Mechanistic Interpretability of Chain-of-Thought Reasoning via Sequential Activation Patching
Organizations: Department of Computer Engineering Izmir Institute of Technology Izmir, Türkiye
Abstract
Large Language Models (LLMs) demonstrate remarkable problem-solving capabilities when guided by Chain-of-Thought (CoT) prompting, yet the internal mechanisms underlying these improvements remain poorly understood. In this work, we investigate where CoT-related causal effects emerge across the generated reasoning trajectory and which attention heads carry signals that contribute to final-answer computation. Because CoT reasoning unfolds over multiple generated tokens, standard activation patching at a single static token position is insufficient to characterize these temporally distributed effects. To address this limitation, we introduce a sequential activation patching framework that traces CoT-conditioned attention-head activations across token positions and aggregates their effects using Part-of-Speech-guided analysis. We further introduce Sequential Multi-Head Patching to evaluate the joint contribution of distributed head sets, together with cross-question and random activation controls. Targeted zero-ablation experiments show that the identified heads are functionally important for successful answer generation and affect several overlapping mechanisms, including reasoning-trajectory maintenance, answer anchoring, exemplar-target separation, and numerical generation. Overall, our results provide evidence for distributed reasoning-support sub-circuits associated with CoT-conditioned computation.
Figures & tables
| Experiment | Metric | Equation Prompt | No-CoT Prompt | CoT Prompt |
| Accuracy | Accuracy | Accuracy | ||
| Normal Run | N/A | 34.38% | 31.25% | 65.63% |
| Sequential Multi-Head Patching | JSD | 9.38% | 12.50% | 0.00% |
| MRR | 9.38% | 9.38% | 6.25% | |
| Sequential Multi-Head Cross Patching | JSD | 6.25% | 6.25% | 9.38% |
| MRR | 18.75% | 12.50% | 6.25% |
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
| ID | Type | Eq | Stat | Logit (No Pat.) | Prob (No Pat.) | JSD | ||
| chal-961 | Addition | 1 | 23.61 | 28.68 | 36.2% | 97.8% | 0.0072 | |
| Heads: L16H13[NNP], L16H10[CD], L13H12[:], L13H0[NNP], L14H5[VBZ], L14H10[JJ], L12H13[VBZ], L14H13[.], L16H8[.], L14H1[NN], L13H4[NN], L12H0[JJ], L15H1[NNS], L13H7[PRP$] | ||||||||
| chal-569 | Addition | 1 | 21.87 | 22.13 | 27.7% | 21.9% | 0.4047 | |
| Heads: L10H7[:], L13H12[.], L8H7[:], L14H5[IN], L10H6[NN], L14H8[NN], L8H3[VBD], L10H12[JJ], L16H10[TO], L14H4[JJ], L9H2[.], L14H2[CD], L10H3[CD], L13H10[NNS], L9H1[IN], L10H9[IN], L13H13[CC], L13H4[DT], L13H1[DT], L12H4[VBZ], L14H10[VBZ], L11H5[VBZ] | ||||||||
| chal-290 | Addition | 1 | 22.23 | 22.82 | 28.2% | 40.6% | 0.2662 | |
| Heads: L13H12[VBD], L20H10[IN], L15H13[:], L14H10[RB], L14H7[CD], L20H12[.], L14H13[.], L14H5[NNS], L13H13[DT], L12H12[TO], L12H6[,], L17H8[VBZ] | ||||||||
