We introduce a novel convolutional neural network architecture, termed the \emph{periodic CNN}, which incorporates periodic boundary conditions into the convolutional layers. Our main theoretical contribution is a rigorous approximation theorem: periodic CNNs can approximate ridge functions depending on $d-1$ linear variables in a $d$-dimensional input space, while such approximation is impossible in lower-dimensional ridge settings ($d-2$ or fewer variables). This result establishes a sharp characterization of the expressive power of periodic CNNs. Beyond the theory, our findings suggest that periodic CNNs are particularly well-suited for problems where data naturally admits a ridge-like structure of high intrinsic dimension, such as image analysis on wrapped domains, physics-informed learning, and materials science. The work thus both expands the mathematical foundation of CNN approximation theory and highlights a class of architectures with surprising and practically relevant approximation capabilities.

Spiking Neural Networks (SNNs) provide an efficient framework for processing dynamic spatio-temporal signals and for investigating the learning principles underlying biological neural systems. A key challenge in training SNNs is to solve both spatial and temporal credit assignment. The dominant approach for training SNNs is Backpropagation Through Time (BPTT) with surrogate gradients. However, BPTT is in stark contrast with the spatial and temporal locality observed in biological neural systems and leads to high computational and memory demands, limiting efficient training strategies and on-device learning. Although existing local learning rules achieve local temporal credit assignment by leveraging eligibility traces, they fail to address the spatial credit assignment without resorting to auxiliary layer-wise matrices, which increase memory overhead and hinder scalability, especially on embedded devices. In this work, we propose Traces Propagation (TP), a forward-only, memory-efficient, scalable, and fully local learning rule that combines eligibility traces with a layer-wise contrastive loss without requiring auxiliary layer-wise matrices. TP outperforms other fully local learning rules on NMNIST and SHD datasets. On more complex datasets such as DVS-GESTURE and DVS-CIFAR10, TP showcases competitive performance and scales effectively to deeper SNN architectures such as VGG-9, while providing favorable memory scaling compared to prior fully local scalable rules, for datasets with a significant number of classes. Finally, we show that TP is well suited for practical fine-tuning tasks, such as keyword spotting on the Google Speech Commands dataset, thus paving the way for efficient learning at the edge.

Reinforcement learning (RL) has proven highly effective in eliciting the reasoning capabilities of large language models (LLMs). Inspired by this success, recent studies have explored applying similar techniques to vision-language models (VLMs), aiming to enhance their reasoning performance. However, directly transplanting RL methods from LLMs to VLMs is suboptimal, as the tasks faced by VLMs are inherently more complex. Specifically, VLMs must first accurately perceive and understand visual inputs before reasoning can be effectively performed. To address this challenge, we propose a two-stage reinforcement learning framework designed to jointly enhance both the perceptual and reasoning capabilities of VLMs. To mitigate the vanishing advantage issue commonly observed in RL training, we first perform dataset-level sampling to selectively strengthen specific capabilities using distinct data sources. During training, the first stage focuses on improving the model's visual perception through coarse- and fine-grained visual understanding, while the second stage targets the enhancement of reasoning abilities. After the proposed two-stage reinforcement learning process, we obtain PeBR-R1, a vision-language model with significantly enhanced perceptual and reasoning capabilities. Experimental results on seven benchmark datasets demonstrate the effectiveness of our approach and validate the superior performance of PeBR-R1 across diverse visual reasoning tasks.

