Unraveling the Hidden Dynamical Structure in Recurrent Neural Policies

Recurrent neural policies are widely used in partially observable control and meta-RL tasks. Their abilities to maintain internal memory and adapt quickly to unseen scenarios have offered them unparalleled performance when compared to non-recurrent counterparts. However, until today, the underlying mechanisms for their superior generalization and robustness performance remain poorly understood. In this study, by analyzing the hidden state domain of recurrent policies learned over a diverse set of training methods, model architectures, and tasks, we find that stable cyclic structures consistently emerge during interaction with the environment. Such cyclic structures share a remarkable similarity with \textit{limit cycles} in dynamical system analysis, if we consider the policy and the environment as a joint hybrid dynamical system. Moreover, we uncover that the geometry of such limit cycles also has a structured correspondence with the policies' behaviors. These findings offer new perspectives to explain many nice properties of recurrent policies: the emergence of limit cycles stabilizes both the policies' internal memory and the task-relevant environmental states, while suppressing nuisance variability arising from environmental uncertainty; the geometry of limit cycles also encodes relational structures of behaviors, facilitating easier skill adaptation when facing non-stationary environments.

Signal-Adaptive Trust Regions for Gradient-Free Optimization of Recurrent Spiking Neural Networks

Recurrent spiking neural networks (RSNNs) are a promising substrate for energy-efficient control policies, but training them for high-dimensional, long-horizon reinforcement learning remains challenging. Population-based, gradient-free optimization circumvents backpropagation through non-differentiable spike dynamics by estimating gradients. However, with finite populations, high variance of these estimates can induce harmful and overly aggressive update steps. Inspired by trust-region methods in reinforcement learning that constrain policy updates in distribution space, we propose \textbf{Signal-Adaptive Trust Regions (SATR)}, a distributional update rule that constrains relative change by bounding KL divergence normalized by an estimated signal energy. SATR automatically expands the trust region under strong signals and contracts it when updates are noise-dominated. We instantiate SATR for Bernoulli connectivity distributions, which have shown strong empirical performance for RSNN optimization. Across a suite of high-dimensional continuous-control benchmarks, SATR improves stability under limited populations and reaches competitive returns against strong baselines including PPO-LSTM. In addition, to make SATR practical at scale, we introduce a bitset implementation for binary spiking and binary weights, substantially reducing wall-clock training time and enabling fast RSNN policy search.

Let's Roll a BiFTA: Bi-refinement for Fine-grained Text-visual Alignment in Vision-Language Models

Recent research has shown that aligning fine-grained text descriptions with localized image patches can significantly improve the zero-shot performance of pre-trained vision-language models (e.g., CLIP). However, we find that both fine-grained text descriptions and localized image patches often contain redundant information, making text-visual alignment less effective. In this paper, we tackle this issue from two perspectives: \emph{View Refinement} and \emph{Description refinement}, termed as \textit{\textbf{Bi}-refinement for \textbf{F}ine-grained \textbf{T}ext-visual \textbf{A}lignment} (BiFTA). \emph{View refinement} removes redundant image patches with high \emph{Intersection over Union} (IoU) ratios, resulting in more distinctive visual samples. \emph{Description refinement} removes redundant text descriptions with high pairwise cosine similarity, ensuring greater diversity in the remaining descriptions. BiFTA achieves superior zero-shot performance on 6 benchmark datasets for both ViT-based and ResNet-based CLIP, justifying the necessity to remove redundant information in visual-text alignment.

WFR-FM: Simulation-Free Dynamic Unbalanced Optimal Transport

The Wasserstein-Fisher-Rao (WFR) metric extends dynamic optimal transport (OT) by coupling displacement with change of mass, providing a principled geometry for modeling unbalanced snapshot dynamics. Existing WFR solvers, however, are often unstable, computationally expensive, and difficult to scale. Here we introduce WFR Flow Matching (WFR-FM), a simulation-free training algorithm that unifies flow matching with dynamic unbalanced OT. Unlike classical flow matching which regresses only a transport vector field, WFR-FM simultaneously regresses a vector field for displacement and a scalar growth rate function for birth-death dynamics, yielding continuous flows under the WFR geometry. Theoretically, we show that minimizing the WFR-FM loss exactly recovers WFR geodesics. Empirically, WFR-FM yields more accurate and robust trajectory inference in single-cell biology, reconstructing consistent dynamics with proliferation and apoptosis, estimating time-varying growth fields, and applying to generative dynamics under imbalanced data. It outperforms state-of-the-art baselines in efficiency, stability, and reconstruction accuracy. Overall, WFR-FM establishes a unified and efficient paradigm for learning dynamical systems from unbalanced snapshots, where not only states but also mass evolve over time.

