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Deep Learning · Large Language Models

Chuxue Cao, Jinluan Yang, Haoran Li, Kunhao Pan, Zijian Zhao, Zhengyu Chen, Yuchen Tian, Lijun Wu, Conghui He, Sirui Han 等

Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic verification-guided framework that dynamically interleaves formal symbolic verification with the natural language generation process, providing real-time feedback to detect and rectify errors as they occur. Distinguished from previous neuro-symbolic methods limited by passive post-hoc validation, our approach actively penalizes intermediate fallacies during the reasoning chain. We operationalize this framework via a novel two-stage training pipeline that synergizes formal logic verification-guided supervised fine-tuning and policy optimization. Extensive evaluation on six benchmarks spanning mathematical, logical, and general reasoning demonstrates that our 7B and 14B models outperform state-of-the-art baselines by average margins of 10.4\% and 14.2\%, respectively. These results validate that formal verification can serve as a scalable mechanism to significantly push the performance boundaries of advanced LLM reasoning.

Wei Ju, Wei Zhang, Siyu Yi, Zhengyang Mao, Yifan Wang, Jingyang Yuan, Zhiping Xiao, Ziyue Qiao, Ming Zhang

Graph Neural Networks (GNNs) have shown remarkable capabilities in learning from graph-structured data with various applications such as social analysis and bioinformatics. However, the presence of label noise in real scenarios poses a significant challenge in learning robust GNNs, and their effectiveness can be severely impacted when dealing with noisy labels on graphs, often stemming from annotation errors or inconsistencies. To address this, in this paper we propose a novel approach called ICGNN that harnesses the structure information of the graph to effectively alleviate the challenges posed by noisy labels. Specifically, we first design a novel noise indicator that measures the influence contradiction score (ICS) based on the graph diffusion matrix to quantify the credibility of nodes with clean labels, such that nodes with higher ICS values are more likely to be detected as having noisy labels. Then we leverage the Gaussian mixture model to precisely detect whether the label of a node is noisy or not. Additionally, we develop a soft strategy to combine the predictions from neighboring nodes on the graph to correct the detected noisy labels. At last, pseudo-labeling for abundant unlabeled nodes is incorporated to provide auxiliary supervision signals and guide the model optimization. Experiments on benchmark datasets show the superiority of our approach over competitive baselines in noisy label scenarios.

Theory · Game Theory

Haoran Sun, Xia Xuanzhi, Xu Chu, Xiaotie Deng

Affine Maximizer Auctions (AMAs), a generalized mechanism family from VCG, are widely used in automated mechanism design due to their inherent dominant-strategy incentive compatibility (DSIC) and individual rationality (IR). However, as the payment form is fixed, AMA's expressiveness is restricted, especially in distributions where bidders' valuations are correlated. In this paper, we propose Correlation-Aware AMA (CA-AMA), a novel framework that augments AMA with a new correlation-aware payment. We show that any CA-AMA preserves the DSIC property and formalize finding optimal CA-AMA as a constraint optimization problem subject to the IR constraint. Then, we theoretically characterize scenarios where classic AMAs can perform arbitrarily poorly compared to the optimal revenue, while the CA-AMA can reach the optimal revenue. For optimizing CA-AMA, we design a practical two-stage training algorithm. We derive that the target function's continuity and the generalization bound on the degree of deviation from strict IR. Finally, extensive experiments showcase that our algorithm can find an approximate optimal CA-AMA in various distributions with improved revenue and a low degree of violation of IR.

