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Deep Learning · Algorithms

Jiayao Tan, Fan Lyu, Chenggong Ni, Fuyuan Hu, Wei Feng, Rui Yao

Universal Test-Time Adaptation (UTTA) tackles the challenge of handling both class and domain shifts in unsupervised settings with stream testing data. Currently, most UTTA methods can only deal with minor shifts and heavily rely on heuristic approaches. To advance UTTA under dual shifts, we propose a novel Active Universal Test-Time Adaptation (AUTTA) framework, Exposing Mixture and Annotating Confusion (EMAC), which incorporates active human annotation into the UTTA setting. To select appropriate samples for annotation in AUTTA, we first identify the mixed regions of target domain samples under dual shifts, highlighting potential candidate samples. We then design a reward-guided active selection strategy to prioritize annotating the most representative samples within this set, maximizing annotation effectiveness. Additionally, to balance the use of pseudo-labels with the limited number of annotations, we propose an adaptation objective designed to address the adaptation imbalance caused by annotation scarcity. Extensive experiments show that the proposed AUTTA approach significantly improves performance and achieves state-of-the-art.

Applications · Neuroscience, Cognitive Science

Shanglin Li, Chu Shiwen, Okan Koc, Yi Ding, Qibin Zhao, Motoaki Kawanabe, Ziheng Chen

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding often suffers from poor generalization due to distribution shifts across domains (e.g., subjects). Learning robust representations that capture underlying task-relevant information would mitigate these shifts and improve generalization. One promising approach is to exploit the underlying hierarchical structure in EEG, as recent studies suggest that hierarchical cognitive processes, such as visual processing, can be encoded in EEG. Yet, most existing decoding methods rely on Euclidean embeddings, which are not well-suited for capturing hierarchical structures. In contrast, hyperbolic spaces, regarded as the continuous analogue of tree structures, provide a natural geometry for representing hierarchical data. In this study, we first demonstrate that EEG data exhibit hyperbolicity and show that hyperbolic embeddings improve generalization. Motivated by these findings, we propose HEEGNet, a hybrid hyperbolic network architecture to capture the hierarchical structure in EEG and learn domain-invariant hyperbolic embeddings. To this end, HEEGNet combines both Euclidean and hyperbolic encoders and employs a novel coarse-to-fine domain adaptation strategy. Extensive experiments on multiple public EEG datasets, covering visual evoked potentials, emotion recognition, and intracranial EEG, demonstrate that HEEGNet achieves state-of-the-art performance.

Deep Learning · Robustness

Paapa Quansah, Pablo Rivas, Ernest Bonnah

Bridging the gap between the formal precision of system specifications and the nuances of human language is critical for reliable engineering, robotics, and AI safety, but it remains a major bottleneck. Prior efforts in grounding formal logic remain fragmented, resulting in datasets that are very small-scale (~2-5k examples), domain-specific, or translate logic into overly technical forms rather than context-rich natural language (NL). Thus, failing to adequately bridge formal methods and practical NLP. To address this gap, we introduce VERIFY, the first large-scale dataset meticulously designed to unify these elements. This dataset contains more than 200k+ rigorously generated triplets, each comprising a Linear Temporal Logic (LTL) formula, a structured, human-readable 'Intermediate Technical Language' (ITL) representation designed as a bridge between logic and text, and a domain-specific NL description contextualized across 13 diverse domains. VERIFY's construction pipeline ensures high fidelity: LTL formulas are enumerated and verified via model checking, mapped to the novel ITL representation using a provably complete formal grammar, and then translated into context-aware NL via LLM-driven generation. We guarantee data quality through extensive validation protocols, i.e., manual expert verification of 10,000 diverse samples. Furthermore, automated semantic consistency checks judged by Llama 3.3 confirmed an estimated >97% semantic correctness. From the initial experiments, we demonstrate VERIFY's scalability, logical complexity, and contextual diversity, significantly challenging standard models such as T5 and Llama 3.

