#01Oct 22, 2026
cs.LG
When to Follow the Teacher: Advantage-Based On-Policy Distillation
Mahdi Sabbaghi, George Pappas, Hamed Hassani and 1 more
Online Policy Distillation (OPD) often outperforms offline methods such as Supervised Fine-Tuning (SFT) by training on trajectories sampled directly from the student. However, standard OPD trains the student to follow the teacher at every state of the trajectory, assuming that teacher guidance is always beneficial. We instead distinguish between what the teacher prefers and what actually helps the current student succeed. We introduce Advantage-Based On-Policy Distillation (AOPD), which weights teacher actions by their counterfactual advantage under the student. Teacher actions that improve the student's expected outcome are reinforced, while those that do not are downweighted. Directly computing these advantages requires trying alternative teacher actions at each step and running new rollouts from each. Instead, we show that the AOPD objective can be estimated using only standard student rollouts and their terminal rewards. Our estimator uses teacher importance weights on the student-sampled actions to provide unbiased advantage-weighted supervision, without any additional rollouts or reward evaluations. This allows AOPD to focus teacher supervision on actions that help the current student while preserving the rollout efficiency of standard OPD. Experiments on math, coding, and Medqa show gains over distillation and RL baselines in both external-teacher and self-distillation settings.
#02Oct 22, 2026
cs.LG
A Fix for Softmax and Cross-Entropy
Jonathan T. Barron, Dan Gnanapragasam, Michael Tschannen
Standard implementations of softmax, log-softmax, and cross-entropy have two numerical bugs. The first bug, Softmax Collapse, rounds the target logit's gradient to zero if that one logit is much larger than the others, resulting in gradients that no longer sum to zero. The second bug, Softmax Cancellation, occurs when student logits are close to teacher logits, and produces non-zero gradients even when the student and teacher logits are equal. We present simple implementations of log-softmax, softmax, and cross-entropy that fix both bugs. Our fix eliminates the previously-observed "Slingshot" phenomenon, speeds up grokking with weight decay, prevents accuracy collapse without weight decay, stops student networks from drifting away from the teacher during distillation, and shows that after memorization, logit growth is bounded by an equilibrium between weight decay and Adam's $ε$ hyperparameter.
#03Oct 22, 2026
cs.LG
BeNice! Closing Looping's Inference-Memory Gap via KV-Sharing
Hayden Prairie, Jacob M. Ryan, Taylor Berg-Kirkpatrick and 1 more
Looped architectures scale quality while keeping parameter count fixed by repeatedly passing activations through the same block of layers. During inference, each recurrence generates independent KV-caches, causing memory to grow linearly. To address this challenge, prior work has proposed KV-sharing (i.e., sharing KV-caches across depth), finding that, in some cases, the KV-cache of the final recurrence can be shared with the earlier recurrences without quality loss, a property we denote as KV-shareability. However, the mechanisms underlying KV-shareability remain poorly understood, with even identically trained looped architectures not consistently exhibiting it. In this paper, we study how KV-shareability can be enabled in looped models. We propose a two-stage method: in the first stage, we use stochastic depth during pretraining, which induces contractive residual dynamics that drive representations toward a common limit across recurrences. In the second stage, we propose BeNice!, a post-training method that broadcasts the final recurrence's KV-cache into the first recurrence, training it to produce compatible residuals while preserving the original model's quality. As a result, BeNice! enables KV-shareability while matching standard finetuning's unshared validation perplexity. Using BeNice!, we show that KV-sharing is complementary to alternative KV-compression methods, composing with memory-efficient sequence mixers (e.g., multi-latent attention, Kimi delta attention) and low-precision KV-cache quantization (e.g., fp8, mxfp8, nvfp4). Finally, in simulated low-memory, long-context inference, KV-sharing improves cache hit rates by up to 31.4%, increases throughput by up to 23.6%, and reduces p90 time-to-first-token by up to 83.6%.
#04Oct 22, 2026
cs.CV
Sensorimotor Alignment: A Platonic Proxy for Embodied Policy Success
Yunfei Xie, Howard H. Qian, Shiyi Lan and 2 more
Robotic foundation models are typically evaluated through costly closed-loop rollouts, which motivates cheap offline proxies for model capability. The Platonic Representation Hypothesis (PRH) suggests that as representations improve, different modalities such as vision and language converge toward a shared statistical model of reality. We ask whether motion trajectories form another such modality: as embodied models become more capable, should their sensory representations converge toward the structure of physical motion? To examine this, we propose Sensorimotor Alignment ($S^2$), a training-free offline metric that measures how well a model's sensory representation aligns with the geometry of physical motion. We find that $S^2$ correlates positively with downstream robot task success across embodied model families, making it a low-cost offline proxy for prioritizing models before closed-loop evaluation. $S^2$ can also identify promising vision-language model (VLM) backbones even before costly fine-tuning into vision-language-action models (VLAs). Beyond this correlation, $S^2$ offers representation-level explanations for phenomena observed in VLAs and world action models (WAMs). With $S^2$, we extend PRH to embodied models and make sensorimotor alignment empirically measurable, offering insight into why an embodied model succeeds beyond its closed-loop success rate.
#05Oct 22, 2026
cs.LG
Questioning Instrumental Convergence in RLVR: Checkpoint Evidence from OLMo-3
Barış Alparslan, Sandy Tanwisuth, Caleb Petterson
Instrumental convergence is often invoked as a general reason to expect capable agents to acquire or express power-seeking subgoals: self-preservation, resource acquisition, deception, or resistance to oversight which poses an important threat to the society. For LLMs, reinforcement learning is the first stage of post-training that directly optimizes behavior against an objective; therefore, it is the stage where convergent instrumental behavior, on IC grounds, likely to appear. Does reinforcement learning with verifiable rewards (RLVR) make a model more likely to express instrumental-convergence behavior, or does this depend on the training regime, evaluation frame, and stage of post-training? We study this question as a checkpoint-conditioned behavioral trajectory rather than as a single before/after safety score. Using InstrumentalEval, we evaluate OLMo-3-7B-Think across SFT, DPO, 13 intermediate RLVR checkpoints, and the final RLVR model. The trajectory is nonmonotonic: instrumental rate rises from 25.0% at SFT to 46.1% near RLVR step 200, then falls to 11.8% at the final checkpoint. Paired item-level tests and step-wise regression support the final SFT-to-RLVR reduction. Prompt framing does not explain this pattern: a harmful-prompt indicator combined with other framing effects explains only 15% of within-checkpoint score variance on average, and Iterative Null-space Projection (INLP) removes a detectable framing direction without changing the SFT-to-final-RLVR gap. Together with preliminary 32B endpoint results (35.53% SFT to 22.37% RLVR final), these findings indicate that RLVR does not monotonically increase instrumental behavior in this setting: the rate rises early, then falls below the SFT baseline. The result is specific to this model family and benchmark, and judge agreement is moderate, so absolute rates should be read cautiously.