| { |
| "task": { |
| "id": "llama3_8b_abc", |
| "name": "A+B+C arithmetic", |
| "summary": "Three-operand addition. The model receives a prompt of the form \"A + B + C = \"", |
| "model": "meta-llama/Meta-Llama-3-8B", |
| "examples": [ |
| {"prompt": "23 + 17 + 19 = ", "answer": "59"}, |
| {"prompt": "42 + 31 + 26 = ", "answer": "99"}, |
| {"prompt": "58 + 14 + 33 = ", "answer": "105"}, |
| {"prompt": "71 + 12 + 45 = ", "answer": "128"}, |
| {"prompt": "16 + 27 + 38 = ", "answer": "81"} |
| ] |
| }, |
| "components": [ |
| { |
| "id": "L15H3_ATTN", |
| "hook": "blocks.15.attn.hook_z", |
| "layer": 15, |
| "head": 3, |
| "role": { |
| "note": "Primary C-transfer head. At the final query position, this head selectively reads the third operand C and writes C-dependent information into the last-token residual stream. Its C edge is the load-bearing route. Corrupt-C patching moves the answer logits toward the C-corrupted answer, but this head alone does not fully overwrite the final prediction.", |
| "additional_note": "Last survivor of iterative head pruning over layers 15-16. Single-head ablation in isolation drops accuracy 1.000 -> 0.758. Paper Fig. 5 shows it attends from the last token to the third operand C, routing C's value into the residual at the '=' position." |
| } |
| }, |
| { |
| "id": "L15H13_ATTN", |
| "hook": "blocks.15.attn.hook_z", |
| "layer": 15, |
| "head": 13, |
| "role": { |
| "note": "Primary B-transfer head. At the final query position, this head selectively reads the second operand B and transfers B-dependent information into the last-token residual stream. Corrupt-B patching through this head strongly shifts the model toward the B-corrupted answer.", |
| "additional_note": "Operand-transfer head at Layer 15. Second-to-last survivor of iterative head pruning. Paper Fig. 5 states that this head attends from the last token to the second operand B." |
| } |
| }, |
| { |
| "id": "L15H31_ATTN", |
| "hook": "blocks.15.attn.hook_z", |
| "layer": 15, |
| "head": 31, |
| "role": { |
| "note": "Backup C-transfer head. In the full circuit this head is mostly redundant with L15H3, but when L15H3 is suppressed it becomes strongly load-bearing. Its functional route is last-token attention to the third operand C, providing an auxiliary C-transfer pathway.", |
| "additional_note": "Secondary transfer head at Layer 15. It is not catastrophic alone but in the critical tail. Paper Table. 4 lists it in the secondary AF1 transfer set." |
| } |
| }, |
| { |
| "id": "L16H1_ATTN", |
| "hook": "blocks.16.attn.hook_z", |
| "layer": 16, |
| "head": 1, |
| "role": { |
| "note": "Tertiary C-transfer backup head. This head carries C-related signal through its last-token attention to the third operand, but it becomes clearly load-bearing only after the stronger C-transfer routes L15H3 and L15H31 are suppressed. Its output is less cleanly helpful in the full circuit, suggesting a mixed or context-dependent C-support role.", |
| "additional_note": "Backup (Tertiary) C-Transfer head at Layer 16. Present in the localized attention heads list in the Paper Tab. 4." |
| } |
| }, |
| { |
| "id": "L16H21_ATTN", |
| "hook": "blocks.16.attn.hook_z", |
| "layer": 16, |
| "head": 21, |
| "role": { |
| "note": "Primary A-transfer head. At the final query position, this head selectively reads the first operand A and transfers A-dependent information into the last-token residual stream. Corrupt-A patching through this head almost completely redirects the model toward the A-corrupted answer.", |
| "additional_note": "A-Operand transfer head at L=16. Paper Fig. 5 states that it attends from the last token to the first operand A; the model effectively cannot solve A+B+C without it." |
| } |
| }, |
| { |
| "id": "L20_MLP", |
| "hook": "blocks.20.hook_mlp_out", |
| "layer": 20, |
| "head": null, |
| "role": { |
| "note": "L20 MLP writes a latent arithmetic feature that depends on all operands. Its last-token output is useful for the arithmetic task and depends on the operands, but it does not directly write the final answer or a clean intermediate such as A+B/B+C. Downstream layers appear to use this latent feature to form the final answer direction.", |
