Exact Dual Geometry of SOC-ICNN Value Functions

Input Convex Neural Networks (ICNNs) are commonly used in a two-stage manner: one first trains a convex network and then minimizes it over its input in a downstream inference problem. Recent second-order-cone ICNNs (SOC-ICNNs) enrich ReLU-based ICNNs with quadratic and conic modules and admit an exact representation as value functions of second-order cone programs (SOCPs). This value-function structure enables an explicit convex-analytic treatment of SOC-ICNN inference. In this paper, we study the exact first-order and local second-order geometry of SOC-ICNNs from the dual viewpoint. We show that supporting slopes, subdifferentials, directional derivatives, and local Hessians can be recovered directly from optimal dual variables. These results provide the geometric primitives for white-box SOC-ICNN inference, going beyond black-box automatic differentiation. Numerical experiments validate the exact multiplier readout, the local Hessian formula, and the set-valued behavior at structurally degenerate inputs. We also provide a step-by-step tutorial showing how the readout mechanism instantiates a complete white-box inference loop. The code is available at https://anonymous.4open.science/r/SOC-ICNN-Theory-BEFC/.

Budget-aware Auto Optimizer Configurator

Optimizer states occupy massive GPU memory in large-scale model training. However, gradients in different network blocks exhibit distinct behaviors, such as varying directional stability and scale anisotropy, implying that expensive optimizer states are not universally necessary and using a global optimizer is often memory-inefficient. We propose the Budget-Aware Optimizer Configurator (BAOC) to reduce memory cost by assigning suitable optimizer configurations to individual blocks under given budgets. Specifically, BAOC samples gradient streams to derive statistical metrics that quantify the potential performance risk of applying cheaper configurations (e.g., low precision or removing momentum). It then solves a constrained allocation problem to minimize total risk under memory and time budgets, selecting a budget-feasible configuration for each block. Experiments across vision, language, and diffusion workloads demonstrate that BAOC maintains training quality while significantly reducing the memory usage of optimizer states. The code is available at https://anonymous.4open.science/r/BAOC-45C6.

DV-World: Benchmarking Data Visualization Agents in Real-World Scenarios

Real-world data visualization (DV) requires native environmental grounding, cross-platform evolution, and proactive intent alignment. Yet, existing benchmarks often suffer from code-sandbox confinement, single-language creation-only tasks, and assumption of perfect intent. To bridge these gaps, we introduce DV-World, a benchmark of 260 tasks designed to evaluate DV agents across real-world professional lifecycles. DV-World spans three domains: DV-Sheet for native spreadsheet manipulation including chart and dashboard creation as well as diagnostic repair; DV-Evolution for adapting and restructuring reference visual artifacts to fit new data across diverse programming paradigms and DV-Interact for proactive intent alignment with a user simulator that mimics real-world ambiguous requirements. Our hybrid evaluation framework integrates Table-value Alignment for numerical precision and MLLM-as-a-Judge with rubrics for semantic-visual assessment. Experiments reveal that state-of-the-art models achieve less than 50% overall performance, exposing critical deficits in handling the complex challenges of real-world data visualization. DV-World provides a realistic testbed to steer development toward the versatile expertise required in enterprise workflows. Our data and code are available at \href{https://github.com/DA-Open/DV-World}{this project page}.

SOC-ICNN: From Polyhedral to Conic Geometry for Learning Convex Surrogate Functions

Classical ReLU-based Input Convex Neural Networks (ICNNs) are equivalent to the optimal value functions of Linear Programming (LP). This intrinsic structural equivalence restricts their representational capacity to piecewise-linear polyhedral functions. To overcome this representational bottleneck, we propose the SOC-ICNN, an architecture that generalizes the underlying optimization class from LP to Second-Order Cone Programming (SOCP). By explicitly injecting positive semi-definite curvature and Euclidean norm-based conic primitives, our formulation introduces native smooth curvature into the representation while preserving a rigorous optimization-theoretic interpretation. We formally prove that SOC-ICNNs strictly expand the representational space of ReLU-ICNNs without increasing the asymptotic order of forward-pass complexity. Extensive experiments demonstrate that SOC-ICNN substantially improves function approximation, while delivering competitive downstream decision quality. The code is available at https://github.com/Kanyooo/SOC-ICNN.