Computer Vision · Vision Models & Multimodal

Israfel Salazar, Manuel Fernández Burda, Shayekh Islam, Arshia Soltani Moakhar, Shivalika Singh, Fabian Farestam, Angelika Romanou, Danylo Boiko, Dipika Khullar, Mike Zhang 等

The evaluation of vision-language models (VLMs) has mainly relied on English-language benchmarks, leaving significant gaps in both multilingual and multicultural coverage. While multilingual benchmarks have expanded, both in size and language, many rely on translations of English datasets, failing to capture cultural nuances. In this work, we propose Kaleidoscope, as the most comprehensive exam benchmark to date for the multilingual evaluation of vision-language models. Kaleidoscope is a large-scale, in-language multimodal benchmark designed to evaluate VLMs across diverse languages and visual inputs. Kaleidoscope covers 18 languages and 14 different subjects, amounting to a total of 20,911 multiple-choice questions. Built through an open science collaboration with a diverse group of researchers worldwide, Kaleidoscope ensures linguistic and cultural authenticity. We evaluate top-performing multilingual vision-language models and find that they perform poorly on low-resource languages and in complex multimodal scenarios. Our results highlight the need for progress on culturally inclusive multimodal evaluation frameworks.

Applications · Everything Else

Aarash Feizi, Shravan Nayak, Xiangru Jian, Kevin Qinghong Lin, Kaixin Li, Rabiul Awal, Xing Han Lu, Johan S Obando Ceron, Juan A. Rodriguez, Nicolas Chapados 等

Building reliable computer-use agents requires grounding: accurately connecting natural language instructions to the correct on-screen elements. While large datasets exist for web and mobile interactions, high-quality resources for desktop environments are limited. To address this gap, we introduce GroundCUA, a large-scale desktop grounding dataset built from expert human demonstrations. It covers 87 applications across 12 categories and includes 56K screenshots, with every on-screen element carefully annotated for a total of over 3.56M human-verified annotations. From these demonstrations, we generate diverse instructions that capture a wide range of real-world tasks, providing high-quality data for model training. Using GroundCUA, we develop the GroundNext family of models that map instructions to their target UI elements. At both 3B and 7B scales, GroundNext achieves state-of-the-art results across five benchmarks using supervised fine-tuning, while requiring less than one-tenth the training data of prior work. Reinforcement learning post-training further improves performance, and when evaluated in an agentic setting on the OSWorld benchmark using o3 as planner, GroundNext attains comparable or superior results to models trained with substantially more data. These results demonstrate the critical role of high-quality, expert-driven datasets in advancing general-purpose computer-use agents.

Jiashun Liu, Johan S Obando Ceron, Han Lu, Yancheng He, Weixun Wang, wenbo su, Bo Zheng, Pablo Samuel Castro, Aaron Courville, Ling Pan

Reinforcement learning (RL) has become a central paradigm for post-training large language models (LLMs) to elicit stronger reasoning. Yet, most recent RL for LLMs (RL4LLM) methods avoid explicit critics, replacing them with average advantage baselines. This shift is largely pragmatic: conventional value functions are computationally expensive to train at LLM scale and often fail under sparse rewards and long reasoning horizons. We revisit this bottleneck from an architectural perspective and introduce Asymmetric Proximal Policy Optimization (**AsyPPO**), a simple and scalable framework that restores the critic’s role while remaining efficient in large-model settings. **AsyPPO** employs a set of lightweight *mini-critics*, each trained on disjoint prompt shards. This design encourages diversity while preserving calibration, reducing value-estimation bias. Beyond robust estimation, **AsyPPO** leverages inter-critic uncertainty to refine the policy update: (i) masking advantages in states where critics agree and gradients add little learning signal, and (ii) filtering high-divergence states from entropy regularization, suppressing spurious exploration. Across multiple reasoning benchmarks, **AsyPPO** consistently improves learning stability and performance over strong baselines, e.g., GRPO, achieving performance gains of $> 6$% on *Qwen3-4b-Base* and about $3$% on *Qwen3-8b-Base* and *Qwen3-14b-Base* over classic PPO. Such results highlight the importance of architectural innovations in critics for scalable, efficient algorithms.

Reinforcement Learning · Deep RL

Johan S Obando Ceron, Walter Mayor, Samuel Lavoie, Scott Fujimoto, Aaron Courville, Pablo Samuel Castro

Recent works have proposed accelerating the wall-clock training time of actor-critic methods via the use of large-scale environment parallelization; unfortunately, these can sometimes still require large number of environment interactions to achieve a desired level of performance. Noting that well-structured representations can improve the generalization and sample efficiency of deep reinforcement learning (RL) agents, we propose the use of simplicial embeddings: lightweight representation layers that constrain embeddings to simplicial structures. This geometric inductive bias results in sparse and discrete features that stabilize critic bootstrapping and strengthen policy gradients. When applied to FastTD3, FastSAC, and PPO, simplicial embeddings consistently improve sample efficiency and final performance across a variety of continuous- and discrete-control environments, without any loss in runtime speed.