A central paradox in fine-tuning Large Language Models (LLMs) with Reinforcement Learning with Verifiable Reward (RLVR) is the frequent degradation of multi-attempt performance (Pass@k) despite improvements in single-attempt accuracy (Pass@1). This is often accompanied by catastrophic forgetting, where models lose previously acquired skills. While various methods have been proposed, the choice and function of the divergence term have been surprisingly unexamined as a proactive solution. We argue that standard RLVR objectives -- both those using the mode-seeking reverse KL-divergence and those forgoing a divergence term entirely -- lack a crucial mechanism for knowledge retention. The reverse-KL actively accelerates this decay by narrowing the policy, while its absence provides no safeguard against the model drifting from its diverse knowledge base. We propose a fundamental shift in perspective: using the divergence term itself as the solution. Our framework, Diversity-Preserving Hybrid RL (DPH-RL), leverages mass-covering f-divergences (like forward-KL and JS-divergence) to function as a rehearsal mechanism. By continuously referencing the initial policy, this approach forces the model to maintain broad solution coverage. Extensive experiments on math and SQL generation demonstrate that DPH-RL not only resolves the Pass@k degradation but improves both Pass@1 and Pass@k in- and out-of-domain. Additionally, DPH-RL is more training-efficient because it computes f-divergence using generator functions, requiring only sampling from the initial policy and no online reference model. Our work highlights a crucial, overlooked axis for improving RLVR, demonstrating that the proper selection of a divergence measure is a powerful tool for building more general and diverse reasoning models.

With the raid evolution of large language models and multimodal models, the mobile-agent landscape has proliferated without converging on the fundamental challenges. This paper identifies four core problems that should be solved for mobile agents to deliver practical, scalable impact: (1) generalization across tasks, APPs, and devices; (2) accuracy, specifically precise on-screen interaction and click targeting; (3) long-horizon capability for sustained, multi-step goals; and (4) efficiency, specifically high-performance runtime on resource-constrained devices. We present AppCopilot, a multimodal, multi-agent, general-purpose mobile agent that operates across applications. AppCopilot operationalizes this position through an end-to-end pipeline spanning data collection, training, finetuning, efficient inference, and PC/mobile application. At the model layer, it integrates multimodal foundation models with robust Chinese-English support. At the reasoning and control layer, it combines chain-of-thought reasoning, hierarchical task planning and decomposition, and multi-agent collaboration. At the execution layer, it enables experiential adaptation, voice interaction, function calling, cross-APP and cross-device orchestration, and comprehensive mobile APP support. The system design incorporates profiling-driven optimization for latency and memory across heterogeneous hardware. Empirically, AppCopilot achieves significant improvements on four dimensions: stronger generalization, higher precision of on screen actions, more reliable long horizon task completion, and faster, more resource efficient runtime. By articulating a cohesive position and a reference architecture that closes the loop from data collection, training to finetuning and efficient inference, this paper offers a concrete roadmap for general purpose mobile agent and provides actionable guidance.

Heart rate prediction is vital for personalized health monitoring and fitness, while it frequently faces a critical challenge when deploying in real-world: data heterogeneity. We classify it in two key dimensions: source heterogeneity from fragmented device markets with varying feature sets, and user heterogeneity reflecting distinct physiological patterns across individuals and activities. Existing methods either discard device-specific information, or fail to model user-specific differences, limiting their real-world performance. To address this, we propose a framework that learns latent representations agnostic to both heterogeneity, enabling downstream predictors to work consistently under heterogeneous data patterns. Specifically, we introduce a random feature dropout strategy to handle source heterogeneity, making the model robust to various feature sets. To manage user heterogeneity, we employ a time-aware attention module to capture long-term physiological traits and use a contrastive learning objective to build a discriminative representation space. To reflect the heterogeneous nature of real-world data, we created and publicly released a new benchmark dataset, ParroTao. Evaluations on both ParroTao and the public FitRec dataset show that our model significantly outperforms existing baselines by 17% and 15%, respectively. Furthermore, analysis of the learned representations demonstrates their strong discriminative power, and one downstream application task confirm the practical value of our model.

