## Heatmap: Layer Activation ### Overview The image is a heatmap visualizing layer activation for a sequence of tokens. The x-axis represents the tokens in a sentence, and the y-axis represents the layer number. The color intensity indicates the activation level, ranging from dark brown (low activation) to light yellow (high activation). ### Components/Axes * **X-axis:** Represents the tokens in the sentence: "A and B = 8 + 5 = 13 \n boxed { 13 } \n\nThus the correct choice is ( D ) 13 . The final answer is $\boxed { ( D ) }<return/>". * **Y-axis:** Labeled "i-th Layer", ranging from 1 to 35 in increments of 2. * **Color Legend:** Located on the right side of the heatmap, ranging from 0.0 (dark brown) to 1.0 (light yellow) in increments of 0.2. ### Detailed Analysis or ### Content Details The heatmap shows the activation levels for each layer in response to each token. * **Layers 1-17:** These layers show consistently high activation (dark brown) across all tokens. * **Layers 19-35:** These layers show varying activation levels depending on the token. Here's a breakdown of activation patterns for specific tokens: * **"A"**: Activation increases from layer 19 to 27, then decreases. * **"and"**: Activation increases from layer 19 to 29, then decreases. * **"B"**: Activation increases from layer 19 to 33, then decreases. * **"="**: Activation increases from layer 19 to 27, then decreases. * **"8"**: Activation increases from layer 19 to 29, then decreases. * **"+"**: Activation increases from layer 19 to 33, then decreases. * **"5"**: Activation increases from layer 19 to 31, then decreases. * **"="**: Activation increases from layer 19 to 27, then decreases. * **"13"**: Activation increases from layer 19 to 23, then decreases. * **"\n boxed"**: Activation increases from layer 19 to 23, then decreases. * **"{"**: Activation increases from layer 19 to 25, then decreases. * **"13"**: Activation increases from layer 19 to 21, then decreases. * **"}"**: Activation increases from layer 19 to 23, then decreases. * **"\n\nThus"**: Activation increases from layer 19 to 23, then decreases. * **"the"**: Activation increases from layer 19 to 27, then decreases. * **"correct"**: Activation increases from layer 19 to 31, then decreases. * **"choice"**: Activation increases from layer 19 to 29, then decreases. * **"is"**: Activation increases from layer 19 to 23, then decreases. * **"("**: Activation increases from layer 19 to 25, then decreases. * **"D"**: Activation increases from layer 19 to 33, then decreases. * **")"**: Activation increases from layer 19 to 27, then decreases. * **"13"**: Activation increases from layer 19 to 21, then decreases. * **"."**: Activation increases from layer 19 to 23, then decreases. * **"The"**: Activation increases from layer 19 to 27, then decreases. * **"final"**: Activation increases from layer 19 to 31, then decreases. * **"answer"**: Activation increases from layer 19 to 29, then decreases. * **"is"**: Activation increases from layer 19 to 23, then decreases. * **"$\boxed"**: Activation increases from layer 19 to 35, then decreases. * **"{"**: Activation increases from layer 19 to 31, then decreases. * **"("**: Activation increases from layer 19 to 27, then decreases. * **"D"**: Activation increases from layer 19 to 31, then decreases. * **")"**: Activation increases from layer 19 to 29, then decreases. * **"}"**: Activation increases from layer 19 to 27, then decreases. * **"<return/>"**: Activation increases from layer 19 to 31, then decreases. ### Key Observations * Lower layers (1-17) have consistently high activation across all tokens. * Higher layers (19-35) show more differentiated activation patterns based on the specific token. * The tokens "$\boxed" and "B" show the highest activation in the higher layers. ### Interpretation The heatmap visualizes how different layers of a neural network respond to different tokens in a sentence. The lower layers seem to capture general features present in all tokens, while the higher layers are more sensitive to the specific meaning and context of each token. The high activation for "$\boxed" in the higher layers suggests that these layers are particularly important for processing the boxed answer. The high activation for "B" may indicate its importance as a variable in the equation.