Transformer Interpretability

We investigate how embedding dimension affects the emergence of an internal "world model" in a transformer trained with reinforcement learning to perform bubble-sort-style adjacent swaps. Models achieve high accuracy even with very small embedding dimensions, but larger dimensions yield more faithful, consistent, and robust internal representations. In particular, higher embedding dimensions strengthen the formation of structured internal representation and lead to better interpretability. After hundreds of experiments, we observe two consistent mechanisms: (1) the last row of the attention weight matrix monotonically encodes the global ordering of tokens; and (2) the selected transposition aligns with the largest adjacent difference of these encoded values. Our results provide quantitative evidence that transformers build structured internal world models and that model size improves representation quality in addition to end performance. We release our metrics and analyses, which can be used to probe similar algorithmic tasks.

Recent language models exhibit significant logical reasoning abilities, yet the mechanisms supporting deductive inference remain poorly understood. This paper studies small transformer-based language models trained from scratch on multi-step deductive tasks, focusing on the distinction between horizontal reasoning, where intermediate steps are generated autoregressively, and vertical reasoning, where inference unfolds implicitly across layers before the first output token is produced. We analyze two synthetic tasks: logical consequence over chains of symbolic implications and root-to-leaf navigation in binary trees. Mechanistic interpretability reveals that Chain-of-Thought supervision enables models to learn rule-based inference rather than statistical shortcuts. In the horizontal setting, a shallow attention-only model develops interpretable circuits for rule completion, rule chaining, and final decision making, largely implemented through induction-head-like mechanisms. We further introduce a truncated pseudoinverse method to decode the information carried by queries, keys, and values. For vertical reasoning, Chain-of-Thought appears to act less as explicit step-by-step guidance and more as a form of curriculum learning, helping the model acquire increasingly complex reasoning patterns. Without Chain-of-Thought, models tend to memorize or exploit dataset biases. These results provide a low-level account of how transformers can implement deductive reasoning and suggest how Chain-of-Thought may serve different functions in horizontal and vertical reasoning.

Large Language Models (LLMs) excel at multi-hop reasoning in distribution, yet fail on unseen compositions, a phenomenon known as the curse of two-hop reasoning. In this work, we argue that this phenomenon can be attributed to a missing supervision on the bridge entity. We formalize this gap by introducing identity bridge, a minimal supervision that enforces a identity mapping on bridge tokens. Under this supervision, even a one-layer transformer with uniform attention (Emb-MLP) can achieve out-of-distribution (OOD) two-hop generalization. We provide a theoretical analysis demonstrating that identity bridge induces an implicit regularization effect, leading the model to establish a direct subject-to-answer association. From an empirical perspective, the performance of standard GPT-2 models aligns closely with simple Emb--MLP models across varying levels of problem complexity. Finally, analyses of fine-tuned mainstream LLMs indicate that correct two-hop predictions consistently coincide with the establishment of a subject-to-answer relationship, extending our findings to realistic settings.

Cross-attention is a core mechanism in encoder-decoder architectures, widespread in many fields, including speech-to-text (S2T) processing. Its scores have been repurposed for various downstream applications--such as timestamp estimation and audio-text alignment--under the assumption that they reflect the dependencies between input speech representation and the generated text. While the explanatory nature of attention mechanisms has been widely debated in the broader NLP literature, this assumption remains largely unexplored within the speech domain. To address this gap, we assess the explanatory power of cross-attention in S2T models by comparing its scores to input saliency maps derived from feature attribution. Our analysis spans monolingual and multilingual, single-task and multi-task models at multiple scales, and shows that attention scores moderately to strongly align with saliency-based explanations, particularly when aggregated across heads and layers. However, it also shows that cross-attention captures only about 50% of the input relevance and, in the best case, only partially reflects how the decoder attends to the encoder's representations--accounting for just 52-75% of the saliency. These findings uncover fundamental limitations in interpreting cross-attention as an explanatory proxy, suggesting that it offers an informative yet incomplete view of the factors driving predictions in S2T models.

How do vision transformers (ViTs) represent and process the world? This paper addresses this long-standing question through the first systematic analysis of 6.6K features across all layers, extracted via sparse autoencoders, and by introducing the residual replacement model, which replaces ViT computations with interpretable features in the residual stream. Our analysis reveals not only a feature evolution from low-level patterns to high-level semantics, but also how ViTs encode curves and spatial positions through specialized feature types. The residual replacement model scalably produces a faithful yet parsimonious circuit for human-scale interpretability by significantly simplifying the original computations. As a result, this framework enables intuitive understanding of ViT mechanisms. Finally, we demonstrate the utility of our framework in debiasing spurious correlations.

