Progressive Approximation in Deep Residual Networks: Theory and Validation

The Universal Approximation Theorem (UAT) guarantees universal function approximation but does not explain how residual models distribute approximation across layers. We reframe residual networks as a layer-wise approximation process that builds an approximation trajectory from input to target, and prove the existence of progressive trajectories where error decreases monotonically with depth. It reveals that residual networks can implement structured, step-by-step refinement rather than end-to-end (E2E) black-box mapping. Building on this, we propose Layer-wise Progressive Approximation (LPA), a theoretically grounded training principle that explicitly aligns each layer with its residual target to realize such trajectories. LPA is architecture-agnostic: we observe progressive behavior in residual FNNs, ResNets, and Transformers across tasks including complex surface fitting, image classification, and NLP with LLMs for generation and classification. Crucially, this enables ``train once, use $N$ models": a single network yields useful predictions at every depth, supporting efficient shallow inference without retraining. Our work unifies approximation theory with practical deep learning, providing a new lens on representation learning and a flexible framework for multi-depth deployment. The source code will be released unpon acceptance at https://(open\_upon\_acceptance).

Mol-Debate: Multi-Agent Debate Improves Structural Reasoning in Molecular Design

Text-guided molecular design is a key capability for AI-driven drug discovery, yet it remains challenging to map sequential natural-language instructions with non-linear molecular structures under strict chemical constraints. Most existing approaches, including RAG, CoT prompting, and fine-tuning or RL, emphasize a small set of ad-hoc reasoning perspectives implemented in a largely one-shot generation pipeline. In contrast, real-world drug discovery relies on dynamic, multi-perspective critique and iterative refinement to reconcile semantic intent with structural feasibility. Motivated by this, we propose Mol-Debate, a generation paradigm that enables such dynamic reasoning through an iterative generate-debate-refine loop. We further characterize key challenges in this paradigm and address them through perspective-oriented orchestration, including developer-debater conflict, global-local structural reasoning, and static-dynamic integration. Experiments demonstrate that Mol-Debate achieves state-of-the-art performance against strong general and chemical baselines, reaching 59.82% exact match on ChEBI-20 and 50.52% weighted success rate on S$^2$-Bench. Our code is available at https://github.com/wyuzh/Mol-Debate.

Think in Latent Thoughts: A New Paradigm for Gloss-Free Sign Language Translation

Many SLT systems quietly assume that brief chunks of signing map directly to spoken-language words. That assumption breaks down because signers often create meaning on the fly using context, space, and movement. We revisit SLT and argue that it is mainly a cross-modal reasoning task, not just a straightforward video-to-text conversion. We thus introduce a reasoning-driven SLT framework that uses an ordered sequence of latent thoughts as an explicit middle layer between the video and the generated text. These latent thoughts gradually extract and organize meaning over time. On top of this, we use a plan-then-ground decoding method: the model first decides what it wants to say, and then looks back at the video to find the evidence. This separation improves coherence and faithfulness. We also built and released a new large-scale gloss-free SLT dataset with stronger context dependencies and more realistic meanings. Experiments across several benchmarks show consistent gains over existing gloss-free methods. Code and data will be released upon acceptance at https://github.com/fletcherjiang/SignThought.

METER: Evaluating Multi-Level Contextual Causal Reasoning in Large Language Models

Contextual causal reasoning is a critical yet challenging capability for Large Language Models (LLMs). Existing benchmarks, however, often evaluate this skill in fragmented settings, failing to ensure context consistency or cover the full causal hierarchy. To address this, we pioneer METER to systematically benchmark LLMs across all three levels of the causal ladder under a unified context setting. Our extensive evaluation of various LLMs reveals a significant decline in proficiency as tasks ascend the causal hierarchy. To diagnose this degradation, we conduct a deep mechanistic analysis via both error pattern identification and internal information flow tracing. Our analysis reveals two primary failure modes: (1) LLMs are susceptible to distraction by causally irrelevant but factually correct information at lower level of causality; and (2) as tasks ascend the causal hierarchy, faithfulness to the provided context degrades, leading to a reduced performance. We belive our work advances our understanding of the mechanisms behind LLM contextual causal reasoning and establishes a critical foundation for future research. Our code and dataset are available at https://github.com/SCUNLP/METER .

MarkovScale: Towards Optimal Sequential Scaling at Inference Time

Sequential scaling is a prominent inference-time scaling paradigm, yet its performance improvements are typically modest and not well understood, largely due to the prevalence of heuristic, non-principled approaches that obscure clear optimality bounds. To address this, we propose a principled framework that models sequential scaling as a two-state Markov process. This approach reveals the underlying properties of sequential scaling and yields closed-form solutions for essential aspects, such as the specific conditions under which accuracy is improved and the theoretical upper, neutral, and lower performance bounds. Leveraging this formulation, we develop MarkovScale, a practical system that applies these optimality criteria to achieve a theoretically grounded balance between accuracy and efficiency. Comprehensive experiments across 3 backbone LLMs, 5 benchmarks, and over 20 configurations show that MarkovScale consistently outperforms state-of-the-art parallel and sequential scaling methods, representing a significant step toward optimal and resource-efficient inference in LLMs. The source code will be open upon acceptance at https://open-upon-acceptance.