Computer Vision · Vision Models & Multimodal

Peiran Wu, Zhuorui Yu, Yunze Liu, Chi-Hao Wu, Enmin Zhou, Junxiao Shen

The rapid progress of large language models (LLMs) has laid the foundation for multimodal models. Nevertheless, visual language models (VLMs) still face significant computational overhead when scaled from images to the video domain. When video data is too large (due to high frame rates and long durations), the inference cost of models increases sharply. This severely hinders their deployment and application in environments that require rapid responses and have limited computation resources. Token compression for input videos is one of the promising directions, as effective compression schemes can significantly reduce computational overhead. Most existing compression methods are based on training-free token merging strategies in either the spatial or temporal dimension. Although these methods reduce computational overhead, their training-free nature inevitably leads to information loss during token compression, resulting in a significant performance drop. To address these challenges, we propose a Memory-Augmented Reinforcement Learning-based Token Compression (MARC) method for efficient video understanding that integrates structured retrieval with RL-based distillation. Our proposed MARC is a retrieve-then-compress method, which employs a Visual Memory Retriever (VMR) tool and a Compression Group Relative Policy Optimization (C-GRPO) training strategy. The Visual Memory Retriever first segments videos into event-level fragments and selects query-relevant clips. The C-GRPO distills reasoning ability from a Teacher Network to a Student Network by encouraging the output of the student network to match the performance of the teacher network. Extensive experiments on six video benchmarks demonstrate that our compression method achieves nearly identical accuracy to the 64-frame Qwen2.5-VL-3B baseline while using only one frame’s worth of tokens as input, resulting in a 95% reduction in visual tokens. Moreover, our approach reduces GPU memory usage by 72% and generation latency by 23.9%. These results demonstrate the strong potential of our compression method as a robust solution for RL-based post-training compression of large-scale models, enabling practical deployment in latency-sensitive and resource-constrained applications such as real-time video question answering, surveillance, and autonomous driving.

Applications · Language, Speech and Dialog

Gukhyeon Lee, Yeachan Kim, SANGKEUN LEE

Adapting large language models (LLMs) using smaller proxy models has been shown to improve training efficiency, where the LLMs remain frozen while the proxies are tuned on top. However, this approach typically requires access to the output probability distributions of LLMs, which are often inaccessible or unstable. To address this limitation, we propose KnowProxy, a knowledge-guided proxy framework in which the proxy is trained with textual knowledge rather than probability distributions. Specifically, we first elicit textual knowledge and reasoning from frozen LLMs through prompting, and then the proxy model learns to adapt this reasoning to target task distributions. We evaluate KnowProxy on diverse reasoning benchmarks with different fine-tuning scenarios. Comprehensive results show that KnowProxy achieves competitive or even better performance without direct access to probability distributions, thereby providing a scalable and versatile alternative to traditional fine-tuning.

Reinforcement Learning · Deep RL

Seungeun (Ross) Rho, Aaron Trinh, Danfei Xu, Sehoon Ha

Scaling unsupervised skill discovery algorithms to high-DoF agents remains challenging. As dimensionality increases, the exploration space grows exponentially, while the manifold of meaningful skills remains limited. Therefore, semantic meaningfulness becomes essential to effectively guide exploration in high-dimensional spaces. In this work, we present **Reference-Grounded Skill Discovery (RGSD)**, a novel algorithm that grounds skill discovery in a semantically meaningful latent space using reference data. RGSD first performs contrastive pretraining to embed motions on a unit hypersphere, clustering each reference trajectory into a distinct direction. This grounding enables skill discovery to simultaneously involve both imitation of reference behaviors and the discovery of semantically related diverse behaviors. On a simulated SMPL humanoid with $359$-D observations and $69$-D actions, RGSD successfully imitates skills such as walking, running, punching, and sidestepping, while also discover variations of these behaviors. In downstream locomotion tasks, RGSD leverages the discovered skills to faithfully satisfy user-specified style commands and outperforms imitation-learning baselines, which often fail to maintain the commanded style.

