For eachstimulus,ourextractedcomputational mechanisms areconsistent withprior scientific literature, and in one case yields a new mechanistic hypothesis.

More than twenty years after its introduction, Annealed Importance Sampling (AIS) remains oneofthemost effectivemethods formarginal likelihood estimation.

Trained models are often composed with post-hoc transforms such as temperature scaling (TS), ensembling and stochastic weight averaging (SWA) to improve performance, robustness, uncertainty estimation, etc. However, such transforms are typically applied only after the base models have already been finalized by standard means. In this paper, we challenge this practice with an extensive empirical study. In particular, we demonstrate a phenomenon that we call post-hoc reversal, where performance trends are reversed after applying post-hoc transforms. This phenomenon is especially prominent in high-noise settings.

In this paper, we present two algorithms of this type and prove that both are consistent under the faithfulness assumption.

Large language models exhibit exciting capabilities, yet can show surprisingly narrow generalization from finetuning. E.g. they can fail to generalize to simple reversals of relations they are trained on, or fail to make simple logical deductions based on trained information. These failures to generalize factual information from fine-tuning can significantly hinder the reasoning capabilities of these models. On the other hand, language models' in-context learning (ICL) shows different inductive biases and deductive reasoning capabilities. Here, we explore these differences in generalization and deductive reasoning between in-context- and fine-tuning-based learning. To do so, we constructed several novel datasets to evaluate and improve models' abilities to make generalizations over factual information from novel data. These datasets are designed to create clean tests of generalization, by isolating the knowledge in the dataset from that in pretraining. We expose pretrained large models to controlled subsets of the information in these datasets -- either through ICL or fine-tuning -- and evaluate their performance on test sets that require various types of generalization. We find overall that in data-matched settings, ICL can generalize several types of inferences more flexibly than fine-tuning (though we also find some qualifications of prior findings, such as cases when fine-tuning can generalize to reversals embedded in a larger structure of knowledge). We build on these findings to propose a method to enable improved generalization from fine-tuning: adding in-context reasoning traces to finetuning data. We show that this method improves generalization across various splits of our datasets and other benchmarks. Our results have implications for understanding the generalization afforded by different modes of learning in language models, and practically improving their performance.

Small Language Models (SLMs) are increasingly being deployed in resource-constrained environments, yet their behavioral robustness to data contamination during instruction tuning remains poorly understood. We systematically investigate the contamination sensitivity of 23 SLMs (270M to 4B parameters) across multiple model families by measuring susceptibility to syntactic and semantic transformation types during instruction tuning: syntactic transformations (character and word reversal) and semantic transformations (irrelevant and counterfactual responses), each applied at contamination levels of 25\%, 50\%, 75\%, and 100\%. Our results reveal fundamental asymmetries in vulnerability patterns: syntactic transformations cause catastrophic performance degradation, with character reversal producing near-complete failure across all models regardless of size or family, while semantic transformations demonstrate distinct threshold behaviors and greater resilience in core linguistic capabilities. Critically, we discover a ``\textit{capability curse}" where larger, more capable models become more susceptible to learning semantic corruptions, effectively following harmful instructions more readily, while our analysis of base versus instruction-tuned variants reveals that alignment provides inconsistent robustness benefits, sometimes even reducing resilience. Our work establishes three core contributions: (1) empirical evidence of SLMs' disproportionate vulnerability to syntactic pattern contamination, (2) identification of asymmetric sensitivity patterns between syntactic and semantic transformations, and (3) systematic evaluation protocols for contamination robustness assessment. These findings have immediate deployment implications, suggesting that current robustness assumptions may not hold for smaller models and highlighting the need for contamination-aware training protocols.

We show that \emph{Sorting by Strip Swaps} (SbSS) is NP-hard by a polynomial reduction of \emph{Block Sorting}. The key idea is a local gadget, a \emph{cage}, that replaces every decreasing adjacency $(a_i,a_{i+1})$ by a guarded triple $a_i,m_i,a_{i+1}$ enclosed by guards $L_i,U_i$, so the only decreasing adjacencies are the two inside the cage. Small \emph{hinge} gadgets couple adjacent cages that share an element and enforce that a strip swap that removes exactly two adjacencies corresponds bijectively to a block move that removes exactly one decreasing adjacency in the source permutation. This yields a clean equivalence between exact SbSS schedules and perfect block schedules, establishing NP-hardness.

We formalize a structural property of the causal (autoregressive) language modeling (CLM) objective: reversal invariance. Formally, the next-token prediction loss assigns identical likelihood to a corpus and its reversal, implying that standard CLM pretraining is direction-blind. This symmetry explains why models trained on reversed text can achieve comparable performance to those trained on forward text, despite the inherently time-asymmetric nature of human language and reasoning. We argue that this invariance represents a limitation of current pretraining objectives rather than a benign artifact. If natural language encodes directional dependencies - phonological, morphological, or causal - a symmetric objective may fail to capture them. We therefore propose viewing pretraining through the lens of temporal asymmetry, motivating future work on loss functions and architectures that explicitly model the arrow of language while retaining standard language modeling capacity.