Figure 8: Accuracy on a polynomial arithmetic task with varying number of operations per expression. Training with multi-token prediction losses increases accuracy across task difficulties. In particular, it also significantly improves out-of-domain generalization performance, albeit at a low absolute level. Tripling the model size, on the other hand, has a considerably smaller effect than replacing next-token prediction with multi-token prediction loss (Figure S16). Shown are two independent runs per configuration with 100M parameter models. <details> <summary>Image 8 Details</summary>  ### Visual Description ## Line Graph: Accuracy vs. # Operations (In-Domain vs. Out-of-Domain) ### Overview The graph illustrates the relationship between the number of operations performed and accuracy (%) for three distinct scenarios (n=1, n=2, n=4). It visually separates "in-domain" (operations 1–5) and "out-of-domain" (operations 6–10) performance using a vertical dashed line at x=6. Accuracy declines consistently across all scenarios as operations increase, with steeper drops observed in the out-of-domain region. ### Components/Axes - **Y-Axis**: Accuracy (%) ranging from 0 to 100 in 20% increments. - **X-Axis**: Number of operations (1–10), with a break between 5 and 6 to denote in-domain/out-of-domain separation. - **Legend**: Located in the top-right corner, mapping: - Red crosses (`✖️`) to **n=1** - Blue stars (`★`) to **n=2** - Green plus signs (`➕`) to **n=4** - **Key Visual Elements**: - Vertical dashed line at x=6 (in-domain/out-of-domain boundary). - Data points connected by dashed lines for trend visualization. ### Detailed Analysis 1. **n=1 (Red Crosses)**: - **In-Domain (1–5 operations)**: Starts at ~90% accuracy at 1 operation, declining to ~30% at 5 operations. - **Out-of-Domain (6–10 operations)**: Drops further to ~10% at 10 operations. - **Trend**: Steady linear decline in both regions. 2. **n=2 (Blue Stars)**: - **In-Domain**: Begins at ~85% accuracy at 1 operation, falling to ~20% at 5 operations. - **Out-of-Domain**: Reaches ~5% at 10 operations. - **Trend**: Slightly steeper decline than n=1, with sharper drops post-x=6. 3. **n=4 (Green Plus Signs)**: - **In-Domain**: Starts at ~80% accuracy at 1 operation, decreasing to ~10% at 5 operations. - **Out-of-Domain**: Plummets to near 0% by 10 operations. - **Trend**: Most pronounced decline, especially in out-of-domain. ### Key Observations - **Universal Decline**: All scenarios show reduced accuracy as operations increase, regardless of domain. - **Out-of-Domain Sensitivity**: Accuracy drops more sharply after x=6, with n=4 experiencing the steepest decline. - **Marker Consistency**: Legend colors and symbols align perfectly with data series (e.g., red crosses for n=1). - **Breakpoint Clarity**: The x-axis break at 5–6 visually reinforces the domain shift. ### Interpretation The data suggests that **operational complexity (higher n)** correlates with reduced model performance, particularly in out-of-domain scenarios. For example: - **n=4** (most complex) achieves only ~10% accuracy in out-of-domain at 10 operations, compared to ~30% for n=1. - The **domain shift** exacerbates performance degradation, with out-of-domain accuracy being 50–70% lower than in-domain for equivalent n values. - The linear trends imply a predictable trade-off between operational complexity and accuracy, highlighting potential limitations in generalizing models to unseen tasks. This graph underscores the importance of domain alignment and operational simplicity in maintaining high accuracy, with implications for model design and deployment strategies. </details> into a task that can be solved locally at the current token and learned with next-token prediction alone. From this point on, multi-token prediction actually hurts on this restricted benchmark-but we surmise that there are higher forms of in-context reasoning to which it further contributes, as evidenced by the results in Section 3.1. In Figure S14, we provide evidence for this explanation: replacing the children stories dataset by a higher-quality 9:1 mix of a books dataset with the children stories, we enforce the formation of induction capability early in training by means of the dataset alone. By consequence, except for the two smallest model sizes, the advantage of multi-token prediction on the task disappears: feature learning of induction features has converted the task into a pure next-token prediction task. ## 4.2. Algorithmic reasoning Algorithmic reasoning tasks allow to measure more involved forms of in-context reasoning than induction alone. We train and evaluate models on a task on polynomial arithmetic in the ring F 7 [ X ] / ( X 5 ) with unary negation, addition, multiplication and composition of polynomials as operations. The coefficients of the operands and the operators are sampled uniformly. The task is to return the coefficients of the polynomials corresponding to the resulting expressions. The number m of operations contained in the expressions is selected uniformly from the range from 1 to 5 at training time, and can be used to adjust the difficulty of both in-domain ( m ≤ 5 ) and out-of-domain ( m> 5 ) generalization evaluations. The evaluations are conducted with greedy sampling on a fixed test set of 2000 samples per number of operations. We train models of two small sizes with 30M and 100M nonembedding parameters, respectively. This simulates the conditions of large language models trained on massive text corpora which are likewise under-parameterized and unable to memorize their entire training datasets. Multi-token prediction improves algorithmic reasoning capabilities as measured by this task across task difficulties (Figure 8). In particular, it leads to impressive gains in out-of-distribution generalization, despite the low absolute numbers. Increasing the model size from 30M to 100M parameters, on the other hand, does not improve evaluation accuracy as much as replacing next-token prediction by multi-token prediction does (Figure S16). In Appendix K, we furthermore show that multi-token prediction models retain their advantage over next-token prediction models on this task when trained and evaluated with pause tokens (Goyal et al., 2023). ## 5. Why does it work? Some speculation Why does multi-token prediction afford superior performance on coding evaluation benchmarks, and on small algorithmic reasoning tasks? Our intuition, developed in this section, is that multi-token prediction mitigates the distributional discrepancy between training-time teacher forcing and inference-time autoregressive generation. We support this view with an illustrative argument on the implicit weights multi-token prediction assigns to tokens depending on their relevance for the continuation of the text, as well as with an information-theoretic decomposition of multi-token prediction loss. ## 5.1. Lookahead reinforces choice points Not all token decisions are equally important for generating useful texts from language models (Bachmann and Nagarajan, 2024; Lin et al., 2024). While some tokens allow stylistic variations that do not constrain the remainder of the text, others represent choice points that are linked with higher-level semantic properties of the text and may decide whether an answer is perceived as useful or derailing . Multi-token prediction implicitly assigns weights to training tokens depending on how closely they are correlated with their successors. As an illustrative example, consider the sequence depicted in Figure 9 where one transition is a hard-to-predict choice point while the other transitions are considered 'inconsequential'. Inconsequential transitions following a choice point are likewise hard to predict in advance. By marking and counting loss terms, we find that Figure 9: Multi-token prediction loss assigns higher implicit weights to consequential tokens. Shown is a sequence in which all transitions except '5 → A' are easy to predict, alongside the corresponding prediction targets in 3-token prediction. Since the consequences of the difficult transition '5 → A' are likewise hard to predict, this transition receives a higher implicit weight in the overall loss via its correlates '3 → A', ..., '5 → C'. <details> <summary>Image 9 Details</summary>  ### Visual Description ## Diagram: Model Predictions vs Ground Truth Sequence ### Overview The diagram compares a sequence of model predictions against a ground truth sequence, visualized through vertical bars and directional arrows. The model predictions deviate from the ground truth in both numerical and categorical values, with color-coded discrepancies highlighted. ### Components/Axes - **Left Section**: "Model predictions" labeled at the top. - **Right Section**: "Ground truth" labeled at the bottom. - **Vertical Bars**: - Model predictions use green numbers (2-5) and red letters (A-E). - Ground truth uses sequential numbers (1-5) and letters (A-B). - **Arrows**: - Green arrows indicate correct transitions in the ground truth. - Red arrows in the model predictions highlight incorrect transitions. ### Detailed Analysis 1. **Model Predictions**: - **Steps 1-3**: Predicts 4 → 3 → 2 (incorrect, ground truth is 1 → 2 → 3). - **Steps 4-5**: Predicts 5 → 4 → 3 (incorrect, ground truth is 4 → 5). - **Steps 6-7**: Predicts A → B → C → D → E (incorrect, ground truth is A → B). - **Color Coding**: Red letters (A-E) in model predictions suggest errors or out-of-sequence predictions. 2. **Ground Truth**: - Linear progression: 1 → 2 → 3 → 4 → 5 → A → B. - Arrows are uniformly green, indicating correct transitions. 3. **Discrepancies**: - **Numerical Errors**: Model overpredicts initial values (4,3,2 instead of 1,2,3). - **Categorical Errors**: Model predicts additional letters (C, D, E) after B, which are absent in ground truth. - **Arrow Mismatch**: Model’s red arrows (e.g., 5 → A) conflict with ground truth’s green arrows (4 → 5 → A → B). ### Key Observations - The model struggles with early numerical predictions, consistently overestimating values. - After step 5, the model introduces extraneous categories (C, D, E) not present in ground truth. - Red arrows in the model’s path visually emphasize prediction errors. ### Interpretation The diagram reveals systematic errors in the model’s ability to: 1. Accurately predict sequential numerical values (steps 1-5). 