Sparsity is Combinatorial Depth: Quantifying MoE Expressivity via Tropical Geometry

While Mixture-of-Experts (MoE) architectures define the state-of-the-art, their theoretical success is often attributed to heuristic efficiency rather than geometric expressivity. In this work, we present the first analysis of MoE through the lens of tropical geometry, establishing that the Top-$k$ routing mechanism is algebraically isomorphic to the $k$-th elementary symmetric tropical polynomial. This isomorphism partitions the input space into the Normal Fan of a Hypersimplex, revealing that \textbf{sparsity is combinatorial depth} which scales geometric capacity by the binomial coefficient $\binom{N}{k}$. Moving beyond ambient bounds, we introduce the concept of \textit{Effective Capacity} under the Manifold Hypothesis. We prove that while dense networks suffer from capacity collapse on low-dimensional data, MoE architectures exhibit \textit{Combinatorial Resilience}, maintaining high expressivity via the transversality of routing cones. In this study, our framework unifies the discrete geometry of the Hypersimplex with the continuous geometry of neural functions, offering a rigorous theoretical justification for the topological supremacy of conditional computation.

To Search or Not to Search: Aligning the Decision Boundary of Deep Search Agents via Causal Intervention

Deep search agents, which autonomously iterate through multi-turn web-based reasoning, represent a promising paradigm for complex information-seeking tasks. However, current agents suffer from critical inefficiency: they conduct excessive searches as they cannot accurately judge when to stop searching and start answering. This stems from outcome-centric training that prioritize final results over the search process itself. We identify the root cause as misaligned decision boundaries, the threshold determining when accumulated information suffices to answer. This causes over-search (redundant searching despite sufficient knowledge) and under-search (premature termination yielding incorrect answers). To address these errors, we propose a comprehensive framework comprising two key components. First, we introduce causal intervention-based diagnosis that identifies boundary errors by comparing factual and counterfactual trajectories at each decision point. Second, we develop Decision Boundary Alignment for Deep Search agents (DAS), which constructs preference datasets from causal feedback and aligns policies via preference optimization. Experiments on public datasets demonstrate that decision boundary errors are pervasive across state-of-the-art agents. Our DAS method effectively calibrates these boundaries, mitigating both over-search and under-search to achieve substantial gains in accuracy and efficiency. Our code and data are publicly available at: https://github.com/Applied-Machine-Learning-Lab/WWW2026_DAS.

Capabilities and Fundamental Limits of Latent Chain-of-Thought

Latent Chain-of-Thought (Latent CoT) models promise efficient reasoning via continuous representations, yet exhibit puzzling performance inconsistencies: excelling at exploration (ProsQA: 97.0%) but failing at computation (GSM8K: 34.1%). We reveal that this trade-off is governed by decisional certainty. Our contributions are threefold: (1) We theoretically characterize the fundamental Exploration-Execution Trade-off, proving that high certainty enables precise execution but inhibits exploration, while low certainty facilitates search but causes error accumulation. (2) We introduce the Symbolic Index--quantifying decisional commitment--as the core mechanism governing this trade-off and establish its causal relationship with both execution stability and exploration capability. (3) We prove that curriculum learning is theoretically necessary, as direct training provably fails due to distributional mismatch. Our framework shifts the design paradigm from binary architectural choices toward adaptive systems that dynamically regulate decisional certainty based on task demands.

Effective Frontiers: A Unification of Neural Scaling Laws

Neural scaling laws govern the prediction power-law improvement of test loss with respect to model capacity ($N$), datasize ($D$), and compute ($C$). However, existing theoretical explanations often rely on specific architectures or complex kernel methods, lacking intuitive universality. In this paper, we propose a unified framework that abstracts general learning tasks as the progressive coverage of patterns from a long-tail (Zipfian) distribution. We introduce the Effective Frontier ($k_\star$), a threshold in the pattern rank space that separates learned knowledge from the unlearned tail. We prove that reducible loss is asymptotically determined by the probability mass of the tail a resource-dependent frontier truncation. Based on our framework, we derive the precise scaling laws for $N$, $D$, and $C$, attributing them to capacity, coverage, and optimization bottlenecks, respectively. Furthermore, we unify these mechanisms via a Max-Bottleneck principle, demonstrating that the Kaplan and Chinchilla scaling laws are not contradictory, but equilibrium solutions to the same constrained optimization problem under different active bottlenecks.

Stabilizing Decentralized Federated Fine-Tuning via Topology-Aware Alternating LoRA

Decentralized federated learning (DFL), a serverless variant of federated learning, poses unique challenges for parameter-efficient fine-tuning due to the factorized structure of low-rank adaptation (LoRA). Unlike linear parameters, decentralized aggregation of LoRA updates introduces topology-dependent cross terms that can destabilize training under dynamic communication graphs. We propose \texttt{TAD-LoRA}, a Topology-Aware Decentralized Low-Rank Adaptation framework that coordinates the updates and mixing of LoRA factors to control inter-client misalignment. We theoretically prove the convergence of \texttt{TAD-LoRA} under non-convex objectives, explicitly characterizing the trade-off between topology-induced cross-term error and block-coordinate representation bias governed by the switching interval of alternative training. Experiments under various communication conditions validate our analysis, showing that \texttt{TAD-LoRA} achieves robust performance across different communication scenarios, remaining competitive in strongly connected topologies and delivering clear gains under moderately and weakly connected topologies, with particularly strong results on the MNLI dataset.