| T-ID | S-ID | T-Stat | S-Stat | Logit (No Pat.) | Prob (No Pat.) | JSD | ||
| chal-961 | chal-674 | 23.61 | 22.07 | 36.2% | 27.1% | 0.3626 | ||
| Cross-Heads: L12H0[CD], L14H5[.], L15H1[:], L14H10[MD], L14H8[DT], L12H12[VBP], L14H13[.], L14H1[NNS], L13H1[,], L8H3[VBZ] | ||||||||
| chal-569 | chal-514 | 21.87 | 23.26 | 27.7% | 55.2% | 0.1864 | ||
| Cross-Heads: L14H5[.], L10H7[:], L13H12[CD], L11H3[NN], L14H8[NN], L14H10[VBZ], L13H4[DT], L13H6[CD], L15H1[NNS], L8H3[IN], L13H1[DT] | ||||||||
| chal-290 | chal-33 | 22.23 | 22.73 | 28.2% | 52.3% | 0.1993 | ||
| Cross-Heads: L13H12[.], L15H8[:], L20H10[NNS], L14H10[.], L14H13[.], L14H1[CD], L12H0[CD], L15H10[NNS], L20H12[IN], L13H1[IN], L14H7[DT], L22H7[VBZ] | ||||||||
| ID | Type | Eq | Stat | Logit (No Pat.) | Prob (No Pat.) | MRR | ||
| chal-961 | Addition | 1 | 23.61 | 19.38 | 36.2% | 0.3% | -0.6122 | |
| Heads: L16H13[NNP], L16H10[CD], L13H12[:], L13H1[NNP], L13H0[NNP], L14H5[VBZ], L14H10[CD], L12H13[VBZ], L16H8[.], L14H13[.], L13H4[NN], L14H1[NN], L12H0[JJ], L15H1[NNS], L13H7[PRP$] | ||||||||
| chal-569 | Addition | 1 | 21.87 | 21.07 | 27.7% | 6.7% | -0.3062 | |
| Heads: L10H7[:], L13H12[NN], L16H10[NNS], L14H5[CC], L14H8[NN], L8H3[VBD], L10H12[JJ], L8H5[JJ], L9H2[.], L10H3[CD], L9H1[CD], L10H9[IN], L13H13[CC], L13H4[DT], L13H10[DT], L14H10[VBZ] | ||||||||
| chal-290 | Addition | 1 | 22.23 | 24.18 | 28.2% | 52.3% | -0.0281 | |
| Heads: L14H10[NN], L13H8[:], L22H7[:], L13H12[VBD], L8H3[EX], L12H12[TO], L20H12[.], L14H7[CD], L15H10[NNS], L15H3[NNP], L13H4[RB], L12H6[,], L14H12[VBZ], L14H13[VBZ], L20H10[VBZ] | ||||||||
| T-ID | S-ID | T-Stat | S-Stat | Logit (No Pat.) | Prob (No Pat.) | MRR | ||
| chal-961 | chal-674 | 23.61 | 21.54 | 36.2% | 14.6% | -0.0750 | ||
| Cross-Heads: L12H0[CD], L14H5[.], L12H12[VBP], L14H10[MD], L14H8[IN], L14H13[.], L14H1[NNS], L13H1[,], L8H3[VBZ] | ||||||||
| chal-569 | chal-290 | 21.87 | 22.71 | 27.7% | 4.6% | -0.3640 | ||
| Cross-Heads: L10H7[:], L13H12[IN], L14H8[TO], L13H10[NN], L15H1[NNP], L9H1[NN], L13H4[.], L16H8[CD], L14H10[CD], L13H7[NNP], L14H5[NNS], L10H12[JJ], L10H9[TO], L10H13[VBZ] | ||||||||
| chal-290 | chal-622 | 22.23 | 23.30 | 28.2% | 35.5% | -0.0634 | ||
| Cross-Heads: L14H10[:], L13H12[.], L15H10[CD], L15H3[CD], L20H12[VBD], L20H10[.], L13H11[VBD], L15H1[NN], L14H7[NNS], L12H0[VBN], L15H7[,], L12H6[PRP], L14H12[VBZ] | ||||||||
| ID | Type | Eq | Stat | Logit (No Pat.) | Prob (No Pat.) | JSD | ||
| chal-961 | Addition | 1 | 23.61 | 21.52 | 36.2% | 27.1% | 0.3626 | |
| Random Heads: L12H5[RAND], L14H5[RAND], L13H4[RAND], L15H10[RAND], L12H9[RAND], L3H4[RAND], L13H1[RAND], L10H9[RAND], L2H9[RAND], L12H4[RAND], L12H13[RAND], L11H11[RAND], L10H6[RAND], L9H2[RAND] | ||||||||
| chal-569 | Addition | 1 | 21.87 | 22.13 | 27.7% | 18.8% | 0.4319 | |