2. Maintain categorical consistency (steps 6-7). The red arrows and letters act as visual flags for misaligned predictions, suggesting the model may require retraining or adjustment to better align with the ground truth sequence. The divergence after step 5 indicates a potential failure to generalize beyond the initial numerical phase. </details> n -token prediction associates a weight of n ( n +1) 2 to choice points via their correlates, and a smaller weight of n to inconsequential points. Please refer to Appendix L.3 for more details. Generally, we believe that the quality of text generations depends on picking the right decisions at choice points, and that n -token prediction losses promote those. ## 5.2. Information-theoretic argument Language models are typically trained by teacher-forcing, where the model receives the ground truth for each future token during training. However, during test time generation is unguided and autoregressive, whereby errors accumulate. Teacher-forcing, we argue, encourages models to focus on predicting well in the very short term, at the potential expense of ignoring longer-term dependencies in the overall structure of the generated sequence. To illustrate the impact of multi-token prediction, consider the following information-theoretic argument. Here, X denotes the next future token, and Y the second-next future token. The production of both of these tokens is conditioned on some observed, input context C , that we omit from our equations for simplicity. When placed before token X , vanilla next-token prediction concerns the quantity H ( X ) , while multi-token prediction with n = 2 aims at H ( X ) + H ( Y ) . We decompose these two quantities as: <!-- formula-not-decoded --> By discarding the term H ( Y | X ) -which appears again when predicting at the following position-we observe that 2-token prediction increases the importance of I ( X ; Y ) by a factor of 2 . So, multi-token predictors are more accurate at predicting tokens X that are of relevance for the remainder of the text to come. In Appendix L.2, we give a relative version of the above equations that shows the increased weight of relative mutual information in a loss decomposition of 2-token prediction loss. ## 6. Related work Language modeling losses Dong et al. (2019) and Tay et al. (2022) train on a mixture of denoising tasks with different attention masks (full, causal and prefix attention) to bridge the performance gap with next token pretraining on generative tasks. Tay et al. (2022) uses the span corruption objective, which replaces spans of tokens with special tokens for the encoder and the decoder then predicts the contents of those spans. Unlike UniLM, this allows full causal training with teacher forcing. Similarly, Yang et al. (2019) train on permuted sequences, while conserving the original positional embeddings, effectively training the model to predict various parts of the sequence given a mix of past and future information. This permuted language modeling is the closest task to ours since it allows predicting beyond the next token. However all of these language modeling tasks train on a small percentage of the input text: on average only 15% of the tokens are backwarded through. For Dong et al. (2019), where the masking is done in BERT style, it is hard to mask more than 15% since it destroys too much information. For Tay et al. (2022), it is technically possible to have a larger proportion but in practice, the settings used have between 15% and 25% of masked tokens. (Yang et al., 2019) also makes it possible to train on the whole sequence since it is only permuted, and no information is lost. Yet, in practice, since the completely random permutation is very hard to reconstruct, only 15% are predicted for training stability reasons. Multi-token prediction in language modelling Qi et al. (2020) argue that multi-token prediction encourages planning, improves representations and prevents the overfitting on local patterns that can result from teacher-forced training. However, their technical approach replicates the residual stream n -fold while ours allows for compute-matched comparisons and makes the residual representations participate more directly in the auxiliary loss terms. Stern et al. (2018) and Cai et al. (2024) propose model finetunings with multitoken prediction for faster inference but do not study the effects of such a loss during pretraining. Pal et al. (2023) use probing methods to show that next-token prediction models are able to predict additional consecutive tokens to a certain extent, but less so than our models which are specifically trained for this task. Jianyu Zhang (2024) observe improvements in language modelling tasks with multi-label binary classification over the occurrence of vocabulary words in the future as an auxiliary learning task. Self-speculative decoding Stern et al. (2018) are, to the best of our knowledge, the first to suggest a speculative decoding scheme for faster inference. Our architecture replaces their linear prediction heads by transformer layers, but is otherwise similar. By reorganizing the order of the forward/backward, we can use all loss terms instead of stochastically picking one head for loss computation. Cai et al. (2024) present a more elaborate self-speculative decoding scheme that uses the topk predictions of each head instead of the best one only. It can be used with the multi-token prediction models we train. Multi-target prediction Multi-task learning is the paradigm of training neural networks jointly on several tasks to improve performance on the tasks of interest (Caruana, 1997). Learning with such auxiliary tasks allows models to exploit dependencies between target variables and can even be preferable in the case of independent targets (Waegeman et al., 2019). While more specifically tailored architectures for multi-target prediction are conceivable (SpyromitrosXioufis et al., 2016; Read et al., 2021), modern deep learning approaches usually rely on large shared model trunks with separate prediction heads for the respective tasks (Caruana, 1997; Silver et al., 2016; Lample et al., 2022) like we do. Multi-target prediction has been shown to be a successful strategy in various domains, e.g. for learning time series prediction with more distant time steps in the future as auxiliary targets (Vapnik and Vashist, 2009) or for learning from videos with several future frames (Mathieu et al., 2016; Srivastava et al., 2016) or representations of future frames (Vondrick et al., 2016) as auxiliary targets. ## 7. Conclusion Wehave proposed multi-token prediction as an improvement over next-token prediction in training language models for generative or reasoning tasks. Our experiments (up to 7B parameters and 1T tokens) show that this is increasingly useful for larger models and in particular show strong improvements for code tasks. We posit that our method reduces distribution mismatch between teacher-forced training and autoregressive generation. When used with speculative decoding, exact inference gets 3 times faster. In future work we would like to better understand how to automatically choose n in multi-token prediction losses. One possibility to do so is to use loss scales and loss balancing (Défossez et al., 2022). Also, optimal vocabulary sizes for multi-token prediction are likely different from those for next-token prediction, and tuning them could lead to better results, as well as improved trade-offs between compressed sequence length and compute-per-byte expenses. Finally, we would like to develop improved auxiliary prediction losses that operate in embedding spaces (LeCun, 2022). ## Impact statement The goal of this paper is to make language models more compute and data efficient. While this may in principle reduce the ecological impact of training LLMs, we shall be careful about rebound effects . All societal advantages, as well as risks, of LLMs should be considered while using this work. ## Environmental impact In aggregate, training all models reported in the paper required around 500K GPU hours of computation on hardware of type A100-80GB and H100. Estimated total emissions were around 50 tCO2eq, 100% of which were offset by Meta's sustainability program. ## Acknowledgements We thank Jianyu Zhang, Léon Bottou, Emmanuel Dupoux, Pierre-Emmanuel Mazaré, Yann LeCun, Quentin Garrido, Megi Dervishi, Mathurin Videau and Timothée Darcet and other FAIR PhD students and CodeGen team members for helpful discussions. We thank Jonas Gehring for his technical expertise and the original Llama team and xFormers team for enabling this kind of research. ## References - Jacob Austin, Augustus Odena, Maxwell Nye, Maarten Bosma, Henryk Michalewski, David Dohan, Ellen Jiang, Carrie Cai, Michael Terry, Quoc Le, et al. 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In Advances in neural information processing systems , pages 5753-5763, 2019. - Rowan Zellers, Ari Holtzman, Yonatan Bisk, Ali Farhadi, and Yejin Choi. Hellaswag: Can a machine really finish your sentence?, 2019. ## A. Additional results on self-speculative decoding <details> <summary>Image 10 Details</summary>  ### Visual Description ## Line Chart: Throughput (Relative) vs Batch Size ### Overview The chart displays the relationship between batch size (x-axis) and throughput (relative) (y-axis) for four distinct configurations labeled k=1 to k=4. Each configuration is represented by a horizontal line with unique markers and colors. Throughput values remain constant across all batch sizes for each k, indicating no dependency on batch size. ### Components/Axes - **X-axis (Batch size)**: Ranges from 1 to 40 in increments of 8 (1, 8, 16, 24, 32, 40). - **Y-axis (Throughput relative)**: Scaled from 0.0 to 3.0 in increments of 0.5. - **Legend**: Located in the bottom-right corner, associating: - **k=1**: Red crosses (`×`) with a solid line. - **k=2**: Blue crosses (`×`) with a dashed line. - **k=3**: Orange crosses (`×`) with a dotted line. - **k=4**: Green crosses (`×`) with a dash-dot line. ### Detailed Analysis 1. **k=1 (Red)**: Throughput = 1.0 (constant across all batch sizes). 2. **k=2 (Blue)**: Throughput = 1.8 (constant across all batch sizes). 3. **k=3 (Orange)**: Throughput = 2.5 (constant across all batch sizes). 