Multiplicative Orthogonal Sequential Editing for Language Models

Knowledge editing aims to efficiently modify the internal knowledge of large language models (LLMs) without compromising their other capabilities. The prevailing editing paradigm, which appends an update matrix to the original parameter matrix, has been shown by some studies to damage key numerical stability indicators (such as condition number and norm), thereby reducing editing performance and general abilities, especially in sequential editing scenario. Although subsequent methods have made some improvements, they remain within the additive framework and have not fundamentally addressed this limitation. To solve this problem, we analyze it from both statistical and mathematical perspectives and conclude that multiplying the original matrix by an orthogonal matrix does not change the numerical stability of the matrix. Inspired by this, different from the previous additive editing paradigm, a multiplicative editing paradigm termed Multiplicative Orthogonal Sequential Editing (MOSE) is proposed. Specifically, we first derive the matrix update in the multiplicative form, the new knowledge is then incorporated into an orthogonal matrix, which is multiplied by the original parameter matrix. In this way, the numerical stability of the edited matrix is unchanged, thereby maintaining editing performance and general abilities. We compared MOSE with several current knowledge editing methods, systematically evaluating their impact on both editing performance and the general abilities across three different LLMs. Experimental results show that MOSE effectively limits deviations in the edited parameter matrix and maintains its numerical stability. Compared to current methods, MOSE achieves a 12.08% improvement in sequential editing performance, while retaining 95.73% of general abilities across downstream tasks. The code is available at https://github.com/famoustourist/MOSE.

UpSafe$^\circ$C: Upcycling for Controllable Safety in Large Language Models

Large Language Models (LLMs) have achieved remarkable progress across a wide range of tasks, but remain vulnerable to safety risks such as harmful content generation and jailbreak attacks. Existing safety techniques -- including external guardrails, inference-time guidance, and post-training alignment -- each face limitations in balancing safety, utility, and controllability. In this work, we propose UpSafe$^\circ$C, a unified framework for enhancing LLM safety through safety-aware upcycling. Our approach first identifies safety-critical layers and upcycles them into a sparse Mixture-of-Experts (MoE) structure, where the router acts as a soft guardrail that selectively activates original MLPs and added safety experts. We further introduce a two-stage SFT strategy to strengthen safety discrimination while preserving general capabilities. To enable flexible control at inference time, we introduce a safety temperature mechanism, allowing dynamic adjustment of the trade-off between safety and utility. Experiments across multiple benchmarks, base model, and model scales demonstrate that UpSafe$^\circ$C achieves robust safety improvements against harmful and jailbreak inputs, while maintaining competitive performance on general tasks. Moreover, analysis shows that safety temperature provides fine-grained inference-time control that achieves the Pareto-optimal frontier between utility and safety. Our results highlight a new direction for LLM safety: moving from static alignment toward dynamic, modular, and inference-aware control.

Sample-Specific Noise Injection For Diffusion-Based Adversarial Purification

Diffusion-based purification (DBP) methods aim to remove adversarial noise from the input sample by first injecting Gaussian noise through a forward diffusion process, and then recovering the clean example through a reverse generative process. In the above process, how much Gaussian noise is injected to the input sample is key to the success of DBP methods, which is controlled by a constant noise level $t^*$ for all samples in existing methods. In this paper, we discover that an optimal $t^*$ for each sample indeed could be different. Intuitively, the cleaner a sample is, the less the noise it should be injected, and vice versa. Motivated by this finding, we propose a new framework, called Sample-specific Score-aware Noise Injection (SSNI). Specifically, SSNI uses a pre-trained score network to estimate how much a data point deviates from the clean data distribution (i.e., score norms). Then, based on the magnitude of score norms, SSNI applies a reweighting function to adaptively adjust $t^*$ for each sample, achieving sample-specific noise injections. Empirically, incorporating our framework with existing DBP methods results in a notable improvement in both accuracy and robustness on CIFAR-10 and ImageNet-1K, highlighting the necessity to allocate distinct noise levels to different samples in DBP methods. Our code is available at: https://github.com/tmlr-group/SSNI.