General Machine Learning · Sequential, Network, and Time Series Modeling

Yuhang Pei, Fanchun Meng, Wenrui Wu, Tao Ren, Yifan Wang, Wei Ju, Chao Zheng, Xiao Luo

This paper studies the problem of single domain generalization in time series classification, which aims to learn a generalized time series classification model using a single source domain. This problem is highly challenging due to unreliable supervision from domain scarcity. Although current approaches employ generative models for data augmentation, these synthesized samples often suffer from low diversity and intrinsic noise, leading to weak generalization ability. Towards this end, we propose a novel approach named Context-driven Diffusion with Progressive Expansion (CURE) for single domain generalization in time series classification. The core of our CURE is to generate both semantic-aware and semantic-free contexts to strategically guide a conditional diffusion model for informative data expansion. In particular, our CURE first conducts representation disentanglement to extract semantic-aware and semantic-free representations from source data. To enhance generalizability through data synthesis, we not only retrieve reference time series trajectories with similar semantics for semantic-aware contexts, but also utilize adversarial strategies to learn semantic-free contexts. These contexts are integrated as joint conditions for a diffusion model, enabling diverse and reliable virtual data. To enhance expansion adaptability and stable optimization, we progressively update our semantic-free contexts via a memory bank and measure boundary properties for dynamic data filtering. Comprehensive experiments on benchmark datasets validate the effectiveness of the proposed CURE in comparison to extensive baselines. Our code is available at https://anonymous.4open.science/r/cure_9C6E/.

Deep Learning · Large Language Models

Ali Abbasi, Chayne Thrash, Haoran Qin, Shansita Sharma, Sepehr Seifi, Soheil Kolouri

Advances in large language models have driven strong performance across many tasks, but their memory and compute costs still hinder deployment. SVD-based compression reduces storage and can speed up inference via low-rank factors, yet performance depends on how rank is allocated under a global compression ratio. Prior methods often use homogeneous ranks for similarly sized matrices, despite large differences in loss sensitivity, or rely on expensive iterative pre-truncation optimization to determine per matrix ranks. We propose **Zero Sum SVD** (**ZS-SVD**), a post-training method that performs *global* singular component selection using activation whitening and first-order calibration loss estimates in whitened coordinates. **ZS-SVD** prunes components across the whole model with a **zero sum** rule that keeps the cumulative predicted loss change near zero, automatically yielding heterogeneous ranks without solving a rank allocation optimization. Motivated by evidence that gradients near pretrained solutions exhibit low rank structure, we also introduce an optional lightweight correction that applies a **single** projected gradient update after truncation, followed by re-truncation. Extensive experiments across multiple LLM architectures show consistent gains across diverse benchmarks and compression ratios.

Deep Learning · Graph Neural Networks

Hourun Li, Yifan Wang, Qinghua Ran, Junyu Luo, Jia Yang, Changling Zhou, Zhiping Xiao, Wei Ju, Xiao Luo, Ming Zhang

This paper investigates fairness-aware graph adaptation, aiming to transfer knowledge from a labeled source graph to an unlabeled target graph while explicitly accounting for fairness. Most prior methods rely on adversarial learning to learn invariant graph representations of sensitive attributes. However, these approaches assume that sensitive attributes of the target domain are available, which often fails in real-world deployments. To address this limitation, we propose \underline{C}ausality-attended Repres\underline{e}ntation Dientang\underline{l}ement with Structural A\underline{l}ignment (CELL) for fairness-aware graph adaptation without requiring target sensitive labels. The key idea of CELL is to build a causal graph that captures the underlying graph-generation mechanism and guides representation disentanglement toward improved fairness. In particular, CELL employs a sensitive encoder and a causal encoder to extract sensitive and causal factors respectively. We encourage disentanglement by minimizing the mutual information between causal and sensitive representations, considering the conditional distribution. To leverage unlabeled target data, we further generate pseudo-labels for both target task labels and sensitive attributes, and use similarity relations to derive unbiased node representations. Finally, to further mitigate domain shift, we build a fairness-aware bipartite graph that provides additional structural supervision for cross-domain alignment. Extensive experiments on benchmark datasets demonstrate that CELL consistently outperforms strong baselines in both predictive performance and fairness.