From Signal Degradation to Computation Collapse: Uncovering the Two Failure Modes of LLM Quantization

Post-Training Quantization (PTQ) is critical for the efficient deployment of Large Language Models (LLMs). While 4-bit quantization is widely regarded as an optimal trade-off, reducing the precision to 2-bit usually triggers a catastrophic ``performance cliff.'' It remains unclear whether the underlying mechanisms differ fundamentally. Consequently, we conduct a systematic mechanistic analysis, revealing two qualitatively distinct failure modes: Signal Degradation, where the computational patterns remain intact but information precision is impaired by cumulative error; and Computation Collapse, where key components fail to function, preventing correct information processing and destroying the signal in the early layers. Guided by this diagnosis, we conduct mechanism-aware interventions, demonstrating that targeted, training-free repair can mitigate Signal Degradation, but remains ineffective for Computation Collapse. Our findings provide a systematic diagnostic framework for PTQ failures and suggest that addressing Computation Collapse requires structural reconstruction rather than mere compensation.

From $P(y|x)$ to $P(y)$: Investigating Reinforcement Learning in Pre-train Space

While reinforcement learning with verifiable rewards (RLVR) significantly enhances LLM reasoning by optimizing the conditional distribution P(y|x), its potential is fundamentally bounded by the base model's existing output distribution. Optimizing the marginal distribution P(y) in the Pre-train Space addresses this bottleneck by encoding reasoning ability and preserving broad exploration capacity. Yet, conventional pre-training relies on static corpora for passive learning, leading to a distribution shift that hinders targeted reasoning enhancement. In this paper, we introduce PreRL (Pre-train Space RL), which applies reward-driven online updates directly to P(y). We theoretically and empirically validate the strong gradient alignment between log P(y) and log P(y|x), establishing PreRL as a viable surrogate for standard RL. Furthermore, we uncover a critical mechanism: Negative Sample Reinforcement (NSR) within PreRL serves as an exceptionally effective driver for reasoning. NSR-PreRL rapidly prunes incorrect reasoning spaces while stimulating endogenous reflective behaviors, increasing transition and reflection thoughts by 14.89x and 6.54x, respectively. Leveraging these insights, we propose Dual Space RL (DSRL), a Policy Reincarnation strategy that initializes models with NSR-PreRL to expand the reasoning horizon before transitioning to standard RL for fine-grained optimization. Extensive experiments demonstrate that DSRL consistently outperforms strong baselines, proving that pre-train space pruning effectively steers the policy toward a refined correct reasoning subspace.

ResAdapt: Adaptive Resolution for Efficient Multimodal Reasoning

Multimodal Large Language Models (MLLMs) achieve stronger visual understanding by scaling input fidelity, yet the resulting visual token growth makes jointly sustaining high spatial resolution and long temporal context prohibitive. We argue that the bottleneck lies not in how post-encoding representations are compressed but in the volume of pixels the encoder receives, and address it with ResAdapt, an Input-side adaptation framework that learns how much visual budget each frame should receive before encoding. ResAdapt couples a lightweight Allocator with an unchanged MLLM backbone, so the backbone retains its native visual-token interface while receiving an operator-transformed input. We formulate allocation as a contextual bandit and train the Allocator with Cost-Aware Policy Optimization (CAPO), which converts sparse rollout feedback into a stable accuracy-cost learning signal. Across budget-controlled video QA, temporal grounding, and image reasoning tasks, ResAdapt improves low-budget operating points and often lies on or near the efficiency-accuracy frontier, with the clearest gains on reasoning-intensive benchmarks under aggressive compression. Notably, ResAdapt supports up to 16x more frames at the same visual budget while delivering over 15% performance gain. Code is available at https://github.com/Xnhyacinth/ResAdapt.