4. **k=4 (Green)**: Throughput = 3.0 (constant across all batch sizes). All lines are perfectly horizontal, confirming no variation in throughput with batch size. The legend colors and markers are consistently applied to their respective data series. ### Key Observations - Throughput is independent of batch size for all k values. - Higher k values correlate with higher relative throughput (k=1: 1.0 → k=4: 3.0). - No outliers or anomalies observed. ### Interpretation The chart demonstrates that throughput scales linearly with the parameter k, while remaining unaffected by batch size. This suggests that the system’s performance is optimized for higher k values, and batch size adjustments do not impact efficiency. The relative throughput values imply a proportional relationship between k and system capacity, potentially indicating parallel processing or resource allocation tied to k. The absence of batch size effects may reflect a design where computational load is evenly distributed regardless of input size. </details> Batch size Figure S10: Decoding speeds and latencies with self-speculative decoding relative to standard autoregressive decoding. We use k heads of a 4-token prediction model and evaluate decoding speeds of a code model as explained in Table S2. All numbers are relative to the autoregressive ( k = 1 ) baseline with the same batch size. Table S2: Relative speedups with self-speculative decoding. For wikipedia and books we prompt a 7B parameter model trained on 500B tokens, and for code we prompt a 7B parameter model trained on 1T tokens of code on 4200 sequences of 512 tokens from a test dataset not seen during training, and generate completions consisting of 512 tokens using greedy self-speculative decoding (Stern et al., 2018) using the indicated number of heads from a 4-token prediction model. Note that the maximal speedup that can be obtained with self-speculative decoding using k heads is k . The last column shows the average number of tokens retrieved from a forward containing this sequence (both verification and prediction). The speedup was evaluated at the maximal batch size of 42, but is constant across batch sizes (Figure S10). | | Wikipedia | Wikipedia | Books | Books | Code | Code | |--------------|--------------|------------------|--------------|------------------|--------------|------------------| | # Heads used | Rel. speedup | Tokens / forward | Rel. speedup | Tokens / forward | Rel. speedup | Tokens / forward | | 1 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 2 | 1.79 | 1.88 | 1.77 | 1.87 | 1.85 | 1.94 | | 3 | 2.35 | 2.57 | 2.32 | 2.56 | 2.54 | 2.78 | | 4 | 2.74 | 3.12 | 2.67 | 3.09 | 3.05 | 3.50 | Table S3: Relative speedups with self-speculative decoding with byte-level models on code. We prompt the 7B parameter models from Section 3.3 on 4096 sequences of 1024 bytes of code not seen during training, and generate completions consisting of 1024 bytes using greedy self-speculative decoding (Stern et al., 2018) as in Table S2. The speedup was evaluated at a batch size of 16. | | n = 8 | n = 8 | n = 16 | n = 16 | n = 32 | n = 32 | |--------------|--------------|------------------|--------------|------------------|--------------|------------------| | # Heads used | Rel. speedup | Tokens / forward | Rel. speedup | Tokens / forward | Rel. speedup | tokens / forward | | 1 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | | 2 | 1.94 | 1.98 | 1.94 | 1.98 | 1.93 | 1.97 | | 4 | 3.67 | 3.84 | 3.63 | 3.81 | 3.62 | 3.80 | | 8 | 6.39 | 7.04 | 6.25 | 6.92 | 6.22 | 6.89 | | 12 | - | - | 8.07 | 9.36 | 8.01 | 9.30 | | 16 | - | - | 9.24 | 11.20 | 9.15 | 11.15 | | 20 | - | - | - | - | 9.83 | 12.61 | | 24 | - | - | - | - | 10.34 | 13.67 | | 28 | - | - | - | - | 10.55 | 14.58 | | 32 | - | - | - | - | 10.84 | 15.35 | Latency (relative) 1.0 0.8 0.6 0.4 0.2 0.0 k=1 k=2 k=3 k=4 ## B. Alternative architectures Table S4: Alternative architectures improve on baseline but not as consistently. Alternative architectures for multi-token prediction are worth exploring to improve efficiency. Here we tried Anticausal, causal and linear and showed no significant improvement with respect to Parallel architecture. | | | | | MBPP | MBPP | MBPP | HumanEval | HumanEval | HumanEval | APPS/Intro | APPS/Intro | APPS/Intro | |----|-------------|--------------|---------|--------|--------|--------|-------------|-------------|-------------|--------------|--------------|--------------| | n | Head type | Architecture | +Layers | @1 | @10 | @100 | @1 | @10 | @100 | @1 | @10 | @100 | | 1 | transformer | parallel | 0 | 30.0 | 53.8 | 73.7 | 22.8 | 36.4 | 62.0 | 2.8 | 7.8 | 17.4 | | | linear | parallel | 0 | 33.6 | 55.0 | 76.2 | 21.9 | 38.5 | 63.7 | 3.1 | 10.1 | 23.0 | | | | anticausal | 0 | 30.8 | 54.8 | 75.3 | 20.9 | 38.4 | 64.5 | 2.0 | 8.7 | 21.6 | | 4 | transformer | causal | 0 | 31.9 | 54.9 | 74.9 | 20.9 | 38.1 | 67.3 | 4.0 | 11.6 | 22.8 | | | | | 0 | 33.8 | 55.9 | 76.9 | 24.0 | 40.1 | 66.1 | 1.6 | 7.1 | 19.9 | | | | parallel | 3 | 33.3 | 55.7 | 77.3 | 22.4 | 39.4 | 66.7 | 2.6 | 9.5 | 22.1 | The architecture described in Section 2 is not the only sensible option, but proved technically viable and well-performing in our experiments. We describe and compare alternative architectures in this section. Replicated unembeddings Replicating the unembedding matrix n times is a simple method for implementing multi-token prediction architectures. However, it requires matrices with shapes ( d, nV ) in the notation of Section 2, which is prohibitive for large-scale trainings. Linear heads Apart from using a single transformer layer for the heads H i , other architectures are conceivable. We experimented with a single linear layer without any nonlinearity as heads, amounting to linear probing of the model's residual representation z . Architectures with more than one layer per head are also possible, but we did not pursue this direction further. Causal and anticausal variant Instead of making the prediction heads P i ( x t + i | z t :1 ) architecturally independent of each other, we can also allow them to rely on other heads' (pre-unembedding) outputs. In a causal variant, later prediction heads are applied on top of the previous ones, i.e. the i -th prediction head P i is given by <!-- formula-not-decoded --> In another anticausal variant, the network starts by predicting the most distant tokens before gradually refining up to the following token: <!-- formula-not-decoded --> These architectures likewise allow a sequential forward/backward order as the parallel architecture from Section 2. This is described in Figure S11. ## D. Finetuning Table S6: Finetuning LLama 2 with multi-token prediction does not significantly improve performance. We tried to finetune LLama 2 with 4-token prediction but this did not yield significant improvements compared to the baseline. We suppose that this new loss changes the initialization too brutally and never really recovers. We still some improvements for example on MBPP Pass@1. All runs use 200B tokens of code. | | | | MBPP | MBPP | MBPP | HumanEval | HumanEval | HumanEval | APPS/Intro | APPS/Intro | APPS/Intro | |----|-------------|---------|--------|--------|--------|-------------|-------------|-------------|--------------|--------------|--------------| | n | Head type | +Layers | @1 | @10 | @100 | @1 | @10 | @100 | @1 | @10 | @100 | | 1 | transformer | 0 | 39.6 | 65.1 | 82.4 | 31.4 | 57.7 | 84.7 | 10.0 | 21.6 | 36.7 | | 4 | linear | 0 | 39.3 | 63.7 | 81.3 | 29.0 | 53.4 | 82.2 | 6.9 | 20.0 | 34.0 | | 4 | transformer | 0 | 38.3 | 62.2 | 80.1 | 27.9 | 53.6 | 82.4 | 5.8 | 18.2 | 34.3 | | 4 | transformer | 3 | 42.5 | 64.4 | 81.3 | 28.7 | 56.9 | 82.4 | 7.8 | 21.2 | 37.3 | Figure S11: Order of the forward/backward in a causal n -token prediction model with n = 2 heads. Like in the forward/backward depicted for parallel prediction heads in Figure 2, we avoid materializing all unembedding layer gradients in memory simultaneously and reduce peak GPU memory usage significantly. The iteration over the heads starts with the one furthest to the trunk. At each head, a gradient from the succeeding prediction heads and from the head's own loss are accumulated for both the head's output and its weights. <details> <summary>Image 11 Details</summary>  ### Visual Description ## Diagram: Data Flow Architecture ### Overview The diagram illustrates a multi-stage data processing pipeline with bidirectional connections between components. It features an Input node feeding into a Trunk, which splits into two parallel processing paths (Head 1 and Head 2). Each head connects to a dedicated Loss function, with numerical labels indicating directional relationships or transformation weights. ### Components/Axes - **Nodes**: - Input (bottom) - Trunk (central) - Head 1 (upper-left) - Head 2 (upper-right) - Loss 1 (right-center) - Loss 2 (far-right) - **Connections**: - Arrows with numerical labels (1-10) indicate directional flow or parameter weights - No explicit legend or color-coding present ### Detailed Analysis 1. **Input → Trunk**: - Two bidirectional connections labeled 1 (Input→Trunk) and 10 (Trunk→Input) 2. **Trunk → Heads**: - Trunk→Head 1: Labeled 2 (forward) and 9 (backward) - Trunk→Head 2: Labeled 3 (forward) and 6 (backward) 3. **Heads → Loss Functions**: - Head 1→Loss 1: Labeled 7 (forward) and 8 (backward) - Head 2→Loss 2: Labeled 4 (forward) and 5 (backward) ### Key Observations - Bidirectional flow exists between all connected components - Numerical labels increase sequentially from Input to Loss functions (1-10) - Loss functions only receive forward connections from their respective heads - No explicit temporal or hierarchical ordering beyond the numerical labels ### Interpretation This diagram likely represents a neural network architecture or optimization pipeline where: 1. Input data flows through a central processing unit (Trunk) 2. Parallel processing occurs in two heads, each specializing in different feature extraction 3. Loss functions evaluate the output quality of each head 4. Bidirectional connections suggest feedback mechanisms for error correction or iterative refinement The numerical labels (1-10) may represent: - Processing stages/steps - Weight magnitudes in a computational graph - Iteration counts in an optimization loop - Data transformation parameters The architecture emphasizes parallel processing with dedicated evaluation paths, suggesting a system designed for comparative analysis between Head 1 and Head 2 outputs. The absence of explicit error metrics or performance indicators limits quantitative interpretation. </details> ## C. Training speeds Table S5: Training time relative to next-token prediction training. The slight overhead when using multi-token prediction here is explained by a suboptimal use of Fully Sharded Data Parallel. In our implementation, when doing separate backward passes for each head, we lose the overlap of layer weight communication and computation, therefore it incurs a very slight overhead that can be removed if reimplemented correctly. | Model | n=1 | n=2 | n=4 | |---------|-------|-------|-------| | 0.3B | 1 | 1.07 | 1.22 | | 0.6B | 1 | 1.05 | 1.13 | | 1.3B | 1 | 1.04 | 1.12 | | 3B | 1 | 1.02 | 1.07 | | 6.7B | 1 | 