Deep Learning · Graph Neural Networks

Yifan Wang, Haodong Zhang, Changhu Wang, Tao Ren, Dongjie Wang, Wei Ju, Chong Chen, Xian-Sheng Hua, Xiao Luo

This paper studies the problem of graph out-of-distribution (OOD) detection, which aims to identify anomaly graphs out of a graph dataset. Prior efforts usually focus on the utilization of topological structures with unsupervised graph learning to foster typical pattern recognition, which overlooks the semantic structure preserved in contextually affine neighborhoods. Towards this end, we propose a novel approach named Contextual Affinity Exploration with Twin Concordance (CLINIC) for graph OOD detection. The core of CLINIC is to explore and exploit the contextual affinity of the graph data samples for discriminative graph representations. In particular, our CLINIC first builds a contextual affinity graph to depict the semantic structure in the hidden space. More importantly, we introduce high-order affinity to enhance geometric understanding of the structure by utilizing a meta-graph neural network. To enhance representation discriminability with high robustness, we introduce twin concordance learning, which not only minimizes the difference of affinity distributions across different views, but also encourages the consistency between contextually affinitive neighbors. Finally, we introduce a compression strategy to expand the decision boundary for enhanced separation between in-distribution and out-of-distribution graphs. Extensive experimental results demonstrate the superiority of our CLINIC across ten real datasets in comparison to various baselines.

Social Aspects · Accountability, Transparency, and Interpretability

Florian Eichin, Yupei Du, Philipp Mondorf, Maria Matveev, Barbara Plank, Michael Hedderich

Post-hoc interpretability methods typically attribute a model’s behavior to its components, data, or training trajectory in isolation. This leads to explanations that lack a unified view and may miss key interactions. While combining existing methods or applying them at different training stages offers broader insights, such approaches usually lack theoretical support. In this work, we present ExPLAIND, a unified framework that integrates all these perspectives. First, we generalize recent work on gradient path kernels, which reformulate models trained by gradient descent as a kernel machine, to realistic settings like AdamW. We empirically validate that a CNN and a Transformer are accurately replicated by this reformulation. Second, we derive novel parameter- and step-wise influence scores from the kernel feature maps. Their effectiveness for parameter pruning is comparable to existing methods, demonstrating their value for model component attribution. Finally, jointly interpreting model components and data over the training process, we use ExPLAIND to analyze a Transformer that exhibits Grokking. Our findings support previously proposed stages of Grokking, while refining the final phase as one of alignment of the outer layers around a representation pipeline learned after the memorization phase. Overall, ExPLAIND provides a theoretically grounded, unified framework to interpret model behavior and training dynamics.

Optimization · Zero-order and Black-box Optimization

Kunjal Panchal, Sunav Choudhary, Yuriy Brun, Hui Guan

Forward-mode automatic differentiation (FmAD) and zero-order (ZO) optimization are increasingly proposed as memory-efficient, backpropagation-free alternatives for large language model (LLM) fine-tuning, yet their benefits are typically evaluated only against standard backpropagation (BP), omitting memory-efficient variants such as activation checkpointing. We present a unified theoretical and empirical comparison of BP, checkpointed BP, FmAD, and ZO for LLM and vision-language model training, showing that while FmAD and ZO reduce activation memory, they trade memory for higher computational cost and longer wall-clock time to convergence, resulting in lower accuracy and slower training, especially under constrained perturbation budgets. Across models, BP with checkpointing outperforms FmAD and ZO variants, including variance-reduced methods, achieving up to 31.1% higher accuracy, 34.8% faster convergence, and 3.8$\times$ fewer computations at comparable memory usage, while also revealing instability-related failure modes in FmAD and ZO. Overall, our results correct a one-sided benchmarking narrative by showing that memory-efficient methods entail fundamentally different trade-offs, and that ignoring these distinctions has led to misleading conclusions about LLM optimization in prior work.

Optimization · Non-Convex

Maria Matveev, Vit Fojtik, Hung-Hsu Chou, Gitta Kutyniok, Johannes Maly

The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime. In this work, we argue that a comprehensive understanding of the generalization performance of gradient descent requires analyzing the interaction between these various forms of implicit regularization. We empirically demonstrate that the learning rate interpolates between low parameter norm and low sharpness of the trained model. We furthermore prove that neither implicit bias alone minimizes the generalization error for diagonal linear networks trained on a simple regression task. These findings demonstrate that focusing on a single implicit bias is insufficient to explain good generalization, and they motivate a broader view of implicit regularization that captures the dynamic trade-off between norm and sharpness induced by non-negligible learning rates.

