Reasoning distillation aims to transfer multi-step reasoning capabilities from large language models to smaller, efficient ones. While recent methods have shown promising gains, they typically rely on static teacher-student hierarchies and frame distillation as trajectory imitation. This is misaligned with the structure of reasoning, where intermediate steps are locally under-specified: global correctness constrains the final answer, but does not uniquely determine each intermediate move. We propose validity-calibrated reasoning distillation, a framework that treats reasoning distillation as a problem of local learning-signal allocation rather than path alignment. Instead of enforcing token-level imitation, we compare the student's and teacher's proposed next-step actions under the same prefix and use their relative local validity to modulate the strength of the distillation update. This yields a dynamic, context-dependent supervision that preserves the teacher's structural guidance while adapting update strength to local reasoning quality. Across math, code, and instruction-following benchmarks, our method outperforms strong distillation baselines. These results indicate that effective LLM reasoning distillation is governed not by rigid trajectory imitation, but by locally calibrated allocation of learning signal.
Yan Zhang, Jiong Tuo, Meng Ding, Yuheng Ma, Di Wang
Sparse linear regression is a fundamental problem in high-dimensional statistics, and its private counterparts leave a large gap between the central and the local model of differential privacy. Shuffled differential privacy (SDP) sits between the two, offering accuracy closer to the central model without the trust requirement of a central curator. This paper studies sparse linear regression under both non-interactive and interactive SDP protocols. In the non-interactive setting, any non-interactive $(ε,δ)$-SDP protocol is shown to incur an $\ell_2$-norm estimation error of $Ω( \frac{\sqrt{dk}}{nε} )$ with dimension $d$, sparsity $k$, and $n$ users, revealing an inherent dimensionality barrier. In addition, a non-interactive algorithm is proposed that achieves an $\ell_2$-norm upper bound of $\tilde{\mathcal{O}}( \sqrt{\frac{k}{n}} + \frac{d\sqrt{k}}{nε})$. To overcome this barrier, we turn to the interactive user-level setting, where each user holds $m$ samples. A two-round interactive algorithm is developed that first recovers the support through a heavy hitter step and then estimates the parameter, achieving an error of $\tilde{\mathcal{O}}( \sqrt{\frac{k}{nm}} + \frac{k}{n\sqrt{m}ε} )$ with no polynomial dependence on $d$. Furthermore, by extending the score attack framework to user-level data, a new lower bound $Ω( \sqrt{\frac{k\log(d/k)}{nm}} + \frac{k\log(d/k)}{n\sqrt{m}ε} )$ is established for any user-level $(ε,δ)$-DP, showing that the proposed algorithm is near-optimal with only a gap of the factor $\log(d/k)$.
Standard federated learning (FL) requires persistent device connectivity across multiple communication rounds, making it unsuitable for dynamic environments such as vehicular networks, where devices frequently join and leave. One-shot FL offers a promising alternative by completing training in a single communication round. However, one-shot FL suffers from model solidification and cannot readily adapt to subsequent client dynamics, including new client contributions and the withdrawal of previous contributions. We therefore consider exact model editing, which removes withdrawn contributions through unlearning or incorporates newly contributed ones through incremental learning without retraining from scratch. We identify that efficient editing fundamentally hinges on learning stability. To this end, we propose F-SOSA, the first stable one-shot FL algorithm that enables rapid and exact model editing. F-SOSA leverages sub-sampling of local models with carefully tuned rate for stable aggregation and performs curvature-aware model fusion to preserve utility. We prove that F-SOSA achieves vanishing training error and reasonably small generalization error bounds. Building on this stability, we further develop two single-round editing algorithms: F-SOSA-U for unlearning and F-SOSA-I for incremental learning. They ensure that the edited model, along with all intermediate algorithmic states, is statistically indistinguishable from retraining while incurring only an expected $O(ρ)$ fraction of its cost, where $ρ$ quantifies stability. Experiments demonstrate that our approach matches retraining performance while reducing cumulative time and communication overhead by at least 36% and 22%, respectively, under realistic urban mobility simulations.
Weijun Yin, Yanqing Yao, Falko Dressler, Di Wang, Youming Tao
Federated zeroth-order optimization (FedZOO) reduces the memory and communication costs of collaborative training for edge intelligence by avoiding backpropagation while communicating only random seeds and scalar coefficients. However, existing methods lack efficient mechanisms for exact unlearning to fully remove the influence of training data when users request deletion. A key insight is that total variation stability of the learning algorithm creates overlap between model distributions before and after data deletion, allowing exact unlearning to reuse computation through coupling. Based on this observation, we jointly design two stable zeroth-order learning algorithms and their corresponding exact-unlearning procedures: \textsc{FedZOO-S} obtains stability through client and mini-batch subsampling, enabling \textsc{FedZOUL-S} to perform efficient unlearning by preserving earlier updates and restarting from the first affected step. \textsc{FedZOO-NS} further combines subsampling with Gaussian noise to increase overlap between update distributions; \textsc{FedZOUL-NS} exploits this overlap through rejection--reflection coupling to reuse affected updates when the coupling is accepted. We prove exact unlearning for both algorithms: the model and saved state have the same joint distribution as retraining with the corresponding learner on retained data. We further establish stability and convergence guarantees for the learning algorithms and derive upper bounds on expected unlearning cost. Experiments demonstrate effective unlearning with competitive model utility and up to $56.1\%$ less cumulative unlearning time than re-optimization. Compared with first-order baselines, our methods reduce communication overhead by up to approximately four orders of magnitude.
Flow-based generative models are typically sampled by solving a deterministic ordinary differential equation (ODE), whereas reinforcement learning (RL) requires stochastic rollouts for exploration and optimization. Existing online RL methods for flow models therefore replace the inference-time ODE with a stochastic differential equation (SDE) during training. Although the ODE and SDE share the same marginal distribution in continuous time, they can behave differently after finite-step discretization. In particular, SDE rollouts often become blurry as exploration noise increases, creating a mismatch between training rollouts and inference-time ODE samples. We introduce LC-GRPO, a flow-based GRPO framework with Langevin correction. Each rollout transition takes an inference-aligned ODE Euler step followed by a stochastic Langevin correction targeting the marginal at the resulting timestep. The required score is recovered directly from the flow velocity, requiring no additional score model, while the transition remains an isotropic Gaussian with tractable likelihood. We theoretically show that, under suitable conditions, a single Langevin correction step reduces the error of an imperfect ODE Euler step and, under matched randomness, yields a more accurate transition than standard Euler--Maruyama discretization of the reverse SDE. Additionally, experiments on SD3.5-Medium, FLUX.1-Dev, and HunyuanVideo show that LC-GRPO consistently improves reward optimization across text-to-image and text-to-video tasks, preserves generation quality, and substantially narrows the gap between stochastic training rollouts and deterministic ODE inference.