1.02 | 1.07 | | 13B | 1 | 1.04 | 1.09 | ## E. Additional results on model scaling behavior Table S7: Scaling model size Full results of scaling model size with n=1,2 and 4. | | | MBPP | MBPP | MBPP | HumanEval | HumanEval | HumanEval | |------------|-----|--------|--------|--------|-------------|-------------|-------------| | Model Size | Fut | @1 | @10 | @100 | @1 | @10 | @100 | | 0.3B | 1 | 1.8 | 10.4 | 29.9 | 1.9 | 5.0 | 10.9 | | 0.3B | 2 | 1.7 | 10.1 | 27.2 | 1.5 | 4.4 | 10.3 | | 0.3B | 4 | 1.0 | 6.3 | 20.1 | 1.2 | 4.0 | 8.6 | | 0.6B | 1 | 4.7 | 21.0 | 45.2 | 2.9 | 8.5 | 16.7 | | 0.6B | 2 | 4.6 | 21.0 | 44.7 | 3.2 | 8.9 | 16.2 | | 0.6B | 4 | 3.0 | 15.6 | 38.0 | 2.7 | 7.7 | 15.5 | | 1.3B | 1 | 6.8 | 27.0 | 51.0 | 4.6 | 13.1 | 24.3 | | 1.3B | 2 | 7.3 | 27.5 | 51.7 | 5.4 | 13.6 | 23.3 | | 1.3B | 4 | 7.4 | 27.6 | 50.1 | 4.8 | 12.3 | 22.5 | | 3B | 1 | 11.1 | 36.4 | 60.4 | 7.2 | 17.2 | 29.8 | | 3B | 2 | 11.8 | 37.2 | 60.5 | 8.0 | 18.2 | 31.2 | | 3B | 4 | 12.7 | 37.6 | 61.1 | 7.2 | 18.5 | 33.3 | | 6.7B | 1 | 23.9 | 54.2 | 74.7 | 12.8 | 29.3 | 51.7 | | 6.7B | 2 | 24.7 | 54.8 | 76.4 | 13.2 | 32.2 | 53.9 | | 6.7B | 4 | 26.0 | 55.8 | 76.0 | 13.8 | 33.2 | 58.5 | | 13B | 1 | 26.0 | 57.1 | 77.0 | 14.1 | 33.6 | 56.0 | | 13B | 2 | 30.5 | 60.5 | 79.4 | 15.2 | 36.9 | 60.0 | | 13B | 4 | 30.5 | 61.0 | 79.2 | 15.8 | 38.6 | 63.5 | ## F. Details on CodeContests finetuning We use the Python subset of the CodeContests (Li et al., 2022) train split with reward annotations ('correct' / 'incorrect') and condition on correct solutions at evaluation time. For evaluation, we generate 1000 samples per problem from the test split for each temperature T ∈ { 0 . 5 , 0 . 6 , 0 . 7 , 0 . 8 , 0 . 9 } , and compute the unbiased estimator for pass@k from Chen et al. (2021) for each value of k and T . It is possible that models that were pretrained with different losses have different respective optimal temperatures for pass@k, so we compute and show k ↦→ max T pass \_ at( k, T ) in Figure 4. In other words, we grant pass@k access to a temperature oracle. For small values of k , pass@k measures the capability of understanding and solving tasks while for large k , it additionally favors diversity in outputs. According to the results in Figure 4, multi-token prediction pretraining leads to finetuned models that are better on both axes. ## G. Additional results on natural language benchmarks We evaluate the models from Section 3.7 on standard natural language processing benchmarks: ARC Challenge (Yadav et al., 2019), COPA (Roemmele et al., 2011), Hellaswag (Zellers et al., 2019), Natural Questions (Kwiatkowski et al., 2019), PIQA (Bisk et al., 2019), SIQA (Sap et al., 2019) and TriviaQA (Joshi et al., 2017). Figure S12: Multiple token training with 7B models doesn't improve performance on choice tasks. This figure shows the evolution of average accuracy of some standard NLP benchmarks (ARC Challenge COPA Hellaswag MMLU Natural Questions PIQA SIQA and TriviaQA. For the 7B models trained on 200B tokens of language data, the 2 future token model has the same performance as the baseline and the 4 future token model regresses a bit. Larger model sizes might be necessary to see improvements on these tasks. <details> <summary>Image 12 Details</summary>  ### Visual Description ## Line Graphs: Performance Metrics Across Datasets ### Overview The image contains seven line graphs arranged in a 3x2 grid (with one graph in the bottom row). Each graph represents the relationship between "global_step" (x-axis) and a performance metric labeled "value" (y-axis). Three data series are plotted per graph, differentiated by line color and legend labels: red (n=1), blue (n=2), and green (n=4). The graphs vary in y-axis scale and dataset-specific labels (e.g., "arc_challenge," "copa"). --- ### Components/Axes - **X-axis**: Labeled "global_step" with markers at 10,000 and 20,000. Consistent across all graphs. - **Y-axis**: Labeled "value," with scales varying per graph (e.g., 0–40 for "arc_challenge," 0–80 for "copa"). - **Legend**: Positioned on the right side of the image. Colors correspond to: - Red: n=1 (single participant) - Blue: n=2 (two participants) - Green: n=4 (four participants) - **Dataset Labels**: Top row graphs labeled "arc_challenge," "copa," "hellaswag"; bottom row labeled "nq," "piqa," "siqa," "tqa." --- ### Detailed Analysis 1. **arc_challenge**: - Y-axis: 0–40. - Red (n=1): Starts at ~25, rises to ~35 by 20k steps. - Blue (n=2): Starts at ~30, rises to ~38. - Green (n=4): Starts at ~35, rises to ~39. - **Trend**: All lines slope upward, with n=4 showing the steepest increase. 2. **copa**: - Y-axis: 0–80. - Red (n=1): Peaks at ~75 around 15k steps, then dips to ~65. - Blue (n=2): Starts at ~60, rises to ~70. - Green (n=4): Starts at ~65, rises to ~75. - **Trend**: n=1 exhibits volatility; n=2 and n=4 show steady growth. 3. **hellaswag**: - Y-axis: 0–60. - Red (n=1): Starts at ~40, rises to ~55. - Blue (n=2): Starts at ~45, rises to ~58. - Green (n=4): Starts at ~50, rises to ~60. - **Trend**: All lines slope upward, with n=4 maintaining the highest value. 4. **nq**: - Y-axis: 0–15. - Red (n=1): Starts at ~5, rises to ~12. - Blue (n=2): Starts at ~7, rises to ~14. - Green (n=4): Starts at ~9, rises to ~15. - **Trend**: Consistent upward slopes; n=4 outperforms others. 5. **piqa**: - Y-axis: 0–75. - Red (n=1): Starts at ~60, rises to ~70. - Blue (n=2): Starts at ~65, rises to ~72. - Green (n=4): Starts at ~68, rises to ~74. - **Trend**: Gradual increases; n=4 leads throughout. 6. **siqa**: - Y-axis: 0–46. - Red (n=1): Starts at ~40, rises to ~45. - Blue (n=2): Starts at ~42, rises to ~44. - Green (n=4): Starts at ~44, rises to ~46. - **Trend**: Minimal differences; n=4 slightly outperforms. 7. **tqa**: - Y-axis: 0–40. - Red (n=1): Starts at ~20, rises to ~30. - Blue (n=2): Starts at ~25, rises to ~32. - Green (n=4): Starts at ~28, rises to ~35. - **Trend**: All lines slope upward; n=4 shows the steepest gain. --- ### Key Observations - **Consistent Trends**: Across all datasets, higher n (participants) correlates with higher "value" at 20k steps. - **Anomalies**: In "copa," the red line (n=1) peaks and dips, suggesting potential instability or overfitting. - **Scale Variability**: Y-axis ranges differ per graph, indicating dataset-specific metric distributions. - **Efficiency Gaps**: Some datasets (e.g., "siqa") show minimal performance differences between n=2 and n=4, while others (e.g., "arc_challenge") exhibit larger gaps. --- ### Interpretation The data suggests that increasing the number of participants (n) generally improves performance (value) over time. However, the relationship is not universally linear: - **Diminishing Returns**: In "siqa," the performance gap between n=2 and n=4 narrows, implying limited benefits from additional participants. - **Volatility**: The "copa" dataset shows instability for n=1, possibly due to noise or task-specific challenges. - **Task Dependency**: Performance trends vary by dataset (e.g., "hellaswag" and "tqa" show steeper gains for n=4 compared to "nq" or "piqa"), suggesting that participant count impacts different tasks differently. The graphs highlight the importance of participant scale in optimizing performance but also underscore the need for dataset-specific analysis to understand efficiency trade-offs. </details> ## H. Additional results on abstractive text summarization In this section, we report comprehensive evaluation results on summarization tasks for the 7B parameter models trained on 200B and 500B tokens of natural language from Section 3.7. Table S8: Comprehensive evaluation on abstractive text summarization. ROUGE-n (n-gram overlap) and ROUGE-L (longest common subsequence overlap) F 1 scores for 7B models trained on 200B and 500B tokens of natural language, respectively. The last three columns correspond to models trained on 500B tokens, the previous three to models trained on 200B tokens. Shown are numbers of the n = 1 baseline and the absolute difference of n = 2 and n = 4 models trained on the same number of tokens. Summary-level ROUGE-L ('ROUGE-Lsum') is reported where it differs from ROUGE-L. Model checkpoints with maximal validation ROUGE-L F 1 are selected separately for each model dataset and model type and reported in the first row corresponding to each dataset. Boldface for numbers within 0.05 difference to the best one for each dataset size separately. | Task | Metric | Baseline 200B | ∆ n =2 | ∆ n =4 | Baseline 500B | ∆ n =2 | ∆ n =4 | |----------------------------------------|------------------|-----------------|-------------|-------------|-----------------|-------------|-------------| | CNN/Dailymail (Nallapati et al., 2016) | evaluation epoch | 2 | 2 | 2 | 2 | 2 | 2 | | | ROUGE-1 | 42.88 | +0.74 | +0.74 | 43.77 | +0.55 | +0.50 | | | ROUGE-2 | 19.56 | +0.52 | +0.53 | 20.34 | +0.52 | +0.34 | | | ROUGE-3 | 11.11 | +0.39 | +0.35 | 11.69 | +0.36 | +0.19 | | | ROUGE-L | 29.72 | +0.66 | +0.49 | 30.51 | +0.48 | +0.37 | | | ROUGE-Lsum | 40.18 | +0.72 | +0.68 | 41.02 | +0.56 | +0.52 | | Multi-News (Fabbri et al., 2019) | evaluation epoch | 1 | 3 | 3 | 2 | 3 | 2 | | Multi-News (Fabbri et al., 2019) | ROUGE-1 | 44.48 | +1.70 | +1.72 | 45.87 | +1.05 | +0.69 | | Multi-News (Fabbri et al., 2019) | ROUGE-2 | 16.88 | +0.44 | +0.70 | 17.56 | +0.42 | +0.40 | | Multi-News (Fabbri et al., 2019) | ROUGE-3 | 9.63 | -0.06 | +0.17 | 9.91 | +0.22 | +0.18 | | Multi-News (Fabbri et al., 2019) | ROUGE-L | 23.82 | +0.17 | +0.40 | 24.22 | +0.20 | +0.26 | | OrangeSum (Eddine et al., 2021) | evaluation epoch | 2 | 2 | 3 | 2 | 1 | 3 | | OrangeSum (Eddine et al., 2021) | ROUGE-1 | 32.95 | +0.41 | +0.35 | 33.37 | +0.32 | +0.78 | | OrangeSum (Eddine et al., 2021) | ROUGE-2 | 13.90 | +0.31 | +0.36 | 14.22 | +0.25 | +0.53 | | OrangeSum (Eddine et al., 2021) | ROUGE-3 | 8.01 | +0.19 | +0.21 | 8.12 | +0.22 | +0.48 | | OrangeSum (Eddine et al., 2021) | ROUGE-L | 23.62 | +0.36 | +0.51 | 23.91 | +0.23 | +0.66 | | pn-summary (Farahani et al., 2021) | evaluation epoch | 1 | 1 | 1 | 1 | 2 | 3 | | pn-summary (Farahani et al., 2021) | ROUGE-1 | 1.03 | +0.02 | 0.00 | 0.92 | +0.09 | +0.05 | | pn-summary (Farahani et al., 2021) | ROUGE-2 | 0.13 | +0.02 | +0.03 | 0.15 | 0.00 | 0.00 | | pn-summary (Farahani et al., 2021) | ROUGE-3 | 0.02 | 0.00 | +0.02 | 0.02 | 0.00 | +0.02 | | pn-summary (Farahani et al., 2021) | ROUGE-L | 1.02 | +0.03 | +0.01 | 0.91 | +0.09 | +0.05 | | SAMSum (Gliwa et al., 2019) | evaluation epoch | 3 | 3 | 3 | 3 | 3 | 3 | | SAMSum (Gliwa et al., 2019) | ROUGE-1 | 51.39 | +0.70 | +0.63 | 52.54 | -0.24 | +0.69 | | SAMSum (Gliwa et al., 2019) | ROUGE-2 | 26.46 | +0.76 | +0.30 | 