Applications · Neuroscience, Cognitive Science

Xinhong Xu, Yimeng Zhang, Qichen Qian, Yuanlong Zhang

Recent work suggests that large-scale, multi-animal modeling can significantly improve neural recording analysis. However, for functional calcium traces, existing approaches remain task-specific, limiting transfer across common neuroscience objectives. To address this challenge, we propose \textbf{CalM}, a self-supervised neural foundation model trained solely on neuronal calcium traces and adaptable to multiple downstream tasks, including forecasting and decoding. Our key contribution is a pretraining framework, composed of a high-performance tokenizer mapping single-neuron traces into a shared discrete vocabulary, and a dual-axis autoregressive transformer modeling dependencies along both the neural and the temporal axis. We evaluate CalM on a large-scale, multi-animal, multi-session dataset. On the neural population dynamics forecasting task, CalM outperforms strong specialized baselines after pretraining. With a task-specific head, CalM further adapts to the behavior decoding task and achieves superior results compared with supervised decoding models. Moreover, linear analyses of CalM representations reveal interpretable functional structures beyond predictive accuracy. Taken together, we propose a novel and effective self-supervised pretraining paradigm for foundation models based on calcium traces, paving the way for scalable pretraining and broad applications in functional neural analysis.

Deep Learning · Everything Else

Hyeonwoo Cho, Donghyeon Baek, Yewon Kim, Bumsub Ham

Recent advancements in Multimodal Large Language Models (MLLMs) have achieved remarkable success in vision-language tasks, yet the quadratic computational complexity arising from the vast number of visual tokens creates significant memory and latency bottlenecks. While visual token reduction (VTR) strategies have been explored to mitigate this burden, existing methods overlook the positional and attentional consistency between the full and reduced sequences, resulting in a distorted representation. To this end, we propose a novel VTR framework that rectifies the positional and attentional distortions while maintaining efficiency. Specifically, we present a simple yet effective calibration method that recovers lost visual attention by modulating attention weights based on relative distances. We also introduce a distinctive anchor selection for token merging to mitigate information loss during feature averaging. Experimental results on multiple benchmarks demonstrate that our method consistently improves the accuracy of various reduction methods, achieving state-of-the-art performance while maintaining computational efficiency. We will make our code publicly available online.

Social Aspects · Accountability, Transparency, and Interpretability

Alaa Anani, Tobias Lorenz, Bernt Schiele, Mario Fritz, Jonas Fischer

Understanding *how* neural networks arrive at their predictions is essential for debugging, auditing, and deployment. Mechanistic interpretability pursues this goal by identifying *circuits*—minimal subnetworks responsible for specific behaviors. However, existing circuit discovery methods are brittle: circuits depend strongly on the chosen concept dataset and often fail to transfer out-of-distribution, raising doubts whether they capture concept or dataset-specific artifacts. We introduce *Certified Circuits*, which provide provable stability guarantees for circuit discovery. Our framework wraps any black-box discovery algorithm with randomized data subsampling to certify that circuit component inclusion decisions are invariant to bounded edit-distance perturbations of the concept dataset. Unstable neurons are abstained from, yielding circuits that are more compact and more accurate. On ImageNet and OOD datasets, certified circuits achieve up to 91\% higher accuracy while using 45\% fewer neurons, and remain reliable where baselines degrade. *Certified Circuits* puts circuit discovery on formal ground by producing mechanistic explanations that are provably stable and better aligned with the target concept. Code released upon publication.

