Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.14022

OPMD: On-Policy Mechanism Distillation Beyond Output Supervision

Yingdong Shi·Zhihong Li·Changming Li·Jingyi Yu·Quan Li·Kan Ren
View original source ↗Read source document ↗Export metadata ↓

Abstract

On-policy distillation (OPD) improves language-model by supervising a student on prefixes sampled from its own policy, but its supervision remains confined to the output space. Consequently, OPD transfers what a teacher predicts without supervising the intermediate computation that produces those predictions. Simply distilling intermediate representations like representation matching is insufficient since teacher and student representations may differ geometrically, and even well-aligned hidden states need not be usable by the student's subsequent computation. We introduce On-Policy Mechanism Distillation (OPMD), which transfers teacher-derived intermediate computation while explicitly accounting for its compatibility with the student. OPMD first constructs a student-compatible teacher that transforms teacher representations into intermediate states usable by the student's downstream computation, then it internalizes these states from on-policy trajectories. OPMD achieves the highest average accuracy among the evaluated distillation baselines in all three teacher--student settings, and generalizes to multi-teacher distillation and cross-family supervised fine-tuning. Further analyses show that mechanism supervision yields more effective reasoning and meaningfully alters the student's intermediate computation and solution strategies, supporting that it transfers information beyond output supervision alone. Together, these results establish mechanism-level supervision as an effective way to move on-policy distillation beyond output supervision, enabling students to learn inner mechanisms they can use and internalize.

Explore related subjects

cs.LGcs.AI

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yingdong Shi, Zhihong Li, Changming Li, Jingyi Yu, Quan Li, Kan Ren. 2026-09-29. OPMD: On-Policy Mechanism Distillation Beyond Output Supervision. https://arxiv.org/abs/2610.14022

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Subspace Node Pruning

Node pruning is the art of removing computational units such as neurons, filters, attention heads, or even entire layers to significantly reduce inference time while retaining network performance. In this work, we show that a broad family of importance measures, from activation-based to Fisher-based, share a common quadratic form. Through a lower-triangular change of basis, this form yields a pruning subspace in which entire nodes can be removed while the impact of the lost units is simultaneously recovered via linear least squares. Furthermore, the importance measures within our subspace are decoupled and additive through an orthogonalization of the layer activations, allowing multi-node pruning within layers without interference between importance scores. Our method, Subspace Node Pruning (SNP), outperforms the compared baselines on VGG-16 and ResNet-50 on ImageNet. On OPT-125M and LLaMA-2 7B, SNP matches the state-of-the-art LLM Surgeon at a 40-shot schedule and outperforms it whenever fewer shots are used, all without any retraining after pruning.

cs.LG↗
arXiv2026

On the growth of the parameters of approximating ReLU neural networks

This work focuses on the analysis of fully connected feed forward ReLU neural networks as they approximate a given, smooth function. In contrast to conventionally studied universal approximation properties under increasing architectures, e.g., in terms of width or depth of the networks, we are concerned with the asymptotic growth of the parameters of approximating networks. Such results are of interest, e.g., for error analysis or consistency results for neural network training. The main result of our work is that, for a ReLU architecture with state of the art approximation error, the realizing parameters grow at most polynomially. The obtained rate with respect to a normalized network size is compared to existing results and is shown to be superior in most cases, in particular for high dimensional input.

cs.LG↗
arXiv2026

Correlations Are Ruining Your Gradient Descent

Natural gradient descent, and the preconditioned optimizers which have followed from it, correct gradient descent by estimating curvature and applying its inverse to the gradient. For any single layer of a deep neural network, this correction can be shown to approximately separate into two factors: one which accounts for correlations in the gradient signal, and one which accounts for correlations in the data arriving at that layer. Herein we show that this second factor can be expressed as a change of basis rather than of curvature and, considered thus, it can be removed from the optimizer entirely and placed within the network itself. Specifically, we show that, once forward weights are corrected, right-sided natural gradient descent can be implemented in a form which has three exactly equivalent forms: a gradient preconditioner, a decorrelating linear transform in the forward pass, or a set of recurrent dynamics in which all updates are Hebbian and rely only upon locally available signals. The (recurrent) decorrelation method we discover aligns closely with proposed methods for inhibitory learning and homeostatic plasticity in the brain. Notably, our transform requires no matrix inverse, no matrix decomposition, and no information beyond that which is available at an individual synapse. It can therefore be applied in distributed and physically constrained systems, including neuromorphic hardware and nervous systems, where existing preconditioners cannot. We demonstrate its effectiveness empirically in convolutional and residual network models while significantly improving a range of approximate biologically plausible methods for credit assignment.

cs.LG↗