27.74 | -0.20 | +0.82 | | SAMSum (Gliwa et al., 2019) | ROUGE-3 | 16.40 | +0.91 | +0.28 | 17.56 | -0.30 | +0.71 | | SAMSum (Gliwa et al., 2019) | ROUGE-L | 42.59 | +0.90 | +0.51 | 43.92 | -0.10 | +0.63 | | ThaiSum (Chumpolsathien, 2020) | evaluation epoch | 2 | 3 | 3 | 3 | 3 | 3 | | ThaiSum (Chumpolsathien, 2020) | ROUGE-1 | 45.08 | +0.63 | +1.12 | 45.48 | +0.77 | +0.91 | | ThaiSum (Chumpolsathien, 2020) | ROUGE-2 | 27.85 | +0.30 | +0.73 | 28.07 | +0.74 | +0.64 | | ThaiSum (Chumpolsathien, 2020) | ROUGE-3 | 15.73 | +0.04 | +0.43 | 15.82 | +0.50 | +0.30 | | ThaiSum (Chumpolsathien, 2020) | ROUGE-L | 44.92 | +0.64 | +1.12 | 45.31 | +0.76 | +0.89 | | WikiSummary (Farahani, 2020) | evaluation epoch | 3 | 3 | 3 | 3 | 3 | 3 | | WikiSummary (Farahani, 2020) | ROUGE-1 | 10.16 | +0.67 | -0.23 | 12.80 | -0.17 | -0.99 | | WikiSummary (Farahani, 2020) | ROUGE-2 | 4.46 | -0.03 | -0.09 | 6.17 | -0.11 | -0.69 | | WikiSummary (Farahani, 2020) | ROUGE-3 | 1.31 | +0.21 | +0.13 | 1.98 | -0.08 | -0.33 | | WikiSummary (Farahani, 2020) | ROUGE-L | 10.11 | +0.65 | -0.28 | 12.69 | -0.17 | -0.99 | | XSum (Narayan et al., 2018) | evaluation epoch | 2 | 2 | 3 | 2 | 2 | 3 | | XSum (Narayan et al., 2018) | ROUGE-1 | 42.16 | +0.71 | +1.07 | 43.42 | +0.78 | +0.67 | | XSum (Narayan et al., 2018) | ROUGE-2 | 19.19 | +0.54 | +0.55 | 20.32 | +0.68 | +0.34 | | XSum (Narayan et al., 2018) | ROUGE-3 ROUGE-L | 10.43 34.03 | +0.38 +0.67 | +0.28 +0.92 | 11.23 35.18 | +0.48 +0.79 | +0.20 +0.63 | Table S9: Performance on abstractive text summarization. ROUGE-L (longest common subsequence overlap) F 1 score for 7B models trained on 200B and 500B tokens of natural language. We finetune the respective models on each task's training data separately for a given number of epochs and select the checkpoints with maximal ROUGE-L F 1 on the validation dataset. The second and fifth column report the numbers for a next-token prediction model, while the third, fourth, sixth and seventh one report the absolute improvements for 2-token and 4-token prediction models trained on the same amount of data, respectively. Boldface for numbers within 0.05 difference to the best one for each dataset size separately. | Dataset | Baseline 200B | ∆ n =2 | ∆ n =4 | Baseline 500B | ∆ n =2 | ∆ n =4 | |---------------|-----------------|----------|----------|-----------------|----------|----------| | CNN/Dailymail | 29.72 | 0.66 | 0.49 | 30.51 | 0.48 | 0.37 | | Multi-News | 23.82 | 0.17 | 0.4 | 24.22 | 0.2 | 0.26 | | OrangeSum | 23.62 | 0.36 | 0.51 | 23.91 | 0.23 | 0.66 | | pn-summary | 1.02 | 0.03 | 0.01 | 0.91 | 0.09 | 0.05 | | SAMSum | 42.59 | 0.9 | 0.51 | 43.92 | -0.1 | 0.63 | | ThaiSum | 44.92 | 0.64 | 1.12 | 45.31 | 0.76 | 0.89 | | WikiSummary | 10.11 | 0.65 | -0.28 | 12.69 | -0.17 | -0.99 | | XSum | 34.03 | 0.67 | 0.92 | 35.18 | 0.79 | 0.63 | | Average | 26.23 | 0.51 | 0.46 | 27.08 | 0.28 | 0.31 | Table S10: Summary statistics for abstractive text summarization evaluations. Reported are averages for ROUGE-n and ROUGE-L metrics across all datasets from Table S8, separately for precision, recall and F 1 score. Both 2-token and 4-token prediction models outperform the next-token prediction baseline. Trained on 500B tokens, 4-token prediction models appear better at recall metrics while 2-token prediction models appear better at precision metrics. Model checkpoints are selected as described in Table S8. Boldface for numbers within 0.05 difference to the best one for each dataset size separately. | Metric | Aspect | Baseline 200B | ∆ n =2 | ∆ n =4 | Baseline 500B | ∆ n =2 | ∆ n =4 | |-------------|-----------|-----------------|----------|----------|-----------------|----------|----------| | ROUGE-1 | F 1 | 33.77 | 0.7 | 0.68 | 34.77 | 0.39 | 0.41 | | ROUGE-1 | precision | 35.76 | 0.88 | 0.83 | 37.03 | 0.42 | -0.04 | | ROUGE-1 | recall | 34.37 | 0.45 | 0.45 | 35.14 | 0.35 | 0.68 | | ROUGE-2 | F 1 | 16.06 | 0.36 | 0.39 | 16.82 | 0.29 | 0.3 | | ROUGE-2 | precision | 16.97 | 0.4 | 0.43 | 17.91 | 0.29 | 0.03 | | ROUGE-2 | recall | 16.34 | 0.28 | 0.35 | 16.99 | 0.32 | 0.48 | | ROUGE-3 | F 1 | 9.08 | 0.26 | 0.23 | 9.54 | 0.18 | 0.22 | | ROUGE-3 | precision | 9.59 | 0.29 | 0.28 | 10.17 | 0.18 | 0.05 | | ROUGE-3 | recall | 9.26 | 0.21 | 0.2 | 9.65 | 0.21 | 0.35 | | ROUGE-L | F 1 | 26.23 | 0.51 | 0.46 | 27.08 | 0.28 | 0.31 | | ROUGE-L | precision | 27.79 | 0.62 | 0.55 | 28.85 | 0.28 | -0.09 | | ROUGE-L | recall | 26.71 | 0.37 | 0.32 | 27.4 | 0.28 | 0.57 | | ROUGE-L sum | F 1 | 27.53 | 0.52 | 0.48 | 28.4 | 0.29 | 0.33 | | ROUGE-L sum | precision | 29.07 | 0.64 | 0.58 | 30.15 | 0.29 | -0.08 | | ROUGE-L sum | recall | 28.13 | 0.35 | 0.33 | 28.81 | 0.29 | 0.6 | ## I. Additional results on mathematical reasoning in natural language Figure S13: Performance on the mathematical reasoning benchmark GSM8K (Cobbe et al., 2021). We evaluate pretrained next-token and multi-token prediction models trained on 200B and 500B tokens of natural language in 8-shot mode using nucleus sampling (Holtzman et al., 2020) with probability mass 0.95 and various sampling temperatures. Reported are the frequencies of the correct final answer to appear among k samples, for k = 1 , 10 , 100 , estimated from 200 samples like in code generation benchmarks (Chen et al., 2021). After 200B tokens, the 2-token prediction model has a clear advantage over the next-token baseline but the order reverses after 500B tokens. The 4-token prediction model is worse throughout. We interpret this similarly to the findings in Section 4.1: the follow-your-nose chains-of-thought required for GSM8K may be difficult to learn from a limited amount of data, attesting to the data efficiency of multi-token prediction training. Once the correct circuits for correct autoregressive chains-of-thought in this domain have formed, however, multi-token prediction comes at a cost. <details> <summary>Image 13 Details</summary>  ### Visual Description ## Line Graphs: Performance Metrics Across Token Counts and Temperature ### Overview The image contains six line graphs arranged in a 2x3 grid, comparing performance metrics (pass@1 and pass@10) for models with 200B and 500B tokens across varying temperatures (0.2–1.4). Each graph includes three data series representing different sampling strategies (n=1, n=2, n=4), color-coded as red, blue, and green respectively. ### Components/Axes - **X-axis**: Temperature (0.2–1.4) in increments of 0.2. - **Y-axis**: - Top row: pass@1 (%) for 200B and 500B tokens. - Middle row: pass@10 (%) for 200B and 500B tokens. - Bottom row: pass@10 (%) for 500B tokens only. - **Legend**: Located in the top-right corner of each graph, mapping: - Red: n=1 - Blue: n=2 - Green: n=4 ### Detailed Analysis #### 200B Tokens (Left Column) 1. **pass@1 (%)**: - **n=1 (Red)**: Starts at ~3.5% (temp=0.2), declines to ~1.2% (temp=1.4). - **n=2 (Blue)**: Starts at ~3.3%, declines to ~1.0%. - **n=4 (Green)**: Starts at ~2.8%, declines to ~0.8%. - **Trend**: All lines slope downward, with n=1 showing the steepest decline. 2. **pass@10 (%)**: - **n=1 (Red)**: Peaks at ~20% (temp=0.6), drops to ~12% (temp=1.4). - **n=2 (Blue)**: Peaks at ~22% (temp=0.6), drops to ~10%. - **n=4 (Green)**: Peaks at ~18% (temp=0.6), drops to ~8%. #### 500B Tokens (Right Column) 1. **pass@1 (%)**: - **n=1 (Red)**: Starts at ~8%, declines to ~1.5%. - **n=2 (Blue)**: Starts at ~6.5%, declines to ~1.2%. - **n=4 (Green)**: Starts at ~5.5%, declines to ~0.9%. 2. **pass@10 (%)**: - **n=1 (Red)**: Peaks at ~30% (temp=0.6), drops to ~15%. - **n=2 (Blue)**: Peaks at ~32% (temp=0.6), drops to ~12%. - **n=4 (Green)**: Peaks at ~28% (temp=0.6), drops to ~10%. 3. **pass@10 (%) (500B Only)**: - **n=1 (Red)**: Peaks at ~60% (temp=0.6), drops to ~40%. - **n=2 (Blue)**: Peaks at ~62% (temp=0.6), drops to ~42%. - **n=4 (Green)**: Peaks at ~58% (temp=0.6), drops to ~38%. ### Key Observations 1. **Performance Degradation**: All metrics decline as temperature increases, with sharper drops at higher temperatures (e.g., temp=1.4). 2. **Sampling Strategy Impact**: Higher n values (more samples) consistently improve performance: - n=4 outperforms n=2 and n=1 across all token counts and metrics. - The gap widens at higher temperatures (e.g., pass@10 for 500B tokens: n=4 at 58% vs. n=1 at 60% at temp=0.6). 3. **Token Count Scaling**: 500B models outperform 200B models by ~2–3× in pass@10 (e.g., 60% vs. 20% at temp=0.6 for pass@10). ### Interpretation The data demonstrates that: - **Larger models (500B tokens)** achieve significantly higher performance than smaller models (200B tokens), particularly in pass@10. - **Sampling diversity (n=4)** mitigates temperature-induced performance drops more effectively than smaller n values. - **Temperature sensitivity** is non-linear: performance peaks at moderate temperatures (0.6–0.8) before declining sharply at higher temperatures (1.2–1.4). This suggests that balancing temperature and sampling strategy is critical for optimizing model outputs, with larger models and higher n values providing robustness against temperature-related degradation. </details> ## J. Additional results on induction learning Figure S14: Induction capability of n -token prediction models trained on higher-quality data. Shown is accuracy on the second token of two token names that have already been mentioned previously. Training on a 9:1 mix of a books dataset and the children storiy dataset, we observe that induction capability forms significantly earlier in training (not shown here) and to a higher degree. We believe that this is explained both because our evaluation dataset no longer contains out-of-distribution tokens (Section 4.1) and because the higher-quality data contained in the books dataset makes induction necessary earlier on (especially for small models, cf. Singh et al. (2023)). In particular, by enforcing the formation of induction capability in the model by means of the dataset - instead of the loss - the advantage of 2-token prediction models on this task disappears except for the smallest models: feature learning converts the task into a pure next-token prediction task. <details> <summary>Image 14 Details</summary>  ### Visual Description ## Line Graph: Induction Success vs. Parameters (M) ### Overview The image is a line graph comparing induction success rates across different parameter scales (M) for two models: a baseline model (n=1) and an optimized model (n=2). The graph shows how induction success improves as parameters increase, with distinct trends for each model. ### Components/Axes - **X-axis**: "Parameters (M)" ranging from 1 to 1000 (logarithmic scale implied by spacing). - **Y-axis**: "Induction success" measured as a decimal from 0.850 to 1.000. - **Legend**: Located in the bottom-right corner, with: - Red solid line: "n=1 (baseline)" - Blue dashed line: "n=2 (ours)" - **Data Points**: Marked with "X" symbols on both lines. ### Detailed Analysis #### Baseline Model (n=1, Red Line) - **Trend**: Starts at 0.850 induction success for 1M parameters, sharply increasing to 0.925 at 3M, then plateauing near 0.999 for parameters ≥10M. - **Key Data Points**: - 1M: 0.850 - 3M: 0.925 - 10M: 0.990 - 30M: 0.995 - 100M: 0.998 - 300M: 0.999 - 1000M: 0.999 #### Optimized Model (n=2, Blue Line) - **Trend**: Begins at 0.875 for 1M parameters, rises steeply to 0.975 at 3M, then plateaus near 0.999 for parameters ≥10M. - **Key Data Points**: - 1M: 0.875 - 3M: 0.975 - 10M: 0.990 - 30M: 0.995 - 100M: 0.998 - 300M: 0.999 - 1000M: 0.999 ### Key Observations 1. **Performance Gap**: The optimized model (n=2) consistently outperforms the baseline (n=1) across all parameter scales, with a larger margin at lower parameters (e.g., 0.10 difference at 1M vs. 0.001 at 1000M). 