| Random Heads: L14H1[RAND], L10H9[RAND], L15H6[RAND], L10H0[RAND], L10H5[RAND], L8H1[RAND], L4H12[RAND], L9H8[RAND], L1H11[RAND], L10H11[RAND], L8H12[RAND], L10H13[RAND], L15H1[RAND], L4H13[RAND], L14H8[RAND], L9H0[RAND], L10H10[RAND], L13H1[RAND], L3H10[RAND], L10H7[RAND], L10H12[RAND], L9H3[RAND] | ||||||||
| chal-290 | Addition | 1 | 22.23 | 29.10 | 28.2% | 38.2% | 0.2812 | |
| Random Heads: L23H1[RAND], L12H13[RAND], L12H4[RAND], L15H1[RAND], L18H2[RAND], L13H13[RAND], L20H9[RAND], L14H8[RAND], L13H1[RAND], L19H2[RAND], L12H7[RAND], L15H8[RAND] | ||||||||
| ID | Type | Eq | Stat | Logit (No Pat.) | Prob (No Pat.) | MRR | ||
| chal-961 | Addition | 1 | 23.61 | 21.43 | 36.2% | 3.3% | -0.3336 | |
| Random Heads: L14H5[RAND], L16H8[RAND], L14H2[RAND], L11H0[RAND], L4H9[RAND], L10H5[RAND], L10H9[RAND], L16H10[RAND], L14H12[RAND], L10H4[RAND], L8H3[RAND], L8H6[RAND], L13H8[RAND], L14H1[RAND], L16H4[RAND] | ||||||||
| chal-569 | Addition | 1 | 21.87 | 21.63 | 27.7% | 25.9% | -0.0214 | |
| Random Heads: L13H12[RAND], L14H5[RAND], L10H5[RAND], L9H10[RAND], L7H8[RAND], L9H6[RAND], L15H7[RAND], L10H8[RAND], L7H13[RAND], L16H10[RAND], L10H12[RAND], L11H10[RAND], L9H2[RAND], L7H2[RAND], L7H3[RAND], L14H12[RAND] | ||||||||
| chal-290 | Addition | 1 | 22.23 | 25.89 | 28.2% | 47.7% | 0.0461 | |
| Random Heads: L15H10[RAND], L15H6[RAND], L20H9[RAND], L14H3[RAND], L14H10[RAND], L14H2[RAND], L12H13[RAND], L13H13[RAND], L12H0[RAND], L12H12[RAND], L1H5[RAND], L13H12[RAND], L17H3[RAND], L12H1[RAND], L12H6[RAND] | ||||||||
| Selection A | Selection B | Head Jaccard (%) | Head Min-Overlap (%) | Mean Common Heads | Layer Jaccard (%) | Layer Min-Overlap (%) |
| Seq. Multi-Head (JSD) | Seq. Multi-Head (MRR) | 56.4 | 78.7 | 8.75 | 69.9 | 91.0 |
| Cross Multi-Head (MRR) | Seq. Multi-Head (MRR) | 44.2 | 68.0 | 7.16 | 66.9 | 89.1 |
| Cross Multi-Head (JSD) | Cross Multi-Head (MRR) | 41.4 | 64.6 | 6.22 | 64.4 | 87.4 |
| Cross Multi-Head (JSD) | Seq. Multi-Head (JSD) | 41.1 | 66.2 | 6.62 | 62.8 | 85.1 |
| Cross Multi-Head (JSD) | Seq. Multi-Head (MRR) | 37.4 | 63.1 | 6.28 | 59.5 | 86.1 |
| Cross Multi-Head (MRR) | Seq. Multi-Head (JSD) | 34.6 | 56.8 | 5.91 | 60.7 | 83.9 |
| Selection family | Mean | Median | Range | Unique heads | Unique layers | Most frequent heads | Most frequent layers |
| Seq. Multi-Head (JSD) | 12.16 | 12.0 | 7–22 | 94 | 23 | L14H10 (21/32), L22H7 (16/32), L10H6 (15/32) | L14 (104), L16 (55), L13 (54), L12 (34), L15 (31) |
| Seq. Multi-Head (MRR) | 12.44 | 12.5 | 7–20 | 99 | 22 | L14H10 (23/32), L16H7 (16/32), L14H13 (16/32) | L14 (100), L16 (61), L13 (54), L15 (35), L12 (34) |
| Cross Multi-Head (JSD) | 11.16 | 11.0 | 5–19 | 90 | 21 | L14H10 (26/32), L13H3 (18/32), L10H6 (15/32) | L14 (94), L13 (58), L16 (45), L15 (41), L12 (30) |
| Cross Multi-Head (MRR) | 11.41 | 11.0 | 6–20 | 89 | 19 | L14H10 (24/32), L13H3 (20/32), L12H0 (16/32) | L14 (110), L16 (53), L13 (51), L12 (36), L15 (36) |
| Random-Activation Multi-Head (JSD) | 12.16 | 12.0 | 7–22 | 175 | 23 | L12H5 (8/32), L13H1 (8/32), L13H3 (7/32) | L14 (56), L12 (48), L13 (47), L10 (32), L15 (29) |
