cs.LGApr 11, 2026
SaveTracing the Thought of a Grandmaster-level Chess-Playing Transformer
Organizations: Shanghai Innovation Institute, Shanghai, China · School of Computer Science, Fudan University, Shanghai, China · School of Mathematics and Statistics, Xi’an Jiaotong University.
Abstract
While modern transformer neural networks achieve grandmaster-level performance in chess and other reasoning tasks, their internal computation process remains largely opaque. Focusing on Leela Chess Zero (LC0), we introduce a sparse decomposition framework to interpret its internal computation by decomposing its MLP and attention modules with sparse replacement layers, which capture the primary computation process of LC0. We conduct a detailed case study showing that these pathways expose rich, interpretable tactical considerations that are empirically verifiable. We further introduce three quantitative metrics and show that LC0 exhibits parallel reasoning behavior consistent with the inductive bias of its policy head architecture. To the best of our knowledge, this is the first work to decompose the internal computation of a transformer on both MLP and attention modules for interpretability. Combining sparse replacement layers and causal interventions in LC0 provides a comprehensive understanding of advanced tactical reasoning, offering critical insights into the underlying mechanisms of superhuman systems. Our code is available at https://github.com/JacklE0niden/Leela-SAEs.
Figures & tables
Figure 1: An overview of our approach for interpreting LC0. We use Transcoders and Lorsas as replacement layers to sparsely decompose the model’s MLP and attention module, identifying interpretable reasoning pathways through feature-steering interventions. By analyzing sparse feature activations along these pathways, we reveal an interpretable computational process underlying the model’s decision-making for any input position.
Figure 2: Visualization interface for feature interpretability. Red squares indicate the spatial activations of specific features. For Lorsa features, each activated square is associated with a -pattern, highlighting its attentional focus (e.g., the black knight, marked in blue). Purple arrows connect each activated square to the target square to which its activation is highly attributed.
| Feature Type | Activation Consistency | Complexity |
| Transcoder | 4.15 | 2.25 |
| Lorsa | 3.73 | 2.54 |
| MLP | 2.05 | 1.45 |
Table 1: Interpretability assessment. Human evaluation scores (1–5 scale) by three player annotators (Elo 2100+, 2000+, and 1000+), measuring activation consistency and perceived complexity across different feature types.
| Feature ID | Interpretation | Verification Rule | Precision | Recall |
| Tc.0.5593 | [Det]Opp.Knight | Act. @ Opp.Knight | 100% | 100% |
| Tc.0.12663 | [Det]OwnPawn | Act. @ OwnPawn | 100% | 100% |
| Lorsa.0.13740 | [Det]Opp.Queen OwnQueen | Act. @ Opp.Queen OwnQueen | 98.5% | 100% |
| Tc.14.120 | [Src]Source square | Act. @ Top-1 predicted source | 88.0% | 1.7% |
| Tc.14.1214 | [Tgt]Target square | Act. @ Top-1 predicted target | 99.2% | 78.7% |
| Tc.14.8947 | [Val]High Value | Act. @ Every squares on chessboard positions predicted value | 89.9% | 41.6% |
Table 2: We present a categorized collection of interpretable Transcoder and Lorsa features, organized by coarse semantic function rather than architectural layer. Features categories are color-coded as follows: Detection Features([Det]) , Source/Target Square Features([Src]/[Tgt]) , Value Features([Val]) , Capture Features([Cap]) , Complex Tactic Features([Tac]) , Spatial Relation Features([Spa]) , Piece Movement Features([Mov]) . Each feature is validated using a manually designed rule, and precision and recall are computed over training dataset. Detailed explanations of the interpretation language and verification rules are provided in Appendix D . We cap the analysis of the 1000 activation times per feature in a random dataset and compute precision and recall based on these samples. Detailed explanations of the interpretation language and verification rules are provided in Appendix D , where we present an illustrative visualization with a single representative feature per category to convey the core semantic pattern in Appendix E . Bolded features indicate those used in the following case study. While some features exhibit lower recall due to feature splitting ( Chanin et al., 2025 ) —where descriptive rules are coarser than actual activations—consistently high precision, particularly for rare tactical patterns, demonstrates the validity of our interpretation.
Figure 3: A complete case study with illustration highlighting the key tactical structure discussed in this section. (A) Input position and extracted reasoning pathways. (B) Finding 1: Mechanistic validation of bishop-movement features that transfer bishop coverage information via targeted attention pattern masking. (C) Finding 2: Copying activation of Lorsa.0.7083 opponent’s rook coverage feature from g7 to h7 alters perceived rook defense and thus suppresses Qxh7+ . (D) Finding 3: The model’s detection of the g2 pawn triggers perceived defensive stability, reducing sensitivity to forced-win opportunities.
| Feature | Act. | Interpretation |
| Steered Feature | ||
| Lorsa.0.7083@h7 | +1x (copy from g7 ) | [Spa] Opponent Rook rank-wise defensive coverage |
| Downstream Features (affected by steering) | ||
| Lorsa.1.9198@h7 | Opponent knight blocks rook protection | |
| Lorsa.1.15014@h7 | Diagonal-assisted queen checking threats near opponent king | |
| Lorsa.1.16036@h7 | Multi-piece attack–defense around king-front pawns | |
Table 3: Causal effects of steering by injecting the opponent’s rook coverage feature Lorsa.0.7083 into h7 . After this intervention, the model perceives h7 as being defended by the black rook on f7 , which suppresses downstream features corresponding to related tactics.