2. **Convergence**: Both models plateau near 0.999 induction success at 1000M parameters, suggesting diminishing returns at scale. 3. **Efficiency**: The optimized model achieves higher success with fewer parameters (e.g., 0.975 at 3M vs. 0.925 for the baseline). ### Interpretation The graph demonstrates that the optimized model (n=2) achieves superior induction success with fewer parameters compared to the baseline (n=1), particularly at smaller scales. This suggests architectural or algorithmic improvements in the optimized model that enhance efficiency. The convergence at 1000M parameters implies that both models reach near-optimal performance at scale, but the optimized model does so with significantly lower resource requirements. The sharp initial rise in the blue line highlights the critical impact of parameter scaling in early stages, while the plateau indicates saturation of performance gains. </details> ## K. Additional results on algorithmic reasoning We investigate the following computation-sharing hypothesis for explaining the efficacy of multi-token prediction as training loss. The prediction difficulty of different tokens in natural text varies greatly. Some tokens may be the continuations of partial words that are uniquely determined from their preceding context without any effort, while others may require to predict theorem names in difficult mathematical proofs or the correct answer to an exam question. Language models with residual connections have been shown to refine their output token distribution with each successive layer, and can be trained with early exit strategies that spend variable amounts of computational resources per token position. Multi-token prediction losses explicitly encourage information-sharing between adjacent token positions and can thus be viewed as a method to learn allocating computational resources in language models more efficiently to the tokens that benefit most of it. To check the truth of this hypothesis, we augment the polynomial arithmetic task from Section 4.2 with a varying number of pause tokens (Goyal et al., 2023) inserted between the question and a token that denotes the beginning of the answer. Pause tokens introduce additional computational resources that can be expended for computations that are expected to be useful later on in the sequence, in other words: to start thinking about the answer. According to the computation-sharing hypothesis , multi-token prediction models learn information-sharing and thus computation-sharing between token positions more easily, and may be better at making use of these additional computational resources than next-token prediction models are. In Figure S15, we show the evaluation results on the polynomial arithmetic task with a fixed number of pause tokens inserted both at training and evaluation time. Multi-token prediction models likewise outperform next-token prediction models on these task variants across task difficulties and model sizes. However, we do not see strong evidence of a widening or shrinking of this gap i.e. we cannot conclude from these experiments on the veracity of the computation-sharing hypothesis. In Table S11, we report results from another experiment in the same spirit: by adding spaces and newlines to HumanEval and MBPP prompts, we add 'pause tokens' in a somewhat natural way. According to these results, multi-token prediction models have a slight advantage at using this additionally provided compute, but the effect is marginal. Figure S15: Accuracy on a polynomial arithmetic task with varying number of operations per expression and pause tokens. We train and evaluate models on the polynomial arithmetic task described in Section 4.2, modified by the addition of pause tokens (Goyal et al., 2023): between the question and the equality sign that indicates the beginning of the answer, we add a constant number of pause tokens both in training and evaluation. For both a variant with five and with ten pause tokens, respectively, we observe comparable improvements from using multi-token prediction to the ones obtained in the case without pause tokens (Figure 8). <details> <summary>Image 15 Details</summary>  ### Visual Description ## Line Graphs: Accuracy vs. Number of Operations with Pause Tokens ### Overview The image contains two line graphs (a and b) comparing model accuracy (%) against the number of operations (1–10) for in-domain and out-of-domain tasks. Each graph represents different numbers of pause tokens (n=1, n=2, n=4). Accuracy declines as operations increase, with distinct trends for in-domain and out-of-domain performance. ### Components/Axes - **X-axis**: "# operations" (1–10), split into "in-domain" (1–5.5) and "out-of-domain" (5.5–10) by a vertical dashed line. - **Y-axis**: "Accuracy (%)" (0–100). - **Legends**: - Top-right corner, with colors: - Red (`n=1`) - Blue (`n=2`) - Green (`n=4`) - **Graph Labels**: - (a) "5 pause tokens" - (b) "10 pause tokens" ### Detailed Analysis #### Graph (a): 5 Pause Tokens - **In-domain**: - **n=1 (red)**: Starts at ~85% (1 op), drops to ~60% (3 ops), ~35% (5 ops), ~20% (7 ops), ~5% (10 ops). - **n=2 (blue)**: Starts at ~90% (1 op), ~70% (3 ops), ~45% (5 ops), ~25% (7 ops), ~10% (10 ops). - **n=4 (green)**: Starts at ~80% (1 op), ~60% (3 ops), ~30% (5 ops), ~15% (7 ops), ~5% (10 ops). - **Out-of-domain**: - **n=1 (red)**: Starts at ~75% (1 op), ~50% (3 ops), ~25% (5 ops), ~10% (7 ops), ~2% (10 ops). - **n=2 (blue)**: Starts at ~85% (1 op), ~65% (3 ops), ~35% (5 ops), ~15% (7 ops), ~3% (10 ops). - **n=4 (green)**: Starts at ~70% (1 op), ~45% (3 ops), ~20% (5 ops), ~8% (7 ops), ~2% (10 ops). #### Graph (b): 10 Pause Tokens - **In-domain**: - **n=1 (red)**: Starts at ~90% (1 op), ~75% (3 ops), ~50% (5 ops), ~30% (7 ops), ~10% (10 ops). - **n=2 (blue)**: Starts at ~95% (1 op), ~80% (3 ops), ~60% (5 ops), ~40% (7 ops), ~15% (10 ops). - **n=4 (green)**: Starts at ~85% (1 op), ~65% (3 ops), ~40% (5 ops), ~25% (7 ops), ~5% (10 ops). - **Out-of-domain**: - **n=1 (red)**: Starts at ~80% (1 op), ~60% (3 ops), ~30% (5 ops), ~10% (7 ops), ~2% (10 ops). - **n=2 (blue)**: Starts at ~85% (1 op), ~65% (3 ops), ~35% (5 ops), ~15% (7 ops), ~3% (10 ops). - **n=4 (green)**: Starts at ~75% (1 op), ~50% (3 ops), ~25% (5 ops), ~10% (7 ops), ~2% (10 ops). ### Key Observations 1. **Pause Token Impact**: Higher `n` (pause tokens) correlates with higher accuracy, especially in in-domain tasks. 2. **In-Domain vs. Out-of-Domain**: In-domain accuracy is consistently higher than out-of-domain for all `n`. 3. **Decline Rate**: Accuracy drops faster for lower `n` (e.g., n=1 declines ~80% from 1 to 10 ops in in-domain). 4. **Threshold**: The split at 5.5 operations suggests a performance threshold where out-of-domain accuracy sharply declines. ### Interpretation The data demonstrates that increasing pause tokens (`n`) improves model robustness, particularly in in-domain scenarios. Out-of-domain performance is more sensitive to operational complexity, with accuracy decaying faster as operations increase. The vertical split at 5.5 operations may indicate a critical point where the model’s ability to generalize diminishes, highlighting the importance of pause tokens in maintaining stability during extended operations. The steeper decline for lower `n` suggests that insufficient pause tokens exacerbate overfitting or instability in dynamic tasks. </details> Table S11: Utilization of additional whitespace tokens in code benchmarks. | Task | Whitespace | n = 1 | n = 4 | |-----------------------------------------------------|----------------------------------------------------------------------------|-------------------------------------|-------------------------------------| | APPS/Intro APPS/Intro HumanEval HumanEval MBPP MBPP | spaces + newline newline spaces + newline newline spaces + newline newline | +0.21 +0.79 -0.72 -0.26 -0.10 +0.03 | +0.34 +0.69 -0.16 +0.10 -0.06 -0.08 | | Average | | -0.01 | +0.14 | Figure S16: Accuracy on a polynomial arithmetic task for two model sizes. We train and evaluate models with 30M and 100M parameters on the polynomial arithmetic task described in Section 4.2. Tripling the model size has a smaller effect on performance than replacing next-token prediction loss by multi-token prediction. Shown are two independent runs per configuration and their means, the 100M parameter models being identical to the ones in Figure 8. <details> <summary>Image 16 Details</summary>  ### Visual Description ## Line Graph: Model Accuracy vs. Operations ### Overview The graph compares the accuracy of machine learning models under varying operational constraints, distinguishing between in-domain (operations 1-6) and out-of-domain (operations 7-10) scenarios. Accuracy declines as the number of operations increases, with distinct trends for different model configurations. ### Components/Axes - **Y-axis**: Accuracy (%) ranging from 0 to 100. - **X-axis**: Number of operations (1-10), split into: - In-domain: Operations 1-6 (left of vertical dashed line). - Out-of-domain: Operations 7-10 (right of vertical dashed line). - **Legend**: Located in the top-right corner, with entries: - **30M**: Red (solid), Blue (dashed), Green (dotted) for n=1, 2, 4. - **100M**: Red (solid), Blue (dashed), Green (dotted) for n=1, 2, 4. ### Detailed Analysis 1. **30M Model**: - **n=1** (Red solid): Starts at ~90% accuracy at 1 operation, dropping to ~10% by 10 operations. - **n=2** (Blue dashed): Begins at ~85%, declining to ~5% by 10 operations. - **n=4** (Green dotted): Starts at ~80%, falling to ~2% by 10 operations. 