In reinforcement learning with verifiable rewards (RLVR), whether entropy rises or falls can depend on choices that matter little under exact sampling, such as whether over-length responses are masked or counted as failures. We trace this to sampler mismatch: rollouts are drawn with top-k/top-p truncation or at a temperature the learner does not apply. We prove that a constant advantage shift then changes the entropy of a softmax policy, at first order and in expectation, with a sign fixed by the sampler. Positive shifts sharpen the policy under any sampler whose likelihood ratio to the policy increases with token probability, including top-k, top-p, min-p, and temperatures below one, and flatten it under flatter samplers. In group-based RLVR with token-level losses, the baseline-dependent part of this drift is set by the token-weighted net advantage, which masking and failing can push to opposite signs. The rest comes from a covariance between advantages and the sampler's sharpness gap and feeds back on itself: in a two-level model, a push away from a sharper sampler takes off in finite time, while a pull toward it saturates. On a 2B model, the entropy slope is linear in shifts of the net advantage under truncated sampling and indistinguishable from flat under exact sampling. Token-level importance ratios leave 98% of the drift, and four clipped minibatch updates per batch amplify it sevenfold. In 100-step runs, a net-zero baseline only delays an entropy explosion, and entropy raised at the start keeps rising only under truncation; cancelling the first-order drift at every step keeps entropy bounded without changing the learner. On a 9B reasoning model forked from an uncorrected run, zeroing the net advantage or renormalizing the learner raises held-out accuracy after ten steps by 8.2 and 8.8 points over the uncorrected rule, with no difference under exact sampling.
We study post-training for dynamically routed mixture-of-experts (MoE) models, focusing on integrating independently optimized specialists while keeping consolidation efficient. Our approach combines calibrated multi-teacher on-policy distillation (C-MOPD), which matches each selected teacher on a local Top-$K$ support with teacher-wise loss normalization and clipping, with an execution path that uses post-capacity bounded-width dispatch, final-route replay, and asynchronous rollout--training overlap. On Turing-20B-A2B, the selected model achieves a four-domain normalized integration score of 0.9988 and retains at least 90.16\% of the measured specialist gain in every domain. At matched $K=32$, the full calibration objective scores 0.9962, compared with 0.9724 without calibration and 0.9834 without clipping. At a matched 8K response cap, the model exceeds both shared SFT and Qwen3-8B on all four reasoning-enabled mathematics and code benchmarks (unweighted mean: 85.92, versus 80.33 for Qwen3-8B and 74.21 for SFT), and improves over SFT on ten of twelve broader evaluation metrics. In a PPU-based profile, the combined execution configuration reduces consolidation step time from 398.7 to 139.3 seconds, an observed 2.86$\times$ speedup over serial execution. These results demonstrate strong specialist integration alongside more efficient consolidation, while reflecting the complete training and execution framework rather than any single component.
Elliot Paquette, Noah Marshall, Lucas Benigni, Guangyuan Wang, Atish Agarwala, Courtney Paquette
Muon and related spectral optimizers have recently demonstrated strong empirical performance as scalable stochastic methods, often outperforming Adam. Yet their behavior remains poorly understood. We analyze stochastic Muon, which orthogonalizes an exponential moving average of minibatch gradients, on a high-dimensional matrix-valued least squares problem, and we compare it with stochastic SignSGD, a simple baseline comparable to Adam. We derive explicit deterministic dynamics that provide a tractable framework for studying learning behavior. We show that Muon has non-linear sensitivity to the effective batch $B_{\rm eff}=B(1+β)/(1-β)$. With exact whitening and small $B_{\rm eff}$ Muon fails to resolve smaller eigenmodes, slowing down convergence. Momentum and finite Newton--Shulz iterations can act as a ridge which lessen this effect. This behavior is in contrast with SignSGD which has no transition, leading to different optimal learning rates, but with matching convergence rate up to a constant factor in the isotropic setting. For anisotropic data, large batch setting Muon performs a square-root preconditioning with respect to the data covariance spectrum while SignSGD provides no preconditioning for generic covariances. We analyze time to target loss in a power law covariance model and derive a phase diagram in the data exponent $α$ and target exponent $ζ$. Muon is favored for steep covariance spectra with rich targets ($α>2$, $ζ<α+1$), SignSGD is favored for flat spectra ($α<1$), and in other regions the winner depends on how the target loss scales with dimension. Our results shed light on why replacing Adam with Muon is not trivial even from a pure optimization perspective.
Shiwei Liu, Linyuan Wang, Nuolin Sun, Libin Hou, Bin Yan
Automatic modulation classification (AMC) of radio signals is a core technology for spectrum monitoring and electromagnetic situational awareness. Deep neural networks (DNNs) play an important role in this field owing to their powerful feature extraction capabilities and end-to-end learning paradigm. However, their vulnerability to adversarial attacks poses serious security challenges to practical deployment. Adversarial training, a common defense, has limitations including poor generalization across attack types and high training costs. Inspired by Just image Transformers (JiT), a diffusion generative model that directly predicts clean images, this paper proposes a JiT-based denoising defense against adversarial examples for radio signal modulation classification. During training, a signal-specific 1D Transformer denoising network is optimized via flow matching to directly predict clean signal samples. It thereby learns a mapping that projects arbitrary examples back onto the low-dimensional manifold of clean signal examples. During inference, arbitrary examples are fed into the trained network and directly projected onto this manifold. This enables denoising defense without prior knowledge of attacks. Experiments on the RML2018.01A dataset were conducted without attack information, using a single empirically selected, fixed denoising start time. Compared with PGD-based adversarial training, the proposed method achieves a relative improvement of at least 20.58% in robust accuracy under PGD attacks. It also achieves a relative improvement of 10.20% in classification accuracy on clean examples. When evaluated against attack types unseen during adversarial training, the proposed method provides stronger defense than adversarial training. In particular, at higher attack strengths, it achieves a relative improvement of at least 39.72% in robust accuracy.