| Move | Orig. | w/o g2 | w/o Tc.0.12663@14 |
| Qxh7+ | 2.04 / 28.8% | 3.59 / 91.7% | 3.53 / 90.6% |
| fxg7+ | 2.26 / 35.8% | -2.29 / 0.26% | -0.79 / 1.20% |
| Qxd7 | 1.95 / 26.1% | -1.42 / 0.61% | -2.24 / 0.28% |
Table 4: Top-3 move logit/probability distributions for the original position, the position without the g2 pawn, and the intervention that ablates Tc.0.12663@14 .
| Subset | All | Confident | Confused | Same- source | baseline |
| Mean path overlap | 7.05% | 1.63% | 8.39% | 13.7% | 0.17% |
Table 5: Path overlaps under different evaluation settings, with values close to zero, suggesting that different moves arise from largely disjoint significant features.
Figure 4: Mean Path Cohesion and Path Coupling between feature sets of top-2 moves across different chess positions in the dataset.
Figure 5: Detailed analysis of feature distributions. (a) Entropy distribution across layers, indicating concentration at specific squares. (b) Spatial layout of features on the board.
Appendix figures & tables15 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6: Overview of the BT4 architecture, featuring SmolGen-enhanced MHSA for modeling chessboard positional relations and an attention-based policy head.
| Puzzle set | Mate-in-1 | Mate-in-2 | Mate-in-3 | Mate-in-4 | Mate-in-5 | All |
| Accuracy | 0.996 | 0.970 | 0.890 | 0.776 | 0.707 | 0.932 |
Table 6: BT4 puzzle accuracy without search on Lichess mate puzzles of varying tactical depth. We sample 20,000 positions for each subset from mate-in-1 to mate-in-4, and 5,000 positions for mate-in-5 due to limited data availability.
Figure 7: Faithfulness of sparse replacement layers. We report the L2 norm error ratio (left) and the explained variance EV (right) of Transcoder and Lorsa modules across transformer layers on a randomly sampled dataset.
Figure 8: Representative feature examples by category: (1) Detection feature [Det] activating on squares occupied by an opponent knight; (2) Source square feature [Src] activating on the square from which the predicted move originates; (3) Value-based feature [Val] activating on high-value positions on the board; (4) Capture feature [Cap] activating on squares from which a piece can capture an opponent’s rook; (5) Tactical feature [Tac] activating in scenarios where our rook is lost due to a check; (6) Spatial-related feature [Spa] activating on squares reflecting board-wide spatial patterns, e.g., squares of the same color as the king; (7) Piece movement feature [Mov] activating on squares representing the movement or coverage area of a piece, here the eight squares surrounding the king.
Figure 9: Effect on policy probability and logit of steering factor on feature activations. (a) Ten random activated features at each steering factor and corresponding change of policy probability and logit. (b) Ten random significant features at each steering factor and corresponding change of policy probability and logit.
Figure 10: Pearson correlation distribution of steering sensitivity. (Left) The impact of randomly selected features on the top policy probability within the steering range. (Right) The distribution of Pearson correlation coefficients. We observe significant clustering in the ranges and , with comparable counts.
Figure 11: The correlation of between feature activation and whether the exchanging-queen is protected in 1000 activation times with the exchanging-queen. The activation value exhibits a Pearson correlation of 0.52.
| Lorsa.1.8260 | Lorsa.7.14502 | Lorsa.8.9586 | |
| Lorsa.1.8260 | 1.00 | 0.82 | 0.84 |
| Lorsa.7.14502 | 0.82 | 1.00 | 0.97 |
| Lorsa.8.9586 | 0.84 | 0.97 | 1.00 |
| Random baseline: | |||
Table 7: Cosine similarity matrix of decoder vectors for bishop-movement Lorsa features (after LC0 post-LayerNorm). High off-diagonal cosine similarities indicate a shared semantic direction across distributed layers.
Figure 12: samples with the highest activations of three bishop-move Lorsa features mentioned in Section 4 finding 1.
Figure 13: samples with the highest activations of features mentioned in Section 4 finding 2.
Figure 14: samples with the highest activations of features mentioned in Section 4 finding 3.
Figure 15: Reasoning pathway for a defensive decision. The model detects an early-layer threat from the opponent’s queen–rook coordination threatening at h7 , and consequently mobilizes a knight to block the mate-in-one threat. Key features involved in this defensive reasoning are visualized.
Figure 16: Reasoning pathway of a case where the model combines offensive and defensive reasoning. The figure shows the input chessboard position, the reasoning pathway supporting the selected policy Qc4+ , and the associated supernode interpretations. Two key features are visualized: Tc.1.12313 represents the awareness of opponent queen’s checkmate threats, and Lorsa.4.11791 exerting diagonal threats against the opposing king.
Figure 17: Reasoning pathway of look-ahead reasoning in a mate-in-two scenario. The reasoning pathway illustrates how the model integrates the immediate sacrifice move ( Ng6+ ) with the anticipation of a subsequent checkmate threat from the rook at h4 . Important correlated features with highly semantic interpretability are visualized below.
Figure 18: Reasoning pathway for a more complex position. BT4 correctly selects Ne5 with probability 42.7%. The pathway suggests that Ne5 opens the d-file for the rook on d1, creates mating pressure by enabling a future Qf7+ , and supports the development of Bg2 . After Ne5 , Bb7 no longer attacks the knight along the diagonal, and Black may respond with Qe7 .