Identifying which tokens and activations truly influence model predictions is critical for both the efficiency and interpretability of large auto-regressive language models. Yet in practice, token importance is typically inferred from attention distributions that entangle contextual relevance with softmax-normalization effects, obscuring relative influence across tokens and heads. We propose $\textbf{RCStat}$, a statistical framework for quantifying contextual influence in attention mechanisms. At its core $\textbf{Relative Contextualization (RC)}$ is a random variable that measures how strongly one subset of tokens contributes to another under the model's internal scoring scheme. RCStat admits computationally efficient bounds on expected influence that can be estimated at inference time. No retraining is required. We apply RCStat to two tasks. For $\textbf{attribution}$, attention heads with high expected RC accurately identify the prompt spans that drive generation, enabling reliable span-level explanations. For $\textbf{key-value cache eviction}$, RC-based adaptive thresholding selectively evicts low-impact KV entries, substantially reducing cache size while preserving generation quality. Across question answering, summarization, and attribution benchmarks, RCStat achieves consistent gains, improving generation quality by 15-40% with upto 36% error reduction for KV eviction, and attribution accuracy by 2-16%. These results demonstrate that explicitly modeling contextual influence provides a principled and practical alternative to attention-based heuristics.

Inference-time steering aims to alter a large language model's (LLM's) responses without changing its parameters, but a central challenge is identifying the internal modules that most strongly govern the target behavior. Existing approaches often rely on simplistic cues or ad hoc heuristics, leading to suboptimal or unintended effects. We introduce REAL, a framework for identifying behavior-relevant modules (attention heads or layers) in Transformer models. For each module, REAL trains a vector-quantized autoencoder (VQ-AE) on its hidden activations and uses a shared, learnable codebook to partition the latent space into behavior-relevant and behavior-irrelevant subspaces. REAL quantifies a module's behavioral relevance by how well its VQ-AE encodings discriminate behavior-aligned from behavior-violating responses via a binary classification metric; this score guides both module selection and steering strength. We evaluate REAL across eight LLMs from the Llama and Qwen families and nine datasets spanning truthfulness enhancement, open-domain QA under knowledge conflicts, and general alignment tasks. REAL enables more effective inference-time interventions, achieving an average relative improvement of 20% (up to 81.5%) over the ITI method on truthfulness steering. In addition, the modules selected by REAL exhibit strong zero-shot generalization in cross-domain truthfulness-steering scenarios.

We introduce methods to quantify how Large Language Models (LLMs) encode and store contextual information, revealing that tokens often seen as minor (e.g., determiners, punctuation) carry surprisingly high context. Notably, removing these tokens -- especially stopwords, articles, and commas -- consistently degrades performance on MMLU and BABILong-4k, even if removing only irrelevant tokens. Our analysis also shows a strong correlation between contextualization and linearity, where linearity measures how closely the transformation from one layer's embeddings to the next can be approximated by a single linear mapping. These findings underscore the hidden importance of filler tokens in maintaining context. For further exploration, we present LLM-Microscope, an open-source toolkit that assesses token-level nonlinearity, evaluates contextual memory, visualizes intermediate layer contributions (via an adapted Logit Lens), and measures the intrinsic dimensionality of representations. This toolkit illuminates how seemingly trivial tokens can be critical for long-range understanding.

Understanding the internal mechanisms of deep neural networks remains a central challenge in machine learning. In computer vision, one promising yet only preliminarily explored approach is feature inversion via inverse networks, which reconstructs images from intermediate representations using trained inverse networks. In this study, we revisit feature inversion via inverse networks, introducing a novel, modular variant that enables a computationally more efficient application of the technique while, in some cases, producing semantically more coherent image reconstructions. We apply our method to large-scale transformer-based vision models, specifically Detection Transformer, Vision Transformer, Swin Transformer, and Data-Efficient Image Transformer, analyzing the resulting reconstructions across network depth. Our main analysis compares Detection Transformer and Vision Transformer, which exhibit the most informative differences among the evaluated architectures. At the same time, results for Swin Transformer and Data-Efficient Image Transformer support the broader applicability of our framework. Our findings reveal gradual representational changes across transformer layers as a shared characteristic of Detection Transformer and Vision Transformer, as well as systematic differences in how they preserve contextual shape and fine-grained image details, and in their robustness to color perturbations. These findings deepen understanding of transformer-based vision models and demonstrate the utility of modular feature inversion as an interpretability tool.

Large-scale pretraining of transformers has been central to the success of foundation models. However, the scale of those models limits our understanding of the mechanisms at play during optimization. In this work, we study the training dynamics of transformers in a controlled and interpretable setting. On the sparse modular addition task, we demonstrate that specialized attention circuits, called clustering heads, can be implemented during gradient descent to solve the problem. Our experiments show that such pathways naturally emerge during training. By monitoring the evolution of tokens via a visual sandbox, we uncover a two-stage learning and the occurrences of loss spikes due to the high curvature of normalization layers. Our findings provide several insights into patterns observed in more practical settings, such as the pretraining of large language models.