GraphWalker: Agentic Knowledge Graph Question Answering via Synthetic Trajectory Curriculum

Agentic knowledge graph question answering (KGQA) requires an agent to iteratively interact with knowledge graphs (KGs), posing challenges in both training data scarcity and reasoning generalization. Specifically, existing approaches often restrict agent exploration: prompting-based methods lack autonomous navigation training, while current training pipelines usually confine reasoning to predefined trajectories. To this end, this paper proposes \textit{GraphWalker}, a novel agentic KGQA framework that addresses these challenges through \textit{Automated Trajectory Synthesis} and \textit{Stage-wise Fine-tuning}. GraphWalker adopts a two-stage SFT training paradigm: First, the agent is trained on structurally diverse trajectories synthesized from constrained random-walk paths, establishing a broad exploration prior over the KG; Second, the agent is further fine-tuned on a small set of expert trajectories to develop reflection and error recovery capabilities. Extensive experiments demonstrate that our stage-wise SFT paradigm unlocks a higher performance ceiling for a lightweight reinforcement learning (RL) stage, enabling GraphWalker to achieve state-of-the-art performance on CWQ and WebQSP. Additional results on GrailQA and our constructed GraphWalkerBench confirm that GraphWalker enhances generalization to out-of-distribution reasoning paths. The code is publicly available at https://github.com/XuShuwenn/GraphWalker

Seeing Like Radiologists: Context- and Gaze-Guided Vision-Language Pretraining for Chest X-rays

Despite recent advances in medical vision-language pretraining, existing models still struggle to capture the diagnostic workflow: radiographs are typically treated as context-agnostic images, while radiologists' gaze -- a crucial cue for visual reasoning -- remains largely underexplored by existing methods. These limitations hinder the modeling of disease-specific patterns and weaken cross-modal alignment. To bridge this gap, we introduce CoGaze, a Context- and Gaze-guided vision-language pretraining framework for chest X-rays. We first propose a context-infused vision encoder that models how radiologists integrate clinical context -- including patient history, symptoms, and diagnostic intent -- to guide diagnostic reasoning. We then present a multi-level supervision paradigm that (1) enforces intra- and inter-modal semantic alignment through hybrid-positive contrastive learning, (2) injects diagnostic priors via disease-aware cross-modal representation learning, and (3) leverages radiologists' gaze as probabilistic priors to guide attention toward diagnostically salient regions. Extensive experiments demonstrate that CoGaze consistently outperforms state-of-the-art methods across diverse tasks, achieving up to +2.0% CheXbertF1 and +1.2% BLEU2 for free-text and structured report generation, +23.2% AUROC for zero-shot classification, and +12.2% Precision@1 for image-text retrieval. Code is available at https://github.com/mk-runner/CoGaze.

SemEval-2026 Task 12: Abductive Event Reasoning: Towards Real-World Event Causal Inference for Large Language Models

Understanding why real-world events occur is important for both natural language processing and practical decision-making, yet direct-cause inference remains underexplored in evidence-rich settings. To address this gap, we organized SemEval-2026 Task 12: Abductive Event Reasoning (AER).\footnote{The task data is available at https://github.com/sooo66/semeval2026-task12-dataset.git} The task asks systems to identify the most plausible direct cause of a target event from supporting evidence. We formulate AER as an evidence-grounded multiple-choice benchmark that captures key challenges of real-world causal reasoning, including distributed evidence, indirect background factors, and semantically related but non-causal distractors. The shared task attracted 122 participants and received 518 submissions. This paper presents the task formulation, dataset construction pipeline, evaluation setup, and system results. AER provides a focused benchmark for abductive reasoning over real-world events and highlights challenges for future work on causal reasoning and multi-document understanding.