| Random-Activation Multi-Head (MRR) | 12.44 | 12.5 | 7–20 | 186 | 23 | L13H3 (7/32), L14H12 (7/32), L15H7 (7/32) | L14 (55), L13 (42), L15 (33), L12 (31), L16 (30) |
| Selection family | Early L0–L7 | Middle L8–L15 | Late L16–L23 | Dominant band | Most frequent layers |
| Seq. Multi-Head (JSD) | 18 (4.6%) | 274 (70.4%) | 97 (24.9%) | Middle | L14 (104), L16 (55), L13 (54), L12 (34), L15 (31), L10 (25) |
| Seq. Multi-Head (MRR) | 15 (3.8%) | 281 (70.6%) | 102 (25.6%) | Middle | L14 (100), L16 (61), L13 (54), L15 (35), L12 (34), L10 (28) |
| Cross Multi-Head (JSD) | 12 (3.4%) | 268 (75.1%) | 77 (21.6%) | Middle | L14 (94), L13 (58), L16 (45), L15 (41), L12 (30), L10 (23) |
| Cross Multi-Head (MRR) | 8 (2.2%) | 277 (75.9%) | 80 (21.9%) | Middle | L14 (110), L16 (53), L13 (51), L12 (36), L15 (36), L10 (22) |
| Random-Activation Multi-Head (JSD) | 87 (22.4%) | 250 (64.3%) | 52 (13.4%) | Middle | L14 (56), L12 (48), L13 (47), L10 (32), L15 (29), L16 (26) |
| Random-Activation Multi-Head (MRR) | 100 (25.1%) | 238 (59.8%) | 60 (15.1%) | Middle | L14 (55), L13 (42), L15 (33), L12 (31), L16 (30), L10 (26) |
| Finding | Example | Question / Prompt | Original Run | Selected-Head Ablation (JSD) | Random-Head Ablation |
| CoT final-anchor / termination failure | chal-906 | Exemplar: Q: John has 24 cookies. He wants to divide them equally among 6 friends. How many cookies will each friend get? A: John has 24 cookies and divides them equally among 6 friends. 24 / 6 = 4. The answer is 4. Target: Q: Jesse’s room is 2 feet long and 12 feet wide. If each tile is of size 4 square feet, how many tiles does she need to cover the whole floor? A: | Jesse’s room is 2 feet long and 12 feet wide. The total area of the room is 2 * 12 = 24 square feet. Each tile is of size 4 square feet. The number of tiles needed to cover the whole floor is 24 / 4 = 6 tiles. The answer is 6. | Jesse’s room is 2 feet long and 12 feet wide. 2 * 12 = 12 feet. 2 feet * 12 feet = 24 feet. 2 feet * 12 feet = 24 feet. 2 feet * 12 feet = 24 feet. … | Jesse’s room is 2 feet long and 12 feet wide. The total area of the room is 2 * 12 = 24 square feet. Each tile is of size 4 square feet. The number of tiles needed to cover the whole floor is 24 / 4 = 6 tiles. The answer is 6. |
| Few-shot exemplar contamination | chal-829 | Exemplar: Q: John has 24 cookies. He wants to divide them equally among 6 friends. How many cookies will each friend get? A: John has 24 cookies and divides them equally among 6 friends. 