Reinforcement Learning · Planning

Vansh Kapoor, Aman Gupta, Hao Chen, Anurag Beniwal, Jing Huang, Aviral Kumar

Multi-step reasoning tasks like mathematical problem solving are vulnerable to cascading failures, where a single incorrect step leads to complete solution breakdown. Current LLM routing methods assign entire queries to one model, treating all reasoning steps as equal. We propose TRIM (Targeted routing in multi-step reasoning tasks), which routes only critical steps$\unicode{x2013}$those likely to derail the solution$\unicode{x2013}$to larger models while letting smaller models handle routine continuations. Our key insight is that targeted step-level interventions can fundamentally transform inference efficiency by confining expensive calls to precisely those steps where stronger models prevent cascading errors. TRIM operates at the step-level: it uses process reward models to identify erroneous steps and makes routing decisions based on step-level uncertainty and budget constraints. We develop several routing strategies within TRIM, ranging from a simple threshold-based policy to more expressive policies that reason about long-horizon accuracy-cost trade-offs and uncertainty in step-level correctness estimates. On MATH-500, even the simplest thresholding strategy surpasses prior routing methods with 5x higher cost efficiency, while more advanced policies match the strong, expensive model's performance using 80% fewer expensive model tokens. On harder benchmarks such as AIME, TRIM achieves up to 6x higher cost efficiency. All methods generalize effectively across math reasoning tasks, demonstrating that step-level difficulty represents fundamental characteristics of reasoning.

Theory · Interpretability and Visualization

Zhuowen Liang, Xiaotian LIN, Zhengxuan Zhang, Yuyu Luo, Haixun Wang, Nan Tang

Large language models (LLMs) are widely applied to data analytics over documents, yet direct reasoning over long, noisy documents remains brittle and error-prone. Hence, we study document question answering (QA) that consolidates dispersed evidence into a structured output (e.g., a table, graph, or chunks) to support reliable, verifiable QA. We propose a two-pillar framework, LiteCoST, to achieve both high accuracy and low latency with small language models (SLMs). Pillar 1: Chain-of-Structured-Thought (CoST). We introduce a CoST template, a schema-aware instruction that guides a strong LLM to produce both a step-wise CoST trace and the corresponding structured output. The process induces a minimal structure, normalizes entities/units, aligns records, serializes the output, and verifies/refines it, yielding auditable supervision. Pillar 2: SLM fine-tuning. The compact models are trained on LLM-generated CoST data in two stages: Supervised Fine-Tuning for structural alignment, followed by Group Relative Policy Optimization (GRPO) incorporating triple rewards for answer/format quality and process consistency. By distilling structure-first behavior into SLMs, this approach achieves LLM-comparable quality on multi-domain long-document QA using 3B/7B SLMs, while delivering 2–4× lower latency than GPT-4o and DeepSeek-R1 (671B). The code is available at https://github.com/HKUSTDial/LiteCoST.

Applications · Neuroscience, Cognitive Science

Jathurshan Pradeepkumar, Xihao Piao, Zheng Chen, Jimeng Sun

Foundation models are reshaping EEG analysis, yet an important problem of EEG tokenization remains a challenge. This paper presents TFM-Tokenizer, a novel tokenization framework that learns a vocabulary of time-frequency motifs from *single-channel* EEG signals and encodes them into discrete tokens. We propose a dual-path architecture with time–frequency masking to capture robust motif representations, and it is model-agnostic, supporting both lightweight transformers and existing foundation models for downstream tasks. Our study demonstrates three key benefits: *Accuracy:* Experiments on four diverse EEG benchmarks demonstrate consistent performance gains across both single- and multi-dataset pretraining settings, achieving up to $11\%$ improvement in Cohen’s Kappa over strong baselines. *Generalization:* Moreover, as a plug-and-play component, it consistently boosts the performance of diverse foundation models, including BIOT and LaBraM. *Scalability:* By operating at the single-channel level rather than relying on the strict 10–20 EEG system, our method has the potential to be device-agnostic. Experiments on ear-EEG sleep staging, which differs from the pretraining data in signal format, channel configuration, recording device, and task, show that our tokenizer outperforms baselines by $14\%$. A comprehensive token analysis reveals strong class-discriminative, frequency-aware, and consistent structure, enabling improved representation quality and interpretability. Code is available at https://github.com/Jathurshan0330/TFM-Tokenizer.