2. **100M Model**: - **n=1** (Red solid): Starts at ~95%, dropping to ~15% by 10 operations. - **n=2** (Blue dashed): Begins at ~90%, declining to ~10% by 10 operations. - **n=4** (Green dotted): Starts at ~85%, falling to ~5% by 10 operations. **Trends**: - All lines exhibit a steep decline in accuracy as operations increase. - 100M models consistently outperform 30M models across all n values. - Out-of-domain performance (operations 7-10) shows a sharper drop compared to in-domain. ### Key Observations - **Performance Degradation**: Accuracy decreases exponentially with more operations, especially beyond 6 operations (out-of-domain). - **Model Robustness**: 100M models maintain higher accuracy than 30M models, suggesting better scalability. - **n=4 Impact**: Higher n values (more operations per step) correlate with faster accuracy decline, particularly in out-of-domain tasks. ### Interpretation The data demonstrates that increasing operational complexity (more operations) reduces model accuracy, with out-of-domain tasks exacerbating this effect. Larger models (100M) exhibit greater resilience, maintaining higher accuracy across operations. The steeper decline in out-of-domain performance highlights the challenge of generalization. The n=4 configurations (most operations per step) underperform, indicating that smaller, more frequent steps may be more effective for maintaining accuracy. This suggests trade-offs between model size, operational granularity, and task domain alignment. </details> Table S12: Optimal temperatures for all numbers in table 1 | Training data | Vocabulary | n | MBPP | MBPP | MBPP | HumanEval | HumanEval | HumanEval | APPS/Intro | APPS/Intro | APPS/Intro | |----------------------|--------------|-----|--------|--------|--------|-------------|-------------|-------------|--------------|--------------|--------------| | Training data | Vocabulary | n | @1 | @10 | @100 | @1 | @10 | @100 | @1 | @10 | @100 | | | | 1 | 0.2 | 0.8 | 0.8 | 0.1 | 0.8 | 0.8 | 0.8 | 0.8 | 0.8 | | | | 8 | 0.1 | 0.8 | 0.8 | 0.1 | 0.8 | 0.8 | 0.4 | 0.4 | 0.4 | | | | 16 | 0.1 | 0.8 | 0.8 | 0.1 | 0.8 | 0.8 | 0.4 | 0.4 | 0.4 | | | | 32 | 0.1 | 0.4 | 0.8 | 0.1 | 0.4 | 0.8 | 0.1 | 0.4 | 0.4 | | | | 1 | 0.1 | 0.8 | 0.8 | 0.1 | 0.8 | 0.8 | 0.1 | 0.4 | 0.8 | | | | 2 | 0.1 | 0.8 | 0.8 | 0.2 | 0.8 | 0.8 | 0.4 | 0.4 | 0.8 | | | | 4 | 0.1 | 0.8 | 0.8 | 0.1 | 0.8 | 0.8 | 0.2 | 0.8 | 0.8 | | | | 6 | 0.1 | 0.8 | 0.8 | 0.2 | 0.8 | 0.8 | 0.4 | 0.4 | 0.8 | | | | 8 | 0.1 | 0.8 | 0.8 | 0.1 | 0.8 | 0.8 | 0.2 | 0.4 | 0.8 | | 1T tokens (4 epochs) | | 1 | 0.1 | 0.8 | 0.8 | 0.1 | 0.8 | 0.8 | 0.1 | 0.4 | 0.8 | | 1T tokens (4 epochs) | | 4 | 0.1 | 0.8 | 0.8 | 0.2 | 0.8 | 0.8 | 0.4 | 0.8 | 0.8 | ## L. Additional intuitions on multi-token prediction ## L.1. Comparison to scheduled sampling In Section 5.2, we argued that multi-token prediction reduces the distribution mismatch between teacher-forced training and autoregressive evaluation of language models. Scheduled sampling (Bengio et al., 2015) is a curriculum learning method that likewise aims to bridge this gap in sequence prediction tasks by gradually replacing more and more input tokens with model-generated ones. While effective in areas such as time series forecasting, scheduled sampling is, in our opinion, inapplicable to language modelling due to the discrete nature of text. Replacing ground truth input sequences by interleavings of ground truth and model-generated tokens frequently results in ungrammatical, factually wrong or otherwise incoherent text, which should be avoided at all cost. Moreover, unlike multi-token prediction, the technique originally developed for recurrent neural networks cannot easily be adapted for parallel training setups like the ones of transformer models. ## L.2. Information-theoretic argument We give details on the information-theoretic terms appearing in the decomposition in Section 5.2 and derive a relative version that similarly allows to decompose multi-token prediction losses. As in Section 5.2, denote by X the next token and by Y the second-next one, and omit conditioning on the preceding context C for ease of notation. In Section 5.2, we decomposed H ( X ) + H ( Y ) -the quantity of interest for 2-token prediction models-as follows: <!-- formula-not-decoded --> Let us explain each of the terms. The entropy terms denote the uncertainty contained in the ground-truth random variables X and Y . 2 The term H ( Y | X ) is a classical next-token entropy for the prefix ( C, X ) . The conditional entropy H ( X | Y ) is a more theoretical entity not modelled by causal models. It describes the uncertainty about X given the prefix C and suffix Y , and therefore captures the local variations of X that do not affect the continuation of the text Y . The mutual information I ( X ; Y ) on the other hand describes the information about Y contained in X (and vice versa) and therefore captures the variations of X which constrain the continuation of the text. However, the argument given in Section 5.2 relies on the assumption that multi-token prediction losses obey a similar decomposition as the sum of the ground-truth entropies themselves. Let us make this rigorous. Denote by p ( x, y ) the joint distribution of X and Y , by p ( x ) (short for p X ( x ) ) the marginal distribution of X and by p ( y ) the one of Y . Denote the densities of the model's predictions by q ( x, y ) , q ( x ) and q ( y ) , respectively, conditional distributions by p ( x | y ) and Kullback-Leibler divergence from q to p by D ( p ∥ q ) and cross-entropy from q to p by H ( p, q ) . Definition L.1. The conditional cross-entropy H ( p X | Y , q X | Y ) of X conditioned on Y from q to p is defined as the 2 In particular, they do not refer to model predictions. expectation under y of the cross-entropy between the distributions p X and q X conditioned on y , in formulas: <!-- formula-not-decoded --> Definition L.2. The relative mutual information I p ∥ q ( X ; Y ) of X and Y from q relative to p is defined by <!-- formula-not-decoded --> We have I p ∥ q ( X ; Y ) = H ( p X , q X ) + H ( p Y , q Y ) -H ( p, q ) , I p ∥ p ( X ; Y ) = I p ( X ; Y ) reduces to standard mutual information under the distribution p and I p ∥ q ( X ; Y ) is symmetric in X and Y but can be negative. We have the following relative version of the decomposition H ( X ) = H ( X | Y ) + I ( X ; Y ) . <!-- formula-not-decoded --> Proof. We calculate <!-- formula-not-decoded --> Symmetrizing, we get the desired relative version of H ( X ) + H ( Y ) = H ( X | Y ) + 2 I ( X ; Y ) + H ( Y | X ) : <!-- formula-not-decoded --> Setting p to be the empirical distribution of the training data, the left-hand side describes the cross-entropy loss used to train 2-token prediction models. The right-hand side gives the decomposition into a local cross-entropy term, a mutual information term with weight two and a shifted next-token cross-entropy term. We interpret this as follows: by adding the term H ( p Y , q Y ) to the loss, 2-token prediction incentivizes models to precompute features which will become useful for predicting Y in the next step and increases the weight of the relative mutual information term in the loss. What does relative mutual information actually mean? By interpreting Kullback-Leibler divergence D ( p ∥ q ) as the average number of bits needed in addition to send data from p with a code optimized for q instead of p , we see that minimizing <!-- formula-not-decoded --> means minimizing the average number of additional bits needed to send data from p with a code optimized for q that treats X and Y as independent compared to one that does not. If this number is small, q managed to exploit the mutual information of X and Y under p . ## L.3. Lookahead reinforces choice points Training with multi-head prediction increases the importance of choice points in the loss in comparison to inconsequential decisions. To make this argument, we present a simplified model of language modelling. Consider a sequential decision task and a model M that is trained in a teacher-forced way on optimal trajectories. We distinguish choice points -transitions that lead to different outcomes - and inconsequential decisions which do not (Figure S17 (a) and (b)). Figure S17: Example of a sequential prediction task with derailing. The goal is to go from the arrow to the trophy. Turning around is not allowed. Most transitions are unique, but there are two turns to be taken correctly, the consequential decisions (a) and (c). Turn (b) is an inconsequential decision : the paths join right after it. Next to transitions (a) and (b), we sketch how a 4-step prediction loss can place more emphasis on consequential transitions than inconsequential ones during teacher-forced training. Next to transition (c), we sketch how a 4-step lookahead can prevent models from taking irreversible suboptimal decisions during autoregressive decoding. <details> <summary>Image 17 Details</summary>  ### Visual Description ## Diagram: Grid-Based Process Flow with Symbolic Elements ### Overview The image depicts a grid-based diagram divided into three labeled sections: **(a)**, **(b)**, and **(c)**. Arrows and dotted lines indicate directional relationships between components. Symbolic elements (a skull and crossbones on the left, a trophy on the right) are positioned at the top of vertical columns, suggesting a narrative or process flow. ### Components/Axes - **Grid Structure**: - The grid is divided into three vertical columns labeled **(a)**, **(b)**, and **(c)**. - **(a)**: A vertical column with a skull and crossbones symbol at the top. - **(b)**: A horizontal path connecting **(a)** to **(c)**, featuring a smaller square at its base. - **(c)**: A vertical column with a trophy symbol at the top. - **Arrows/Dotted Lines**: - Dashed arrows connect the skull symbol in **(a)** to the smaller square in **(b)**. - Dotted lines extend from the smaller square in **(b)** to the trophy in **(c)**. - **Symbols**: - **Skull and Crossbones**: Positioned at the top-left of the grid, aligned with column **(a)**. - **Trophy**: Positioned at the top-right of the grid, aligned with column **(c)**. ### Detailed Analysis - **Column (a)**: - Contains 6 stacked rectangular cells. - The skull and crossbones symbol is centered at the top of the column. - **Column (b)**: - Contains 3 horizontal cells forming a path. - A smaller square is centered at the base of the path. - **Column (c)**: - Contains 6 stacked rectangular cells. - The trophy symbol is centered at the top of the column. - **Directional Flow**: - The dashed arrows from **(a)** to **(b)** suggest a transition from the skull symbol to the smaller square. - The dotted lines from **(b)** to **(c)** imply progression from the smaller square to the trophy. ### Key Observations 1. **Symbolic Narrative**: The skull (risk/obstacle) in **(a)** transitions to the trophy (success) in **(c)** via the path in **(b)**. 