#01Nov 5, 2026
math.OC
Last-Iterate Convergence of Stochastic Gradient Methods for Unbounded Problems
Kevin Kurian Thomas Vaidyan, Ahmet Alacaoglu, Michael P. Friedlander
Last-iterate convergence guarantees for stochastic gradient methods have attracted significant attention as practical implementations typically return the last iterate instead of an average of the iterates. In this paper, we study two approaches for analyzing the last-iterate convergence of proximal and projected stochastic gradient methods without bounded domain or bounded variance assumptions, where black-box variational inference serves as a running example. Under two related assumptions relaxing the bounded variance, we show near-optimal anytime rate $\widetilde{\mathcal{O}}(1/\sqrt{T})$ for the last iterate. Moreover, when the horizon $T$ is known, we remove the logarithmic factor and obtain the optimal order $\mathcal{O}(1/\sqrt{T})$, matching the order known under bounded variance or bounded domain assumptions.
#02Nov 5, 2026
cs.LO
Typed Knowledge over Constructive Institutions
Hans-Martin Will
Type theories designed for mathematics or program verification need only that a proposition holds; proof irrelevance in conversion erases, at the kernel level, how a claim was established. A persistent knowledge store, by contrast, must retain that record: who established a claim, by which derivation or external tool, and under which assumptions. This volume presents the theory of Eigenius---a store of typed knowledge over constructive institutions---and develops its metatheory from that requirement. The kernel theory is a dependent type theory with cumulative universes, an impredicative universe of propositions, inductive families, and an intensional identity type. Proof irrelevance is an axiom with an explicit witness rather than a conversion rule, so proofs of a proposition are provably equal yet remain distinct terms. Definitional equality is joinability under an orthogonal rewriting system---confluent, injective on type formers, and decidable by a type-free test---while a separate subsumption judgment covers universe cumulativity, codomain-covariant function types, and declared class inclusions. We prove consistency via a set-theoretic model; develop a justification logic over the kernel's propositions to track evidence and support; organize environments as an institution so that store extensions are signature morphisms and external verdicts enter via comorphisms; formulate a typed knowledge-graph theory with records, classes, and refinements; and prove the correctness of conversion, normalization by evaluation, and bidirectional type checking relative to termination. A Lean 4 formalization accompanies the volume.
#03Nov 5, 2026
cs.LG
Spectral symmetry fingerprints in equivariant representations
Jiacheng Cen, Anyi Li, Ning Lin and 3 more
Symmetry governs the organization of physical structures, while symmetry breaking reveals their transformations. In geometric deep learning, symmetry imposes rank constraints on equivariant representations, limiting the expressive capacity of equivariant graph neural networks (GNNs). Here we show that these constraints can instead be exploited: the singular-value spectra of equivariant representations provide a unified fingerprint of structural symmetry. We introduce spectral symmetry fingerprints (SymFP), which enable discrete point-group identification through rank-template matching and continuous symmetry analysis by quantifying spectral energy beyond target rank constraints. SymFP is orientation invariant and architecture agnostic, enabling a parameter-free GNN implementation. Its spectra can be reused across multiple target groups, and the resulting leakage scores satisfy subgroup monotonicity. Across synthetic structures, molecules, coordination complexes and large biological assemblies, SymFP accurately identifies point groups, tracks controlled symmetry breaking and reveals local and degree-resolved symmetry changes that can be obscured by global geometric measures. These results establish the spectral structure of equivariant representations as a general framework for characterizing symmetry across physical systems.
#04Nov 5, 2026
cs.CV
PSGAgent: Enhancing MLLMs' Dynamic Visual Perception for Panoptic Scene Graph Generation via Agentic Reasoning
Qingyun Liu, Yuankun Liu, Jiaye Feng and 6 more
Panoptic Scene Graph generation (PSG) requires holistic yet fine-grained reasoning over complex relations among objects. However, current Multimodal Large Language Models (MLLMs) applied to PSG suffer from a perception bottleneck: they function as static observers limited by fixed-resolution views. As a result, models often overlook critical relations involving small or peripheral objects and struggle to differentiate ambiguous predicates in complex scenes. To address these limitations, we propose PSGAgent, an agentic framework that enhances visual perception for PSG through a think-act-observe loop. PSGAgent allows MLLMs to dynamically refine their visual perception using two tools: a Region Zoom-In Tool for local exploration of small or boundary relations and a Visual Highlight Tool for relation-focused segmentation that filters out irrelevant contextual noise. To optimize decision-making, we construct a two-stage training pipeline. First, we create a high-quality, error-aware Multimodal Chain-of-Thought (M-CoT) dataset that provides robust supervision for cold-start learning. Then, we design a novel hierarchical reward mechanism integrated with Group Sequence Policy Optimization (GSPO) to enable strategic and adaptive tool usage. Extensive experiments on the PSG benchmark show that PSGAgent achieves SOTA performance, demonstrating strong capability in both holistic and fine-grained scene understanding.
#05Nov 5, 2026
cs.CV
WeLM-Image: A Unified Image Generation Model towards Visual Intelligence
Canmiao Fu, Chen Li, Guohui Zhang and 13 more
We present \textbf{WeLM-Image}, a unified image foundation model that integrates multimodal understanding into text-to-image generation, instruction-guided editing, and multi-reference synthesis. Designed for single-GPU deployment in WeChat's large-scale consumer applications, the model processes text, reference images, and target latents as one interleaved sequence. A Mixture-of-Transformers (MoT) backbone combines shared attention with independent understanding and generation parameters to limit optimization interference. Equipping each path with Mixture-of-Experts (MoE) modules provides sparse capacity, with 31.7B stored parameters and approximately 5.4B generation parameters activated per target latent token. A generation-oriented data engine combines a knowledge-grounded visual vocabulary with large-scale visual clustering to balance semantic coverage and editing tasks, while training-time evaluation guides iterative data refinement. Bilingual annotations and verified editing supervision support progressive training up to native 1.5K resolution. We optimize generation and editing separately with rubric- and checklist-based rewards, then consolidate the specialized policies through noise-aware on-policy distillation. In the reported overall comparisons, the 1536-resolution model ranks first among the evaluated open-source models on PRISM-Bench, Qwen-Image-Bench, and UnicBench. MeanFlow-based few-step distillation yields WeLM-Image-Turbo, which generates a $1024\times1024$ image in 4.98\,s on a single NVIDIA H20 GPU using eight guidance-free steps.