Be Careful When Fine-tuning On Open-Source LLMs: Your Fine-tuning Data Could Be Secretly Stolen!

Fine-tuning on open-source Large Language Models (LLMs) with proprietary data is now a standard practice for downstream developers to obtain task-specific LLMs. Surprisingly, we reveal a new and concerning risk along with the practice: the creator of the open-source LLMs can later extract the private downstream fine-tuning data through simple backdoor training, only requiring black-box access to the fine-tuned downstream model. Our comprehensive experiments, across 4 popularly used open-source models with 3B to 32B parameters and 2 downstream datasets, suggest that the extraction performance can be strikingly high: in practical settings, as much as 76.3% downstream fine-tuning data (queries) out of a total 5,000 samples can be perfectly extracted, and the success rate can increase to 94.9% in more ideal settings. We also explore a detection-based defense strategy but find it can be bypassed with improved attack. Overall, we highlight the emergency of this newly identified data breaching risk in fine-tuning, and we hope that more follow-up research could push the progress of addressing this concerning risk. The code and data used in our experiments are released at https://github.com/thu-coai/Backdoor-Data-Extraction.

Variational Regularized Unbalanced Optimal Transport: Single Network, Least Action

Recovering the dynamics from a few snapshots of a high-dimensional system is a challenging task in statistical physics and machine learning, with important applications in computational biology. Many algorithms have been developed to tackle this problem, based on frameworks such as optimal transport and the Schr\"odinger bridge. A notable recent framework is Regularized Unbalanced Optimal Transport (RUOT), which integrates both stochastic dynamics and unnormalized distributions. However, since many existing methods do not explicitly enforce optimality conditions, their solutions often struggle to satisfy the principle of least action and meet challenges to converge in a stable and reliable way. To address these issues, we propose Variational RUOT (Var-RUOT), a new framework to solve the RUOT problem. By incorporating the optimal necessary conditions for the RUOT problem into both the parameterization of the search space and the loss function design, Var-RUOT only needs to learn a scalar field to solve the RUOT problem and can search for solutions with lower action. We also examined the challenge of selecting a growth penalty function in the widely used Wasserstein-Fisher-Rao metric and proposed a solution that better aligns with biological priors in Var-RUOT. We validated the effectiveness of Var-RUOT on both simulated data and real single-cell datasets. Compared with existing algorithms, Var-RUOT can find solutions with lower action while exhibiting faster convergence and improved training stability.

Modeling Cell Dynamics and Interactions with Unbalanced Mean Field Schrödinger Bridge

Modeling the dynamics from sparsely time-resolved snapshot data is crucial for understanding complex cellular processes and behavior. Existing methods leverage optimal transport, Schr\"odinger bridge theory, or their variants to simultaneously infer stochastic, unbalanced dynamics from snapshot data. However, these approaches remain limited in their ability to account for cell-cell interactions. This integration is essential in real-world scenarios since intercellular communications are fundamental life processes and can influence cell state-transition dynamics. To address this challenge, we formulate the Unbalanced Mean-Field Schr\"odinger Bridge (UMFSB) framework to model unbalanced stochastic interaction dynamics from snapshot data. Inspired by this framework, we further propose CytoBridge, a deep learning algorithm designed to approximate the UMFSB problem. By explicitly modeling cellular transitions, proliferation, and interactions through neural networks, CytoBridge offers the flexibility to learn these processes directly from data. The effectiveness of our method has been extensively validated using both synthetic gene regulatory data and real scRNA-seq datasets. Compared to existing methods, CytoBridge identifies growth, transition, and interaction patterns, eliminates false transitions, and reconstructs the developmental landscape with greater accuracy.