#01Nov 5, 2026
cs.LG
Same Answer, Different Future: Matched Predictions Do Not Imply Matched Belief Updating in Language Models
Weihan Li, Junhao Wu, Xinlei Chen and 1 more
Language models can produce similar probabilistic predictions after observing outcomes, reading summaries, receiving instructions, or undergoing activation interventions. Whether these routes induce equivalent belief states remains unclear: agreement in current predictions does not establish how a model will respond to subsequent evidence. We investigate this distinction in a Bernoulli inference task with an analytic Bayesian reference. Across three open-weight language models, we prepare states through four textual routes and two activation-level interventions, measure both next-outcome continuations and explicit probabilistic estimates, and append identical new evidence from each prepared state. We quantify the persistence of the initial belief through its effective evidence weight, the number of new observations it is worth. We find that the format of evidence decides which readouts express its content: outcome sequences primarily affect continuations, whereas summaries and stated rates primarily affect explicit estimates. Moreover, effective weights differ substantially across routes, with summaries receiving weights that scale weakly with their stated observation counts and elicitation questions changing inferred weights by orders of magnitude. In a one-shot steering setting, an intervention that reproduces a natural record's immediate prediction loses most of its effect under subsequent evidence. These results show that agreement in current readouts is insufficient to establish equivalence in belief updating: how a belief is acquired and how it is read jointly determine its subsequent dynamics.
#02Nov 5, 2026
cs.AI
TCSExam: Evaluating Frontier LLMs on the Full Range of TCS Research
Yifan Luo, Zhengying Liu, Yang Yuan and 2 more
Can large language models (LLMs) advance theoretical computer science and resolve its long-standing open conjectures? To study progress toward this goal, we introduce TCSExam, a unified framework and benchmark covering the full range of TCS research. It evaluates theorem proving, solver engineering, and constructions alongside direct attempts to resolve open conjectures, capturing both concrete research accomplishments and progress toward long-standing research goals. TCSExam-Full contains 100 expert-reviewed tasks, with submissions checked by the Lean kernel or an executable task checker. TCSExam-Lite selects 20 tasks, five per track, reducing the number of task attempts by 80% at the same per-attempt budget. We evaluate eight agents on Full and nine on Lite. The TCSExam Index combines all four tracks: GPT-6 Astra leads Full (71.9), and Opus 5.5 leads Lite (72.3). Full and Lite rankings are strongly aligned across eight shared agents (Spearman's $ρ=0.93$), supporting Lite as a compact, discriminative benchmark. The evaluations yield improved solver outputs and mathematical constructions, together with independently verified special cases and bounds from open-conjecture attempts. TCSExam provides an extensible framework with task sources, Docker build recipes, and evaluation tools for reproducible use.
#03Nov 5, 2026
cs.AI
When Bigger Becomes Brittle: Why Compression Hurts More as Language Models Scale
Gautam Gupta, Dikshant Kukreja, Unique Kumar and 7 more
Quantization and pruning reduce the cost of deploying language models, but their effects are usually reported as benchmark scores. Such scores record only the loss that remains at the output. Inside the model, compression damages some components more than others, and the rest of the network can partly compensate. The observed loss therefore reflects both the damage and this compensation, which benchmark scores cannot separate. How the two combine, and whether their balance changes with model size, remains unclear. We study this compensation for in-context retrieval, a capability carried by a small, identifiable set of attention heads. To separate the two, the expected loss from ablating these heads is decomposed exactly into the part restored by the rest of the network, attributed to the components responsible, and the part that reaches the output. This decomposition is then compared across model sizes. For damage of comparable size, smaller models restore most of the loss, whereas larger models retain most of it, because the compensating responses offset less of it as models grow. Compressing the heads produces the same pattern. Compression that is nearly harmless in small models can therefore be costly in large ones.
#04Nov 5, 2026
cs.LG
Invariance before structure: two modes of emergent compression in representation learning
Hardik Rajpal, Dan Goodman
Learned representations show striking invariance across biological and artificial neural networks, with different substrates and variations driven by drift, heterogeneity and initialisation. To understand this invariance, we propose Emergent Adaptive Representation Learning (EARL), a framework that distinguishes two modes of emergence in learned representations: state-space compression, where a learned representation gains predictive power over its own future beyond what the network's units can predict individually, and parameter-space compression, where networks with different micro-level parameters converge to the same representation. We formalise both as Fisher sensitivities and introduce ensemble-level information-theoretic measures for each. In a recurrent reservoir with a trained bottleneck, parameter-space compression rises within the first few epochs of training and partly independently of the task, whereas state-space compression rises about 30 epochs later and only when the network begins to learn the temporal structure of the task. These results suggest that invariance to the substrate and task-specific emergent structure are acquired in distinct phases of learning.
#05Nov 5, 2026
cs.AI
Circe: Training-Free LLM Self-Evaluation via Component Interaction Consistency
Shuyi Miao, Zheng Li, Xu Xie and 4 more
As large language models (LLMs) are increasingly deployed in real-world applications, evaluating the correctness of their responses is crucial for reliable use. However, such evaluation is challenging because reference answers are rarely available in practice. Existing reference-free methods mainly rely on output signals, which may assign high scores to incorrect responses and thus do not necessarily reflect correctness. This motivates exploring the model's internal computation for complementary correctness signals. Recent studies exploit internal states, but they mainly analyze hidden-state trajectories across layers, which record only the combined updates of attention and feed-forward networks (FFNs) and overlook how these components interact. We therefore propose Circe, a training-free self-evaluation method that assesses a response using both internal and external signals, without reference answers or repeated sampling. For internal signals, we first introduce component interaction consistency (CIC), which measures the directional alignment between attention updates in earlier layers and attention-induced FFN output changes in later layers. We further incorporate representation geometry (RG) to characterize normalized displacement and angular changes along layerwise hidden-state trajectories. For the external signal, we convert the mean negative log-likelihood of generated tokens into a bounded likelihood confidence (LC) score. Finally, we fuse CIC, RG, and LC into a unified correctness score. Experiments on five LLMs and six benchmarks across four domains show that our method distinguishes correct from incorrect responses more effectively than existing baselines, and generalizes to multilingual, multimodal, and open-world settings.