Hessian-Enhanced Token Attribution (HETA): Interpreting Autoregressive LLMs

Large Language Models (LLMs) are increasingly deployed across diverse applications, raising critical questions for governance, accountability, and data provenance. Understanding which training data most influenced a model's output remains a fundamental open problem. We address this challenge through training data attribution (TDA) for auto-regressive LLMs by expanding upon the inverse formulation: How would training data be affected if the model had seen the generated output during training? Our method perturbs the base model using bidirectional gradient optimization (gradient ascent and descent) on a generated text sample and measures the resulting change in loss across training samples. Our framework supports attribution at arbitrary data granularity, enabling both factual and stylistic attribution. We evaluate our method against baselines on pretrained models with known datasets, and show that it outperforms previous work on influence metrics, thereby enhancing model interpretability, an essential requirement for accountable AI systems.

Feature attribution methods promise to identify which input features matter for a model output. In generative language models, however, it is often unclear what should count as a feature in the first place. In autoregressive language models, earlier generated tokens are both outputs of the model and inputs to later predictions. In diffusion language models, generation proceeds through iterative denoising or unmasking rather than fixed left-to-right prediction, so local explanation may target a state of diffusion rather than a next token. We argue that this ambiguity is not merely an implementation detail, but a conceptual limitation of carrying classifier-era feature attribution directly into generative language modeling. We introduce the Attribution Contract, a specification for feature-attribution claims that names what output is being explained, which features are eligible to receive attribution, what generative process is assumed, what is held fixed, and what model score is being attributed. The contract clarifies why the same attribution method can answer different questions depending on how it is instantiated. We argue that many disagreements about feature attribution in generative language models are not disagreements about attribution algorithms, but about unstated explanatory contracts. Using autoregressive and diffusion language models as case studies, we show when attribution to earlier generated tokens, intermediate states, or denoising stages is informative, when it is misleading, and why feature-attribution methods in generative language models should be evaluated as method-contract pairs.

The generative nature of Large Language Models (LLMs) is reflected in the conditional probabilities they compute to sample each response token given the previous tokens. These probabilities encode the distributional structure that the model learns in training and exploits in inference. In this work, we use these probabilities to situate LLMs within the mathematical theory of stochastic processes. We use this framework to design a model-agnostic probabilistic token attribution measure, using Bayes rule to invert the next-token log-probabilities so as to capture the models internal representation of the distribution over token sequences. The representation is independent of the models computational structure. This representation yields the conditional probability of the response given the prompt, and of the response given the prompt with a token marginalized away. Our attribution score is the log of the ratio of these probabilities. We further compute the entropies of a single prompts token distributions, conditioned on the remaining context. The interplay between entropy and attribution score sheds light on LLM behavior. We evaluate 8 models across 7 prompts and investigate anomalies, token sensitivity, response stability, model stability, and training convergence, thereby improving interpretability and guiding users to focus on uncertain or unstable parts of the generation.