Deep Learning · Large Language Models

Ziyue Li, Yang Li, Tianyi Zhou

Large language models (LLMs) perform inference by following a fixed depth and order, non-recurrent execution of all layers. We reveal the wide existence of training-free, flexible, dynamic "program-of-layers (PoLar)", where pretrained layers can be packed as modules and then skipped or looped to form a customized program for each input. For most inputs, substantially shorter program executions can achieve the same or better accuracy, while incorrect predictions of the original LLM can be corrected by alternative programs with fewer layers. These observations indicate that inference admits multiple valid latent computations beyond the standard forward pass. To efficiently achieve PoLar in practice, we propose a lightweight PoLar prediction network, which learns to generate execution programs that dynamically skip or repeat pretrained layers for each input. Experiments on mathematical reasoning benchmarks demonstrate that PoLar consistently improves accuracy over standard inference and prior dynamic-depth methods, often while executing fewer layers, and that these gains persist under out-of-distribution evaluation. Our results suggest that fixed-depth execution captures only a narrow subset of an LLM’s latent reasoning capacity.

Deep Learning · Large Language Models

Yuesen Tang, Yiming Yang, Tengfei Bao, Yu Tong

Recent Multimodal Large Language Models (MLLMs) have advanced cross-modal reasoning by extending Chain-of-Thought (CoT) prompting to visual tasks. However, existing methods still rely heavily on explicit textual reasoning steps, leading to information loss, unstable perception–reasoning interaction, and high computational cost. Inspired by human cognition, we argue that effective visual reasoning emerges from a dynamic interplay between perception and latent thought, rather than a purely linear verbalization process. Motivated by this insight, we propose Latent-Driven Progressive Visual Reasoning (LDPVR), a framework that formulates multimodal reasoning as a Markov Chain of Recursive State Simplification, where explicit textual states are progressively refined under the guidance of latent transitions. Central to LDPVR is Interleaved Latent Grounding, which leverages latent semantic intent to actively retrieve fine-grained visual evidence and drive robust state evolution, enabling the model to iteratively reduce uncertainty before committing to simplified textual states. To optimize this process, we introduce a three-stage curriculum combining supervised fine-tuning, latent-text distillation, and reinforcement learning via Group Relative Policy Optimization (GRPO). Experiments on six multimodal reasoning benchmarks demonstrate that LDPVR improves reasoning accuracy while maintaining low inference latency. Code will be made public.

Deep Learning · Large Language Models

Jie Deng, Shining Liang, Jun Li, Hongzhi Li, Yutao Xie

Large reasoning models (LRMs) typically solve reasoning-intensive tasks by generating long chain-of-thought (CoT) traces, leading to substantial inference overhead. We identify a reproducible inference-time phenomenon, termed \textbf{\emph{Self-Compression}}: when multiple independent and answerable questions are presented within a single prompt, the model spontaneously produces shorter reasoning traces for each question. This phenomenon arises from \emph{multi-question contextual pressure} during generation and consistently manifests across models and benchmarks. Building on this observation, we propose ConPress (Learning from Contextual Pressure, a lightweight self-supervised fine-tuning approach. ConPress constructs multi-question prompts to induce self-compression, samples the resulting model outputs, and parses and filters per-question traces to obtain concise yet correct reasoning trajectories. These trajectories are directly used for supervised fine-tuning, internalizing compressed reasoning behavior in single-question settings without external teachers, manual pruning, or reinforcement learning. With only 8k fine-tuning examples, ConPress reduces reasoning token usage by 59\% on MATH500 and 33\% on AIME25, while maintaining competitive accuracy.

Applications · Chemistry, Physics, and Earth Sciences

Jaemin Seo, Su Rin Lee, JaeYong Lee

Deep learning methods based on backward stochastic differential equations (BSDEs) have emerged as competitive alternatives to physics-informed neural networks (PINNs) for solving high-dimensional partial differential equations (PDEs). By leveraging probabilistic representations, BSDE approaches can avoid the curse of dimensionality and often admit second-order-free training objectives that do not require explicit Hessian evaluations. It has recently been established that the commonly used Euler–Maruyama (EM) time discretization induces an intrinsic bias in BSDE training losses. While high-order schemes such as Heun can fully eliminate this bias, such schemes re-introduce second-order spatial derivatives and incur substantial computational overhead. In this work, we provide a principled analysis of EM-induced loss bias and propose an unbiased, second-order-free training framework that preserves the computational advantages of BSDE methods.