Computer Vision · Vision Models & Multimodal

Tianhui Liu, Hetian Pang, Xin Zhang, Tianjian Ouyang, Zhiyuan Zhang, Jie Feng, Yong Li, Pan Hui

Understanding urban socioeconomic conditions through visual data is a challenging yet essential task for sustainable urban development and policy planning. In this work, we introduce CityLens, a comprehensive benchmark designed to evaluate the capabilities of Large Vision-Language Models (LVLMs) in predicting socioeconomic indicators from satellite and street view imagery. We construct a multi-modal dataset covering a total of 17 globally distributed cities, spanning 6 key domains: economy, education, crime, transport, health, and environment, reflecting the multifaceted nature of urban life. Based on this dataset, we define 11 prediction tasks and utilize 3 evaluation paradigms: Direct Metric Prediction, Normalized Metric Estimation, and Feature-Based Regression. We benchmark 17 state-of-the-art LVLMs across these tasks. These make CityLens the most extensive socioeconomic benchmark to date in terms of geographic coverage, indicator diversity, and model scale. Our results reveal that while LVLMs demonstrate promising perceptual and reasoning capabilities, they still exhibit limitations in predicting urban socioeconomic indicators. CityLens provides a unified framework for diagnosing these limitations and guiding future efforts in using LVLMs to understand and predict urban socioeconomic patterns.

Social Aspects · Trustworthy Machine Learning

Yunseok Han, Yejoon Lee, Jaeyoung Do

Large Reasoning Models (LRMs) exhibit strong performance, yet often produce rationales that sound plausible but fail to reflect their true decision process, undermining reliability and trust. We introduce a formal framework for *reasoning faithfulness*, defined by two testable conditions: *stance consistency* (a coherent stance linking reasoning to answer) and *causal influence* (the stated reasoning causally drives the answer under output-level interventions), explicitly decoupled from accuracy. To operationalize this, we present **RFEval**, a benchmark of 7,186 instances across seven tasks that probes faithfulness via controlled, output-level counterfactual interventions. Evaluating twelve open-source LRMs, we find unfaithfulness in 49.7% of outputs, predominantly from stance inconsistency. Failures are concentrated in brittle, convergent domains such as math and code, and correlate more with post-training regimes than with scale: within-family ablations indicate that adding current RL-style objectives on top of supervised fine-tuning can *reduce* reasoning faithfulness, even when accuracy is maintained. Crucially, *accuracy is neither a sufficient nor a reliable proxy for faithfulness*: once controlling for model and task, the accuracy–faithfulness link is weak and statistically insignificant. Our work establishes a rigorous methodology for auditing LRM reliability and shows that trustworthy AI requires optimizing not only for correct outcomes but also for the structural integrity of the reasoning process. Our code and dataset can be found at project page: https://aidaslab.github.io/RFEval/

Deep Learning · Generative Models and Autoencoders

Chi Zhang, Xixi Hu, Bo Liu, Qiang Liu

The slow, sequential nature of autoregressive (AR) language models has driven the adoption of parallel decoding methods. However, these non-autoregressive models often sacrifice generation quality because they struggle to model the complex joint distribution of token sequences. To narrow this performance gap, we introduce Gumbel Distillation, a novel distillation technique that enables parallel decoders to learn this distribution effectively. Our method leverages the Gumbel-Max trick to create a deterministic mapping from a latent Gumbel noise space to the output tokens of a high-performing AR teacher. As a model-agnostic technique, Gumbel Distillation seamlessly integrates with diverse parallel decoding architectures, including MDLM and BD3-LM. Experiments on LM1B and OpenWebText show that Gumbel Distillation substantially improves the generation quality of parallel language models, achieving a 30.0% improvement in MAUVE Score and 10.5% in generative perplexity over MDLM trained on OpenWebText dataset.

Reinforcement Learning · Multi-agent

Keyu Li, Jin Gao, Dequan Wang

While Multi-Agent Systems (MAS) are increasingly deployed for complex workflows, their emergent properties—particularly the accumulation of bias—remain poorly understood. Because real-world MAS are too complex to analyze entirely, evaluating their ethical robustness requires first isolating their foundational mechanics. In this work, we conduct a baseline empirical study investigating how basic MAS topologies and feedback loops influence prejudice. Contrary to the assumption that multi-agent collaboration naturally dilutes bias, we hypothesize that structured workflows act as echo chambers, amplifying minor stochastic biases into systemic polarization. To evaluate this, we introduce Discrim-Eval-Open, an open-ended benchmark that bypasses individual model neutrality through forced comparative judgments across demographic groups. Analyzing bias cascades across various structures reveals that architectural sophistication frequently exacerbates bias rather than mitigating it. We observe systemic amplification even when isolated agents operate neutrally, and identify a 'Trigger Vulnerability' where injecting purely objective context drastically accelerates polarization. By stripping away advanced swarm complexity to study foundational dynamics, we establish a crucial baseline: structural complexity does not guarantee ethical robustness. Our code is available at https://github.com/weizhihao1/MAS-Bias.