To Retrieve or To Think? An Agentic Approach for Context Evolution

Current context augmentation methods, such as retrieval-augmented generation, are essential for solving knowledge-intensive reasoning tasks.However, they typically adhere to a rigid, brute-force strategy that executes retrieval at every step. This indiscriminate approach not only incurs unnecessary computational costs but also degrades performance by saturating the context with irrelevant noise. To address these limitations, we introduce Agentic Context Evolution (ACE), a framework inspired by human metacognition that dynamically determines whether to seek new evidence or reason with existing knowledge. ACE employs a central orchestrator agent to make decisions strategically via majority voting.It aims to alternate between activating a retriever agent for external retrieval and a reasoner agent for internal analysis and refinement. By eliminating redundant retrieval steps, ACE maintains a concise and evolved context. Extensive experiments on challenging multi-hop QA benchmarks demonstrate that ACE significantly outperforms competitive baselines in accuracy while achieving efficient token consumption.Our work provides valuable insights into advancing context-evolved generation for complex, knowledge-intensive tasks.

Multi-agent Undercover Gaming: Hallucination Removal via Counterfactual Test for Multimodal Reasoning

Hallucination continues to pose a major obstacle in the reasoning capabilities of large language models (LLMs). Although the Multi-Agent Debate (MAD) paradigm offers a promising solution by promoting consensus among multiple agents to enhance reliability, it relies on the unrealistic assumption that all debaters are rational and reflective, which is a condition that may not hold when agents themselves are prone to hallucinations. To address this gap, we introduce the Multi-agent Undercover Gaming (MUG) protocol, inspired by social deduction games like "Who is Undercover?". MUG reframes MAD as a process of detecting "undercover" agents (those suffering from hallucinations) by employing multimodal counterfactual tests. Specifically, we modify reference images to introduce counterfactual evidence and observe whether agents can accurately identify these changes, providing ground-truth for identifying hallucinating agents and enabling robust, crowd-powered multimodal reasoning. MUG advances MAD protocols along three key dimensions: (1) enabling factual verification beyond statistical consensus through counterfactual testing; (2) introducing cross-evidence reasoning via dynamically modified evidence sources instead of relying on static inputs; and (3) fostering active reasoning, where agents engage in probing discussions rather than passively answering questions. Collectively, these innovations offer a more reliable and effective framework for multimodal reasoning in LLMs. The source code can be accessed at https://github.com/YongLD/MUG.git.

Rethinking Domain-Specific LLM Benchmark Construction: A Comprehensiveness-Compactness Approach

Numerous benchmarks have been built to evaluate the domain-specific abilities of large language models (LLMs), highlighting the need for effective and efficient benchmark construction. Existing domain-specific benchmarks primarily focus on the scaling law, relying on massive corpora for supervised fine-tuning or generating extensive question sets for broad coverage. However, the impact of corpus and question-answer (QA) set design on the precision and recall of domain-specific LLMs remains unexplored. In this paper, we address this gap and demonstrate that the scaling law is not always the optimal principle for benchmark construction in specific domains. Instead, we propose Comp-Comp, an iterative benchmarking framework based on a comprehensiveness-compactness principle. Here, comprehensiveness ensures semantic recall of the domain, while compactness enhances precision, guiding both corpus and QA set construction. To validate our framework, we conducted a case study in a well-renowned university, resulting in the creation of XUBench, a large-scale and comprehensive closed-domain benchmark. Although we use the academic domain as the case in this work, our Comp-Comp framework is designed to be extensible beyond academia, providing valuable insights for benchmark construction across various domains.

Seeing Beyond the Scene: Enhancing Vision-Language Models with Interactional Reasoning

Traditional scene graphs primarily focus on spatial relationships, limiting vision-language models' (VLMs) ability to reason about complex interactions in visual scenes. This paper addresses two key challenges: (1) conventional detection-to-construction methods produce unfocused, contextually irrelevant relationship sets, and (2) existing approaches fail to form persistent memories for generalizing interaction reasoning to new scenes. We propose Interaction-augmented Scene Graph Reasoning (ISGR), a framework that enhances VLMs' interactional reasoning through three complementary components. First, our dual-stream graph constructor combines SAM-powered spatial relation extraction with interaction-aware captioning to generate functionally salient scene graphs with spatial grounding. Second, we employ targeted interaction queries to activate VLMs' latent knowledge of object functionalities, converting passive recognition into active reasoning about how objects work together. Finally, we introduce a lone-term memory reinforcement learning strategy with a specialized interaction-focused reward function that transforms transient patterns into long-term reasoning heuristics. Extensive experiments demonstrate that our approach significantly outperforms baseline methods on interaction-heavy reasoning benchmarks, with particularly strong improvements on complex scene understanding tasks. The source code can be accessed at https://github.com/open_upon_acceptance.

FedConv: A Learning-on-Model Paradigm for Heterogeneous Federated Clients

Federated Learning (FL) facilitates collaborative training of a shared global model without exposing clients' private data. In practical FL systems, clients (e.g., edge servers, smartphones, and wearables) typically have disparate system resources. Conventional FL, however, adopts a one-size-fits-all solution, where a homogeneous large global model is transmitted to and trained on each client, resulting in an overwhelming workload for less capable clients and starvation for other clients. To address this issue, we propose FedConv, a client-friendly FL framework, which minimizes the computation and memory burden on resource-constrained clients by providing heterogeneous customized sub-models. FedConv features a novel learning-on-model paradigm that learns the parameters of the heterogeneous sub-models via convolutional compression. Unlike traditional compression methods, the compressed models in FedConv can be directly trained on clients without decompression. To aggregate the heterogeneous sub-models, we propose transposed convolutional dilation to convert them back to large models with a unified size while retaining personalized information from clients. The compression and dilation processes, transparent to clients, are optimized on the server leveraging a small public dataset. Extensive experiments on six datasets demonstrate that FedConv outperforms state-of-the-art FL systems in terms of model accuracy (by more than 35% on average), computation and communication overhead (with 33% and 25% reduction, respectively).