A key barrier to interpreting large language models is polysemanticity, where neurons activate for multiple unrelated concepts. Sparse autoencoders (SAEs) have been proposed to mitigate this issue by transforming dense activations into sparse, more interpretable features. While prior work suggests that SAEs promote monosemanticity, no quantitative comparison has examined how concept activation distributions differ between SAEs and their base models. This paper provides the first systematic evaluation of SAEs against base models through activation distribution lens. We introduce a fine-grained concept separability score based on the Jensen-Shannon distance, which captures how distinctly a neuron's activation distributions vary across concepts. Using two large language models (Gemma-2-2B and DeepSeek-R1) and multiple SAE variants across five datasets (including word-level and sentence-level), we show that SAEs reduce polysemanticity and achieve higher concept separability. To assess practical utility, we evaluate concept-level interventions using two strategies: full neuron masking and partial suppression. We find that, compared to base models, SAEs enable more precise concept-level control when using partial suppression. Building on this, we propose Attenuation via Posterior Probabilities (APP), a new intervention method that uses concept-conditioned activation distributions for targeted suppression. APP achieves the smallest perplexity increase while remaining highly effective at concept removal.

Large Language Models (LLMs) such as ChatGPT have rendered visible the fragility of contemporary knowledge infrastructures by simulating coherence while bypassing traditional modes of citation, authority, and validation. This paper introduces the Situated Epistemic Infrastructures (SEI) framework as a diagnostic tool for analyzing how knowledge becomes authoritative across hybrid human-machine systems under post-coherence conditions. Rather than relying on stable scholarly domains or bounded communities of practice, SEI traces how credibility is mediated across institutional, computational, and temporal arrangements. Integrating insights from infrastructure studies, platform theory, and epistemology, the framework foregrounds coordination over classification, emphasizing the need for anticipatory and adaptive models of epistemic stewardship. The paper contributes to debates on AI governance, knowledge production, and the ethical design of information systems by offering a robust alternative to representationalist models of scholarly communication.

Large language models represent significant investments in computation, data, and engineering expertise, making them extraordinarily valuable intellectual assets. Nevertheless, these AI assets remain vulnerable to unauthorized redistribution and commercial exploitation through fine-tuning or black-box deployment. Current fingerprinting approaches face a fundamental trade-off: intrinsic methods require full parameter access, while backdoor-based techniques employ statistically anomalous triggers easily detected and filtered by adversaries. To address these limitations, we introduce FPEdit, a novel framework that leverages knowledge editing to inject semantically coherent natural language fingerprints through sparse, targeted modifications to model weights. Our approach introduces Promote-Suppress Value Vector Optimization, which simultaneously enhances target token likelihood while suppressing competing tokens, ensuring robust fingerprint integration without degrading core model functionality. Extensive experiments show that FPEdit achieves 95-100% fingerprint retention under both full-parameter fine-tuning and parameter-efficient adaptation, while preserving performance on downstream benchmarks. Moreover, FPEdit remains robust under quantization, pruning, and stochastic decoding, and can embed 10 fingerprint pairs into LLaMA2-7B in under 2 minutes using less than 30 GB of GPU memory, which represents a substantial reduction in resource requirements. These advances establish FPEdit as the first fingerprinting approach to simultaneously achieve robustness against adaptation, resistance to detection, and preservation of model utility, thereby providing a minimally invasive solution for reliable provenance verification of large language models in adversarial deployment scenarios.

Deep reinforcement learning (DRL) agents excel in solving complex decision-making tasks across various domains. However, they often require a substantial number of training steps and a vast experience replay buffer, leading to significant computational and resource demands. To address these challenges, we introduce a novel theoretical result that leverages the Neyman-Rubin potential outcomes framework into DRL. Unlike most methods that focus on bounding the counterfactual loss, we establish a causal bound on the factual loss, which is analogous to the on-policy loss in DRL. This bound is computed by storing past value network outputs in the experience replay buffer, effectively utilizing data that is usually discarded. Extensive experiments across the Atari 2600 and MuJoCo domains on various agents, such as DQN and SAC, achieve up to 383% higher reward ratio, outperforming the same agents without our proposed term, and reducing the experience replay buffer size by up to 96%, significantly improving sample efficiency at a negligible cost.