Deep Learning · Robustness

Young Sang Choi, Vincent Jeanselme, Pierre Elias, Shalmali Joshi

Multimodal learning is of continued interest in artificial intelligence-based applications, motivated by the potential information gain from combining different data modalities. However, modalities observed in the source environment may differ from the modalities observed in the target environment due to multiple factors, including cost, hardware failure, or the perceived *informativeness* of a given modality. This change in missingness patterns between the source and target environment has not been carefully studied. Naïve estimation of the information gain associated with including an additional modality without accounting for missingness may result in improper estimates of that modality's value in the target environment. We formalize the problem of missingness, demonstrate its ubiquity, and show that the subsequent distribution shift induces bias when the missingness process is not explicitly accounted for. To address this issue, we introduce $\text{ICYM}^2\text{I}$ (In Case You Multimodal Missed It), a framework for the evaluation of predictive performance and information gain under missingness through inverse probability weighting-based correction. We demonstrate the importance of the proposed adjustment to estimate information gain under missingness on synthetic, semi-synthetic, and real-world datasets.

Computer Vision · Image and Video Generation

Hangjie Yuan, Weihua Chen, Jun CEN, Hu Yu, Jingyun Liang, Shuning Chang, Zhihui Lin, Tao Feng, Pengwei Liu, Jiazheng Xing 等

Autoregressive large language models (LLMs) have unified a vast range of language tasks, inspiring preliminary efforts in autoregressive (AR) video generation. Existing AR video generators either diverge from standard LLM architectures, depend on bulky external text encoders, or incur prohibitive latency due to next-token decoding. In this paper, we introduce Lumos-1, an LLM-based unified model for AR video generation with efficient discrete diffusion. Firstly, to fit videos with LLMs, we identify that 1D RoPE is ill-suited for visual spatiotemporal correlation modeling, and while demonstrated to be useful, naive 3D RoPE exhibits imbalanced frequency spectra. Therefore, we propose MM‑RoPE, which preserves the original textual RoPE while seamlessly accommodating video data with comprehensive frequency spectra and scaled 3D positions. Secondly, to fit the video data's nature and overcome the inefficiency of next-token decoding, we adopt a parallel and mask-based discrete diffusion with the intra-frame bidirectional and inter-frame causal attention masks. Based on this attention mask, we uncover the frame‑wise loss imbalance issue caused by spatial information redundancy and propose Autoregressive Discrete Diffusion Forcing, which introduces temporal tube masking during training with a compatible inference‑time masking policy to avoid quality degradation. Despite using only 48 GPUs for pre-training, limited data and a discrete tokenizer, Lumos-1 achieves results surpassing those of Show-o2 on GenEval, COSMOS-Video2World on VBench-I2V, and OpenSoraPlan on VBench-T2V.

Shuhang Chen, Yunqiu Xu, Junjie Xie, Aojun Lu, Tao Feng, ZEYING HUANG, ZHANG NING, Yi Sun, Yi Yang, Hangjie Yuan

Despite significant progress, multimodal large language models continue to struggle with visual mathematical problem solving. Some recent works recognize that visual perception is a bottleneck in visual mathematical reasoning, but their solutions are limited to improving the extraction and interpretation of visual inputs. Notably, they all ignore the key issue of whether the extracted visual cues are faithfully integrated and properly utilized in subsequent reasoning. Motivated by this, we present CogFlow, a novel cognitive-inspired three-stage framework that incorporates a knowledge internalization stage, explicitly simulating the hierarchical flow of human reasoning: perception$\Rightarrow$internalization$\Rightarrow$reasoning. In line with this hierarchical flow, we holistically enhance all its stages. We devise Synergistic Visual Rewards to boost perception capabilities in parametric and semantic spaces, jointly improving visual information extraction from symbols and diagrams. To guarantee faithful integration of extracted visual cues into subsequent reasoning, we introduce a Knowledge Internalization Reward model in the internalization stage, bridging perception and reasoning. Moreover, we design a Visual-Gated Policy Optimization algorithm to further enforce the reasoning is grounded with the visual knowledge, preventing models seeking shortcuts that appear coherent but are visually ungrounded reasoning chains. Moreover, we contribute a new dataset MathCog for model training, which contains samples with over 120K high-quality perception-reasoning aligned annotations. Comprehensive experiments and analysis on commonly used visual mathematical reasoning benchmarks validate the superiority of the proposed CogFlow. Project page: https://shchen233.github.io/cogflow.