General Machine Learning · Transfer, Multitask and Meta-learning

Guanglong Sun, Hongwei Yan, Liyuan Wang, Zhiqi KANG, Shuang Cui, Hang Su, Jun Zhu, Yi Zhong

To cope with uncertain changes of the external world, intelligent systems must continually learn from complex, evolving environments and respond in real time. This ability, collectively known as general continual learning (GCL), encapsulates practical challenges such as online datastreams and blurry task boundaries. Although leveraging pretrained models (PTMs) has greatly advanced conventional continual learning (CL), these methods remain limited in reconciling the diverse and temporally mixed information along a single pass, resulting in sub-optimal GCL performance. Inspired by meta-plasticity and reconstructive memory in neuroscience, we introduce here an innovative approach named **Me**ta **Po**st-Refinement (MePo) for PTMs-based GCL. This approach constructs pseudo task sequences from pretraining data and develops a bi-level meta-learning paradigm to refine the pretrained backbone, which serves as a prolonged pretraining phase but greatly facilitates rapid adaptation of representation learning to downstream GCL tasks. MePo further initializes a meta covariance matrix as the reference geometry of pretrained representation space, enabling GCL to exploit second-order statistics for robust output alignment. MePo serves as a plug-in strategy that achieves significant performance gains across a variety of GCL benchmarks and pretrained checkpoints in a rehearsal-free manner (e.g., 15.10%, 13.36%, and 12.56% on CIFAR-100, ImageNet-R, and CUB-200 under Sup-21/1K).

Deep Learning · Large Language Models

Ruobing Zuo, Hanrui Zhao, Gaolei He, Zhengfeng Yang, Jianlin Wang

Automated proving of polynomial inequalities is a fundamental challenge in automated mathematical reasoning, where rich algebraic structure and a rapidly growing certificate search space hinder scalability. Purely symbolic approaches provide strong guarantees but often scale poorly as the number of variables or the degree increases, due to expensive algebraic manipulations and rapidly growing intermediate expressions. In parallel, LLM-guided methods have made notable progress, particularly on competition-style inequalities with a small number of variables. To address the remaining scalability challenges, we propose NSPI, a neuro-symbolic framework that combines the complementary strengths of LLMs and symbolic computation for polynomial-inequality proving. Concretely, an LLM proposes a conjecture in the form of an approximate polynomial Sum-Of-Squares (SOS) decomposition; we refine it via symbolic computation to obtain an exact polynomial SOS representation, which directly proves the target inequality, and we further certify the proof in Lean, yielding an end-to-end pipeline from heuristic discovery to machine-checked proof. Experiments on challenging benchmarks involving polynomials with up to 10 variables demonstrate the effectiveness and scalability of the proposed method.

General Machine Learning · Causality

Valentyn Melnychuk, Vahid Balazadeh, Stefan Feuerriegel, Rahul G. Krishnan

Foundation models based on prior-data fitted networks (PFNs) have shown strong empirical performance in causal inference by framing it as an in-context learning problem. However, it is unclear whether PFN-based causal estimators provide uncertainty quantification that is consistent with classical frequentist estimators. In this work, we address this gap by analyzing the frequentist consistency of PFN-based estimators for the average treatment effect (ATE). (1) We show that existing PFNs, when interpreted as Bayesian ATE estimators, can exhibit prior-induced confounding bias: the prior is not asymptotically overwritten by data, which, in turn, prevents frequentist consistency. (2) As a remedy, we suggest employing a calibration procedure based on a one-step posterior correction (OSPC). We show that the OSPC helps to restore frequentist consistency and can yield a semi-parametric Bernstein–von Mises theorem for calibrated PFNs (i.e., both the calibrated PFNs and the classical semi-parametric efficient estimators converge with growing data size). (3) Finally, we implement OSPC through tailoring martingale posteriors on top of the PFNs. In this way, we are able to recover nuisance-function posterior distributions from PFNs, required by the OSPC. In multiple (semi-)synthetic experiments, PFNs calibrated with our martingale posterior OSPC produce ATE uncertainty that (i) asymptotically matches frequentist uncertainty and (ii) is often best calibrated in finite samples among other Bayesian ATE estimators.