| "additional_note": "L20 is the retained representative of the graded L17-L21 causal MLP block. Direct zero-ablation drops acc 1.0 to 0.737. Corrupt-operand patching gives balanced flip rates across A/B/C (0.253/0.242/0.273) with corrupt-answer logit gains +2.03/+2.20/+2.31, showing that the output carries operand-dependent task signal without isolating a specific arithmetic operation (i.e. it does not do any intermediate A+B or A+C or B+C type calculation). L20 is better described as a latent feature-builder." |
| } |
| }, |
| { |
| "id": "L29_MLP", |
| "hook": "blocks.29.hook_mlp_out", |
| "layer": 29, |
| "head": null, |
| "role": { |
| "note": "L29 MLP's output points toward the correct answer in projection tests, but is not needed by itself in the full circuit. Directly removing or mean ablating L29 MLP does not reduce accuracy, so its answer-related signal is best described as redundant with other computation.", |
| "additional_note": "L29 is retained as a disagreement case between attribution methods. Evidence for answer-related output: candidate-target logit lens has answer top-5 = 0.394 while pair-sum and operand targets stay near zero; Evidence against isolated necessity: direct zero-ablation leaves accuracy unchanged." |
| } |
| }, |
| { |
| "id": "L31_MLP", |
| "hook": "blocks.31.hook_mlp_out", |
| "layer": 31, |
| "head": null, |
| "role": { |
| "note": "L31 MLP's output strongly points toward the correct answer in projection tests, but this projection is not answer-specific. The true answer gets a high logit, but operands and pair sums also receive high mean logits. Directly removing or mean ablating L31 barely changes accuracy, so its signal is redundant in the full circuit.", |
| "additional_note": "L31 is retained as the clearest lens-positive but causally redundant MLP. It has the strongest single-MLP answer lens signal (answer top-5 = 0.566), at the same time, isolated direct zero-ablation barely changes accuracy, and corrupt-operand patching produces zero flips for A/B/C. Its high mean logits for answer, pair sums, and individual operands suggest broad final-logit amplification rather than a clean arithmetic operation." |
| } |
| }, |
| { |
| "id": "L26H3_ATTN", |
| "hook": "blocks.26.attn.hook_z", |
| "layer": 26, |
| "head": 3, |
| "role": { |
| "note": "L26H3 attention head's output points toward the correct answer in projection tests, but its attention mostly goes to the <BOS> token rather than the operand tokens. Removing this head does not reduce accuracy, so this answer-related signal is not needed by itself in the full circuit.", |
| "additional_note": "L26H3 is a paper-named BOS-attention-sink case. Evidence for answer-related output: per-head logit lens ranks it 2/480 over layers 17-31, with top-1 = 0.162 and top-3 = 0.394. Evidence that it is not reading operands: at the last query position, attention mass is BOS = 0.587 and operand sum A+B+C = 0.027. Evidence against isolated necessity: when L26H3 and the other high-lens late attention heads are zeroed cumulatively, accuracy remains 1.0, including after L26H3 is removed. This matches the paper's Sec. 4.5 and Appendix A.4 claim that these answer-predicting heads show a BOS-sink pattern rather than an interpretable operand-reading pattern." |
| } |
| }, |
| { |
| "id": "L28H18_ATTN", |
| "hook": "blocks.28.attn.hook_z", |
| "layer": 28, |
| "head": 18, |
| "role": { |
| "note": "L28H18 attention head's output is the strongest late-attention projection toward the correct answer, but its attention is mostly on <BOS> and positional tokens rather than operands. Removing it does not reduce accuracy, so this answer-related signal is not needed by itself in the full circuit.", |
| "additional_note": "L28H18 is the strongest paper-named late-attention lens hit. Evidence for answer-related output: per-head logit lens ranks it 1/480 over layers 17-31. Evidence that it is not primarily reading operands: at the last query position, attention mass is BOS = 0.445 and operand sum A+B+C = 0.102. The remaining non-BOS mass is concentrated more on positional anchors such as '=' than on operands. Evidence against isolated necessity: when L28H18 and the other high-lens late attention heads are zeroed cumulatively, accuracy remains 1.0, including after L28H18 is removed. This matches the paper's Sec. 4.5 and Appendix A.4 claim that these answer-predicting heads show a BOS-sink pattern rather than an interpretable operand-reading pattern." |
| } |
| } |
| ] |
| } |
|
|
