NeurIPS 2026 Papers

Knowledge distillation (KD) has become a widely adopted approach for compressing large language models (LLMs). Existing distillation paradigms for LLMs can be broadly categorized into black-box and white-box approaches. Black-box methods typically transfer the chains of thought (CoTs) generated by teacher models to student models, yet they fail to convey the intrinsic knowledge embedded within teacher models. White-box methods aim to alleviate this limitation by leveraging internal representations from teacher models. However, they still face two major challenges. First, it is difficult to identify which knowledge is essential for distillation in student models. Second, it is challenging to transfer this key knowledge from teacher models accurately. To tackle these challenges, we propose KPD, a novel Knowledge Probing-based white-box Distillation framework for LLMs, which is designed to precisely distill the knowledge that the student model lacks and can be incorporated into diverse distillation approaches. Specifically, to identify critical knowledge gaps in student models, we introduce an uncertainty-based probing method that extracts tokens prone to student errors as critical knowledge. To locate the corresponding knowledge in the teacher model, we utilize cumulative gradient calculation to probe where such knowledge is stored and then distill the target layers. Extensive experiments across multiple datasets demonstrate that KPD boosts traditional distillation methods by 0.34%-4.56% in Rouge-L scores. Further ablations show that probing both the student and teacher yields more precise distillation. Our code is available at https://anonymous.4open.science/r/KPD-CA0D.

Deep learning has driven substantial progress in modeling fMRI responses, yet most existing approaches are optimized for a single objective---such as neural encoding, stimulus decoding, or post hoc interpretation---making it difficult to obtain a coherent account of neural representations. We introduce a unified framework that connects vision foundation models to brain activity while supporting neural analysis from multiple complementary perspectives. Our approach replaces black-box features with a sparse, interpretable representation composed of visual prototypes, and links these prototypes to voxel responses through a linear readout. This design makes the model transparent at both levels: prototype activations expose the visual concepts present in the stimulus, while the learned linear weights characterize each voxel's selectivity. Using this interface, we identify which visual concepts drive neural responses and where they appear in the image, reveal cortical organization through voxel tuning in prototype space, and perform controlled stimulus synthesis to probe cortical selectivity through targeted interventions. Together, these results establish prototype-based representations as a unified and interpretable foundation for studying visual representations in the human brain.

Large language models (LLMs) increasingly solve difficult problems by producing reasoning traces before emitting a final response. However, it remains unclear how accuracy and decision commitment evolve along a reasoning trajectory, and whether intermediate trace segments provide answer-relevant information beyond generic length or stylistic effects. Here, we propose a trajectory-probing protocol for evaluating how a reasoning model's predicted answer evolves along a partial reasoning trace. The protocol 1) generates a model's full reasoning trace, 2) truncates it at fixed token-percentiles, and 3) injects each partial trace back into the model, measuring the model's induced answer distribution. We apply the protocol to five open-source reasoning models (Qwen3-4B/-8B/-14B and gpt-oss-20b/-120b) across three benchmarks (GPQA Diamond, MMLU-Pro, and Omni-MATH-2). The protocol reveals that accuracy and decision commitment consistently increase as the percentage of provided reasoning tokens grows, and length, form, and token-identity controls confirm that gains stem from instance-specific semantic content rather than context length or generic reasoning style effects. Furthermore, weak-to-strong cross-model probing experiments reveal when stronger models recover from incorrect partial traces and when they instead anchor to them. Together, these results provide a reproducible, model-agnostic measurement of reasoning-trace dynamics that generalizes across answer formats and can reveal model-specific failure modes invisible to aggregate accuracy.

Learning to generalise from limited data is a fundamental challenge for both artificial and biological systems. A common strategy is to extract reusable structure from abundant unlabelled data, enabling efficient adaptation to new tasks from limited labelled data. This two-stage paradigm is now standard in modern training pipelines, where pretraining is followed by fine-tuning or linear probing. We provide an analytical model of this process: structure extraction is formalized as principal component analysis on unlabelled data, and downstream learning as linear regression on a separate labelled dataset. In the high-dimensional regime, we derive exact expressions for training and generalisation error showcasing their dependence on representation dimensionality, unlabelled and labelled sample sizes, and task alignment. Our results show that pretrained representations strongly influence downstream generalisation, and we characterize the optimal representation size as a function of task parameters: with abundant pretraining data but scarce downstream data, maximally compressed representations are optimal, whereas with limited pretraining data, higher-dimensional representations generalise better. Furthermore, we establish an exact trade-off between pretraining and supervision, quantifying how much unlabelled data is required to replace a single labelled sample. Beyond our idealised model, we observe similar phenomenology in autoencoders and pretrained LLMs. Altogether, we highlight that optimising representation size is critical, giving conditions for when compression during pretraining improves generalisation.

The linear representation hypothesis (LRH) holds that high-level concepts are encoded as linear directions in a model's feature space, and grounds much of mechanistic interpretability, from probing to sparse autoencoders to steering vectors. We argue the standard test for it is too lenient. A high linear-probe accuracy shows that a concept is linearly readable from the representation, not that it is one of the representation's privileged directions of variance, which is what the LRH actually claims. These two readings come apart in any high-dimensional, richly structured representation, and the gap matters. The structure that linear probing ignores is precisely where compositional generalization, out-of-distribution behavior, and the validity of post-hoc feature decomposition live. We propose three asymmetric diagnostics that operationalize the strong reading: reverse predictivity, spectral concentration, and out-of-distribution generalization. We validate them in a fully observed simulation where ground truth is known, then apply them to pretrained vision encoders on SVG-World, our deterministic generative benchmark with paired visual styles. Pretraining produces structure beyond what a forward probe can certify, but the linear-feature reading systematically overstates how much. Probing on its own is not enough to license the mechanistic claims that rest on it.