DiffuSpeech: Silent Thought, Spoken Answer via Unified Speech-Text Diffusion

Current speech language models generate responses directly without explicit reasoning, leading to errors that cannot be corrected once audio is produced. We introduce \textbf{``Silent Thought, Spoken Answer''} -- a paradigm where speech LLMs generate internal text reasoning alongside spoken responses, with thinking traces informing speech quality. To realize this, we present \method{}, the first diffusion-based speech-text language model supporting both understanding and generation, unifying discrete text and tokenized speech under a single masked diffusion framework. Unlike autoregressive approaches, \method{} jointly generates reasoning traces and speech tokens through iterative denoising, with modality-specific masking schedules. We also construct \dataset{}, the first speech QA dataset with paired text reasoning traces, containing 26K samples totaling 319 hours. Experiments show \method{} achieves state-of-the-art speech-to-speech QA accuracy, outperforming the best baseline by up to 9 points, while attaining the best TTS quality among generative models (6.2\% WER) and preserving language understanding (66.2\% MMLU). Ablations confirm that both the diffusion architecture and thinking traces contribute to these gains.

Learn More with Less: Uncertainty Consistency Guided Query Selection for RLVR

Large Language Models (LLMs) have recently improved mathematical reasoning through Reinforcement Learning with Verifiable Reward (RLVR). However, existing RLVR algorithms require large query budgets, making annotation costly. We investigate whether fewer but more informative queries can yield similar or superior performance, introducing active learning (AL) into RLVR. We identify that classic AL sampling strategies fail to outperform random selection in this setting, due to ignoring objective uncertainty when only selecting by subjective uncertainty. This work proposes an uncertainty consistency metric to evaluate how well subjective uncertainty aligns with objective uncertainty. In the offline setting, this alignment is measured using the Point-Biserial Correlation Coefficient (PBC). For online training, because of limited sampling and dynamically shifting output distributions, PBC estimation is difficult. Therefore, we introduce a new online variant, computed from normalized advantage and subjective uncertainty. Theoretically, we prove that the online variant is strictly negatively correlated with offline PBC and supports better sample selection. Experiments show our method consistently outperforms random and classic AL baselines, achieving full-dataset performance while training on only 30% of the data, effectively reducing the cost of RLVR for reasoning tasks.

Rethinking Self-Training Based Cross-Subject Domain Adaptation for SSVEP Classification

Steady-state visually evoked potentials (SSVEP)-based brain-computer interfaces (BCIs) are widely used due to their high signal-to-noise ratio and user-friendliness. Accurate decoding of SSVEP signals is crucial for interpreting user intentions in BCI applications. However, signal variability across subjects and the costly user-specific annotation limit recognition performance. Therefore, we propose a novel cross-subject domain adaptation method built upon the self-training paradigm. Specifically, a Filter-Bank Euclidean Alignment (FBEA) strategy is designed to exploit frequency information from SSVEP filter banks. Then, we propose a Cross-Subject Self-Training (CSST) framework consisting of two stages: Pre-Training with Adversarial Learning (PTAL), which aligns the source and target distributions, and Dual-Ensemble Self-Training (DEST), which refines pseudo-label quality. Moreover, we introduce a Time-Frequency Augmented Contrastive Learning (TFA-CL) module to enhance feature discriminability across multiple augmented views. Extensive experiments on the Benchmark and BETA datasets demonstrate that our approach achieves state-of-the-art performance across varying signal lengths, highlighting its superiority.

Note2Chat: Improving LLMs for Multi-Turn Clinical History Taking Using Medical Notes

Effective clinical history taking is a foundational yet underexplored component of clinical reasoning. While large language models (LLMs) have shown promise on static benchmarks, they often fall short in dynamic, multi-turn diagnostic settings that require iterative questioning and hypothesis refinement. To address this gap, we propose \method{}, a note-driven framework that trains LLMs to conduct structured history taking and diagnosis by learning from widely available medical notes. Instead of relying on scarce and sensitive dialogue data, we convert real-world medical notes into high-quality doctor-patient dialogues using a decision tree-guided generation and refinement pipeline. We then propose a three-stage fine-tuning strategy combining supervised learning, simulated data augmentation, and preference learning. Furthermore, we propose a novel single-turn reasoning paradigm that reframes history taking as a sequence of single-turn reasoning problems. This design enhances interpretability and enables local supervision, dynamic adaptation, and greater sample efficiency. Experimental results show that our method substantially improves clinical reasoning, achieving gains of +16.9 F1 and +21.0 Top-1 diagnostic accuracy over GPT-4o. Our code and dataset can be found at https://github.com/zhentingsheng/Note2Chat.

Accelerating Generative Recommendation via Simple Categorical User Sequence Compression

Although generative recommenders demonstrate improved performance with longer sequences, their real-time deployment is hindered by substantial computational costs. To address this challenge, we propose a simple yet effective method for compressing long-term user histories by leveraging inherent item categorical features, thereby preserving user interests while enhancing efficiency. Experiments on two large-scale datasets demonstrate that, compared to the influential HSTU model, our approach achieves up to a 6x reduction in computational cost and up to 39% higher accuracy at comparable cost (i.e., similar sequence length).