2. **Path Complexity**: The smaller square in **(b)** may represent a critical decision point or checkpoint. 3. **No Numerical Data**: The diagram lacks quantitative values, legends, or axis markers. ### Interpretation The diagram likely represents a metaphorical process, such as a journey from danger (skull) to achievement (trophy), with intermediate steps requiring navigation through a defined path. The absence of numerical data suggests it is conceptual rather than statistical. The smaller square in **(b)** could symbolize a pivotal choice or barrier that must be overcome to reach the trophy. The use of dashed and dotted lines may indicate uncertainty or variability in the transition between stages. ## Notes - **Language**: All text is in English. - **Missing Elements**: No legend, numerical data, or axis titles are present. - **Spatial Relationships**: Symbols and arrows are aligned to emphasize hierarchical progression from left to right. </details> More formally, assume that the language model is deployed in a reinforcement learning setting like in reinforcement learning from human feedback (Ouyang et al., 2022) (states are prompts followed by the partial sequence of tokens x t :1 generated so far, actions are single tokens x t +1 to generate, rewards are external R ( x t :1 ) ). The quantity <!-- formula-not-decoded --> is the value of the state x t :1 following the policy π , while <!-- formula-not-decoded --> quantifies the importance of the decision x t +1 on the value thereafter. Choice points can formally be viewed as steps t for which σ π ( x t :1 ) is large, while inconsequential points are steps where it is low. Note that for completion models, there is no explicit reward, and our argument is merely meant to illustrate what we mean by choice points . Derailing denotes a situation where autoregressive generation of trajectories from M at inference time results in bad outcomes after M made a mistake on a choice point. Even if subsequently, M acts optimally given this choice, the final outcome can be significantly worse than the outcome of the optimal trajectory. Staying in the teacher-forced setting, we ask: What is the impact of training M with n -step prediction instead of nextstep prediction on this task? Say x t → x t +1 is a choice point in an optimal trajectory with the suboptimal choice being x t → ˜ x t +1 (Figure S17 (a)). Assume that the trajectories preceding x t and succeeding x t +1 and ˜ x t +1 consist of inconsequential transitions, the latter denoted by ˜ x t + j → ˜ x t + j +1 . We will compare the losses of a teacher-forced next-step prediction model and a teacher-forced n -step prediction model on the partial trajectory ( x t -n +1 , . . . x t ) . For the next-step prediction model, the predictions are ( x t -n +2 , . . . , x t , ˜ x t +1 ) with a single wrong prediction. The predictions of an n -step prediction model at time t -n + i , i = 1 , . . . , n are ( x t -n + i +1 , . . . , x t , ˜ x t +1 , . . . , ˜ x t + i ) with i wrong predictions. In other words, an n -step prediction model receives 1 + . . . + n = n ( n +1) 2 loss terms pertaining to such a choice point and its consequences, while each inconsequential transition (Figure S17 (b)) is only reinforced n times as often as in a next-step prediction model. In other words, choice points receive on average n +1 2 times more importance in the loss of n -step prediction models than in next-step prediction models. As argued in Section 5.1, we believe that this model captures important features of training and inference with language models: choice points are semantically important turning points in the generated texts, such as the final answer to a question or a specific line of code, while inconsequential decisions can be a choice among synonyms or of variable names in code. Apart from this training dynamics point of view, we hypothesize that n -step prediction also allows the formation of circuits that specifically spot inconsistencies between predictions for earlier and later steps. For instance, if in an early layer of the model, it can be predicted that a decision x t → ˜ x t +1 leads to suboptimal outcomes ˜ x t + n (Figure S17 (c)), subsequent layers can reduce the probability of x t → ˜ x t +1 in the model's next-step prediction. Such behaviors also happen in next-step prediction models given enough capacity, but our experiments in Section 4.2 point to the fact that circuits of this kind are formed more easily in multi-step architectures that enforce the required information ˜ x t + n to be available to the model when predicting ˜ x t +1 . We believe that this situation appears frequently in natural language and code modelling, for instance where an initial answer to a question contradicts the results of the chain of thought brought forward with the intention to justify it. In more general terms, this situation arises whenever predicting first ˜ x n + i for some 1 < i ≤ n and then ˜ x n +1 based on ˜ x n + i is easier than predicting ˜ x n +1 directly. We discuss this phenomenon of factorization orders in the next section and present a specific instance of it that frequently appears in modelling natural language. ## L.4. Factorization orders Causal language modelling factorizes probabilities over text sequences x t · · · x 1 classically as <!-- formula-not-decoded --> While moving forward in time is certainly the most natural choice of factorization order, there exist cases where it is suboptimal. In inflectional languages, for instance, agreement between related sentence parts is a frequent pattern with one word directing the grammatical forms of others. Consider the German sentence Wie konnten auch Worte meiner durstenden Seele genügen? 3 Friedrich Hölderlin, Fragment von Hyperion (1793) where "genügen" requires a dative case object and then "Seele" requires the possessive pronoun "mein" to be in female singular dative form "meiner" and the participle "durstend" to be in female singular dative form in weak declination "durstenden" because it follows "meiner". In other words, the factorization order Wie konnten auch Worte → genügen → Seele → meiner → durstenden? is arguably an easier one for constructing the above sentence. Humans as well as language models therefore have to perform this factorization (which deviates from the causal order in which predictions take place!) within their latent activations, and a 4 -token prediction loss makes this easier as it explicitly encourages models to have all information about the successive 4 tokens in its latent representations. 3 roughly: How could words be enough for my thirsty soul? ## M. Training hyperparameters Table S13: Overview of all training hyperparameters used. We schedule all learning rates with a linear warmup and cosine decay (Loshchilov and Hutter, 2017) to a fraction of the peak learning rate which is depicted in the last column ('decay ratio'). All experiments use the Adam (Kingma and Ba, 2015) optimizer with β 1 = 0 . 9 , β 2 = 0 . 95 and decoupled L 2 weight decay (Loshchilov and Hutter, 2019) coefficient 0 . 1 . We clip gradients to a maximal Euclidean norm of 1 . 0 in all experiments except CodeContests finetunings, where we use 0 . 1 instead. Summarization finetunings correspond to three epochs on all datasets except BigPatent (1 epoch). Byte-level models use the architecture with replicated unembeddings from Appendix B. | Model | Batch size ( 2 20 ) | Steps | Tokens (B) | Warmup steps | Peak LR | Context length | Decay ratio | |---------------------------------|-----------------------|---------|--------------|----------------|------------|------------------|---------------| | Model scaling (Section 3.1) | | | | | | | | | 0.3B | 8 | 10,850 | 91.0 | 1000 | 3 × 10 - 4 | 4096 | 0.03 | | 0.6B | 8 | 10,850 | 91.0 | 1000 | 3 × 10 - 4 | 4096 | 0.03 | | 1.3B | 8 | 10,850 | 91.0 | 1000 | 3 × 10 - 4 | 4096 | 0.03 | | 3B | 8 | 10,850 | 91.0 | 1000 | 3 × 10 - 4 | 4096 | 0.03 | | 7B | 8 | 25,000 | 209.7 | 2000 | 3 × 10 - 4 | 4096 | 0.03 | | 13B | 8 | 25,000 | 209.7 | 1000 | 3 × 10 - 4 | 4096 | 0.03 | | Code models (Section 3) | | | | | | | | | 7B 200B | 8 | 25,000 | 209.7 | 2000 | 3 × 10 - 4 | 4096 | 0.03 | | 7B 500B | 7 | 68,570 | 503.3 | 2000 | 3 × 10 - 4 | 4096 | 0.03 | | 7B 1T | 7 | 136,240 | 1000.0 | 2000 | 3 × 10 - 4 | 4096 | 0.03 | | Byte-level models (Section 3.3) | | | | | | | | | 7B 314GB | 12 | 25,000 | 314.6 | 2000 | 3 × 10 - 4 | 8192 | 0.03 | | Language models (Section 3.7) | | | | | | | | | 7B 200B | 8 | 25,000 | 209.7 | 2000 | 3 × 10 - 4 | 4096 | 0.10 | | 7B 500B | 8 | 60,000 | 503.3 | 2000 | 3 × 10 - 4 | 4096 | 0.10 | | Induction task (Section 4.1) | | | | | | | | | 1M - 1B | 0.25 | 100,000 | 26.2 | 2000 | 10 - 4 | 2048 | 0.03 | | 1M - 1B (Appendix J) | 0.5 | 50000 | 26.2 | 2000 | 10 - 4 | 2048 | 0.03 | | Arithmetic task (Section 4.2) | | | | | | | | | 30M | 0.25 | 100,000 | 26.2 | 2000 | 10 - 4 | 1024 | 0.03 | | 100M | 0.25 | 100,000 | 26.2 | 2000 | 10 - 4 | 2048 | 0.03 | | Summarization (Section 3.7) | | | | | | | | | BigPatent | 0.125 | 76,680 | 10.1 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | CNN/Dailymail | 0.125 | 7,140 | 0.9 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | Multi-News | 0.125 | 3,330 | 0.4 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | OrangeSum | 0.125 | 360 | 0.0 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | pn-summary | 0.125 | 3,450 | 0.5 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | SAMSum | 0.125 | 60 | 0.0 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | ThaiSum | 0.125 | 23,640 | 3.1 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | WikiSummary | 0.125 | 2,550 | 0.3 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | XSum | 0.125 | 2,760 | 0.4 | 100 | 3 × 10 - 5 | 4096 | 0.03 | | CodeContests (Section 3.6) | | | | | | | | | 7B | 0.25 | 13,000 | 3.6 | 400 | 5 × 10 - 5 | 4096 | 0.004 | Table S14: Overview of model architectures used for scaling analyses. | Name | Dimension | Layers | Heads | |-------------|-------------|----------|---------| | 1M | 128 | 5 | 4 | | 3M | 256 | 4 | 8 | | 10M | 384 | 6 | 8 | | 30M | 512 | 10 | 8 | | 100M | 768 | 14 | 12 | | 300M | 1024 | 25 | 16 | | 1B | 1536 | 36 | 24 | | 0.3B | 1024 | 18 | 16 | | 0.6B | 1280 | 27 | 20 | | 1.3B | 2048 | 24 | 16 | | 3B | 2560 | 36 | 20 | | 6.7B ('7B') | 4096 | 32 | 32 | | 13B | 5120 | 40 | 40 |