Knowledge Distillation During Mid-Training Favors Reasoning over Factual Recall

Logit-based knowledge distillation (KD) is used to train smaller language models (LMs) via supervision from stronger teachers, but whether its benefits are consistent across training stages remains unclear. Through controlled experiments, we find that forward Kullback-Leibler (KL) distillation--the standard KD formulation--with post-trained teachers behaves fundamentally differently during mid-training, an intermediate phase of self-supervised learning on curated corpora. Surprisingly, while forward KD simultaneously improves reasoning and factual recall during pre-training relative to standard next-token prediction (NTP), it instead slows factual recall acquisition during mid-training despite continued reasoning gains. We trace this stage dependence to an asymmetry in teacher confidence across data domains and the student's evolving knowledge state: teachers are more confident on procedural than knowledge-intensive data, while students acquire low-entropy factual knowledge earlier in training. To mitigate this imbalance, we propose Switch Distillation, a simple mid-training objective that distills on tokens where the teacher is confident, using teacher predictive entropy as a lightweight routing signal, and otherwise falls back to cross-entropy. Switch Distillation consistently outperforms existing distillation objectives across teacher sizes. Relative to standard NTP, it achieves 1.61-1.71x the reasoning performance and 1.13-1.19x the knowledge and commonsense performance while preserving 96.7-96.8% of factual recall. Crucially, these benefits persist after post-training: Switch Distillation closes the factual recall gap while maintaining 1.25-1.32x and 1.13-1.20x gains in reasoning and knowledge and commonsense, respectively.

Knowing but Not Saying: Preventing Factual Access Failures in LLM SFT via Recall-Anchored Distillation

Supervised fine-tuning (SFT) can degrade factual behavior outside the target domain. This degradation is often described as catastrophic forgetting, yet open-ended factual failures do not necessarily imply that the underlying facts have been erased. In this work, we identify a more specific phenomenon, factual access failure: after domain SFT, models can still recognize or rank the correct answer under constrained evaluation, while failing to produce it in closed-book generation. Through benchmark-level comparisons, same-fact multiple-choice and generation probes, and failure-mode analysis, we show that SFT-induced factual degradation reflects both genuine wrong-answer generations and expression-level failures such as verbosity, formatting mismatch, and exact-match artifacts. To address this problem, we introduce Recall-Anchored Distillation (RAD), a base-anchored self-distillation objective that preserves out-of-distribution generation behavior by aligning the adapted model with the original base model's soft continuation distribution on unlabeled OOD text. RAD requires no gold OOD answers, external judges, or labeled factual data. Across three backbones fine-tuned on MedMCQA, RAD recovers a consistent portion of the lost OOD recall while preserving target-domain adaptation. Compared with replay on the same OOD text, RAD shows that the key preservation signal is the base model's soft distribution rather than additional text exposure alone.

Cross-Lingual Exploration for Parametric Knowledge

Parametric knowledge in Large Language Models is not equally accessible across languages. As a result, standard inference techniques often struggle to surface localized facts, leading to failures in cross-lingual knowledge transfer and consistency. In this work, we investigate techniques for accessing hidden factual knowledge by exploring cross-lingual prompting strategies. We identify four inherent dimensions of cross-lingual exploration that directly govern parametric knowledge retrieval and evaluate them on multilingual factual benchmarks covering 17 typologically diverse languages. Our results demonstrate that cross-lingual exploration significantly improves knowledge transfer and factual recall, representing a more efficient compute Pareto frontier than native-language scaling. Furthermore, we observe corresponding improvements in cross-lingual consistency, exceeding what can be explained by accuracy gains alone. Overall, our work establishes multilingual prompt exploration as a highly effective inference-time strategy for unlocking latent parametric knowledge.

Beyond Importance: Interchange-Sobol Sensitivity Reveals Task-Specific Content Channels in Transformer Components

Mechanistic interpretability methods summarize a transformer component by a single importance score, conflating two distinct roles: a component may matter because it transports task-relevant content, or because the forward computation degrades when its contribution is removed. We introduce \emph{Interchange-Group Sobol Decomposition} (IGSD), a paired-intervention framework that compares matched activation replacement with zero ablation on the same component, estimates two Sobol-style variance indices, and uses their signed difference to separate the two roles, with intervention validity monitored by a symmetric off-manifold diagnostic $\widehat{\mathrm{ST}}>1$. In factual recall, IGSD identifies an early-layer content channel in both GPT-2 small and Qwen2.5-1.5B that standard importance methods underestimate. A controlled subject and relation donor design shows that the early channel transports relation-frame content while late attention transports subject-retrieval content, refining at head granularity to the known $\mathrm{Attn}_{L9H8}$ head. Late-layer clamping confirms that the early signal is expressed through downstream transformations rather than residual pass-through. These results show that replacement and deletion are not interchangeable controls and their divergence provides a practical statistical diagnostic for content transport in transformer components.

PolyFact: Comparing Consistency-Driven Post-training Methods for Cross-Lingual Factual Recall

Large language models (LLMs) trained predominantly on English data encode substantial world knowledge, yet often fail to express it reliably in other languages, a phenomenon known as cross-lingual factual inconsistency. To study this, we introduce PolyFact, a fully parallel multilingual factual QA dataset of 60K Wikidata-grounded facts across 12 typologically diverse languages, and propose consistency-driven GRPO with cross-lingual reward pooling. We compare our method against supervised fine-tuning (SFT) and the consistency-enhancement baselines DCO and CM-Align on OLMo-2-1124-7B and Qwen-2.5-7B, and analyze whether light continual pretraining (CPT) on parallel data provides a useful foundation for post-training. No single method dominates: SFT maximises in-distribution accuracy but not consistency, DCO yields the strongest consistency gains but fails to transfer to free-form generation, and our GRPO variant achieves the strongest transfer to free-form recall and unseen languages on the multilingual base model. CPT mildly aids monolingual models but harms multilingual ones. Mechanistic analyses suggest that GRPO is associated with reduced language specialization, consistent with greater sharing of representations across languages. We release our code, models, and dataset publicly.

Expert-Aware Causal Tracing of Factual Recall in Sparse MoE Language Models

Activation patching can identify a mixture-of-experts (MoE) block whose clean output restores a corrupted factual prediction. However, because the block output combines contributions from multiple routed experts, block-level rescue does not establish whether the recovery localizes to an individual expert or depends on the routed expert set. We study this question on single-token COUNTERFACT contrasts by corrupting subject-token embeddings, restoring clean block outputs, and then restoring clean-minus-noised expert updates under fixed routing. In Qwen3-30B-A3B-Base, a discovery sweep selects layer 44, and held-out analysis identifies L44E069 as a recurrent routed contributor with positive specificity over same-layer active experts. Its effect is fact-matched and improves true-token probability and rank, which explains part of the layer rescue. In Mixtral-8x7B-v0.1, the selected recurrent singleton is not specific; matched-size controls instead show specificity of the clean-routed top-2 set. These findings show that successful MoE-block restoration does not necessarily imply localization to a single expert.