24 / 6 = 4. The answer is 4. Target: Q: For the walls of the house he would use 11 nails in all to secure large planks of wood. If each plank needs 3 pieces of nails to be secured and an additional 8 nails were used, how many planks does John need for the house wall? A: | John needs 11 - 8 = 3 nails for the house wall. He needs 3 / 3 = 1 plank. The answer is 1. | John has 24 planks of wood. He wants to divide them equally among 6 friends. If each plank needs 3 pieces of nails to be secured and an additional 8 nails were used, how many planks does John need for the house wall? A: John has 24 planks of wood. He wants to divide them equally among 6 friends. How many planks does John need for the house wall? A: … | John needs 11 nails to secure the large planks of wood. Each plank needs 3 nails to be secured and an additional 8 nails were used. John needs 4 planks for the house wall. The answer is 4. |
| Reasoning-state / arithmetic trajectory corruption | chal-674 | Exemplar: Q: Emily reads 15 pages of a book every day. How many pages will she read in 8 days? A: Emily reads 15 pages every day. In 8 days, 15 * 8 = 120. The answer is 120. Target: Q: The Ferris wheel in paradise park has 18 seats. Each seat can hold 15 people. If 10 seats are broken, how many people can ride the Ferris wheel at the same time? A: | There are 18 - 10 = 8 seats that are not broken. So, 8 x 15 = 120 people can ride the Ferris wheel at the same time. The answer is 120. | The Ferris wheel has 18 - 10 = 5 broken seats. There are 18 - 5 = 15 regular seats. 18 / 15 = 2 / 1. The answer is 2. | There are 18 - 10 = 8 seats that are still open. So, 8 x 15 = 120 people can ride the Ferris wheel at the same time. The answer is 120. |
| Finding | Example | Question / Prompt | Original Run | Selected-Head Ablation (JSD) | Random-Head Ablation |
| No-CoT exemplar-answer copying | chal-569 | Exemplar: Q: Every day Ryan spends 5 hours on learning Chinese and some more hours on learning English. If he spends 2 hours more on learning English than on learning Chinese, how many hours does he spend on learning English? A: The answer is 7.0. Target: Q: Rachel had to complete 9 pages of math homework, 11 pages of reading homework and 29 more pages of biology homework. How many pages of math and reading homework did she have to complete? A: The answer is | 20.0 | 7.0 | 20.0 |
| No-CoT salient operand copying | chal-821 | Exemplar: Q: Last week Fred had 33 dollars and Jason had 95 dollars. Over the weekend Fred delivered newspapers earning 16 dollars and washed cars earning 74 dollars. How much money did Fred earn over the weekend? A: The answer is 90.0. Target: Q: Paul had some books. After selling 137 in a garage sale he had 105 left. How many books did he have at the start? A: The answer is | 242.0 | 105.0 | 10.0 |
| Direct-equation operand copying | chal-163 | Equation-only prompt: 28.0 - 15.0 = | 28.0 - 15.0 = 13.0 | 28.0 - 15.0 = 28.0 | 28.0 - 15.0 = 13.0 |
| Direct-equation numeric-generation corruption | chal-196 | Equation-only prompt: 4.0 * 7.0 = | 4.0 * 7.0 = 28.0 | 4.0 * 7.0 = 1980.00000000000000000000 | 4.0 * 7.0 = 28.0 |
LLM Interpretability
Large language model (LLM) interpretability studies how internal representations and computations produce outputs, and how they can be explained or controlled.
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