arXiv subjects

Xin Huang

Publications and source records attributed to Xin Huang.

At least 19 recordsLinked to original sources

arXiv2026

ProGeo-RC: Prototype-guided Semantic Reliability and Geometric Error Calibration for Semi-supervised Cardiac Image Segmentation

Semi-supervised medical image segmentation aims to train reliable segmentation models using limited labeled data and abundant unlabeled data. However, existing methods typically rely on prediction confidence or model consistency to estimate pseudo-label reliability, but these criteria are insufficient to characterize both semantic reliability and geometric plausibility. To address this issue, we propose ProGeo-RC, a prototype-guided semantic reliability and geometric error calibration framework for semi-supervised medical image segmentation. ProGeo-RC consists of two key modules: Prototype-guided Semantic Reliability Estimation (PSRE) and Structured Semantic-Geometric Error Calibration (S-SGEC). PSRE uses probabilistic class prototypes to estimate the semantic reliability of unlabeled predictions and calibrate pixel-wise teacher pseudo labels, while S-SGEC introduces signed-distance-field-based geometric constraints to refine ambiguous boundaries and suppress spurious foreground responses outside target structures. Experiments on the ACDC and MVAA-CT datasets show that ProGeo-RC achieves better performance compared with representative semi-supervised segmentation methods. Under the 10\% labeled setting on ACDC, ProGeo-RC improves DSC and Jaccard by 0.37\% and 0.49\% over the corresponding second-best results, while reducing 95HD and ASD by 0.61 and 0.21, respectively. These results indicate that joint semantic reliability estimation and geometric error calibration can provide more reliable pseudo supervision for semi-supervised medical image segmentation.

cs.CV↗

arXiv2026

RadarFill: Observation-Constrained Gap Filling of Systematic Blind Zones in 3-D Weather Radar Reflectivity Mosaics

Ground-based weather radar mosaics contain systematic blind zones, especially at low altitudes, where missing reflectivity lacks corresponding complete observations for direct verification. We present RadarFill, an observation-constrained conditional diffusion framework for gap filling in three-dimensional radar reflectivity mosaics. RadarFill conditions on partially observed reflectivity and an observation mask, enforces available observations throughout reverse sampling, and preserves valid measurements in the final field. For training and controlled evaluation, structured synthetic missingness is designed from altitude-dependent missing-data statistics and the vertical nesting of blind zones in an operational 3-D radar mosaic product. Across 4,384 held-out test times and representative convective and typhoon cases, RadarFill recovers principal precipitation structures and moderate-to-strong echoes under extensive low-level missingness and generally outperforms conventional interpolation and a learning-based reference model. For real blind-zone evaluation, RadarFill model is applied directly to Fujian Province and compared with 90 matched volume scans from an independent phased-array radar. Within the principal 1-2 km low-level blind zones, RadarFill yields lower reflectivity errors than conventional interpolation, and the gap-filled precipitation structures show broad agreement with independent observations. In two controlled nowcasting experiments, improvements in RadarFill-initialized fields persist into subsequent forecasts, with the largest benefits at low altitudes and short lead times. These results provide complementary evidence from controlled synthetic missingness, independent radar observations, and downstream nowcasting, supporting the potential of observation-constrained conditional generation for gap filling in real 3-D radar blind zones.

physics.ao-ph↗

arXiv2026

Alperin weight bijections and dimensions of simple modules

We propose a new refinement of the (blockwise) Alperin weight conjecture taking dimensions of simple modules (or degrees of irreducible Brauer characters) into consideration. This is similar to Giannelli's refinement of the (Alperin--)McKay conjecture. We prove this new refinement for blocks with a cyclic or Klein four defect group, for inertial blocks (which include the Broué--Puig nilpotent blocks), and for $p$-blocks of $p$-solvable groups.

math.GR↗

arXiv2026

FlatCake: A Flat KVCache Storage Architecture for LLM Serving

KV cache reuse accelerates LLM serving, but existing systems manage host DRAM and NVMe SSD as a tiered hierarchy where DRAM acts as an intermediate cache. Production LLM workloads break both premises of this hierarchy. First, bimodal reuse defeats DRAM temporal filtering, since workloads are dominated either by one-shot blocks with long reuse distances or by multi-gigabyte agentic sessions that exceed DRAM capacity, putting SSD on the critical read path. Second, DRAM staging and eviction-ordered layout bottleneck SSD restoration. Holding host staging buffers for in-flight prefixes causes contention under load that aborts prefetches, while incremental eviction scatters a session's blocks across the SSD and prevents large sequential reads. We present FlatCake, a flat KV storage architecture that exposes host DRAM and NVMe SSD as peer media in a unified 64-bit address space. Exploiting the fact that KV blocks are write-once, immutable, and reused at session scope, FlatCake places each block directly onto its target medium in session-contiguous, layer-major order at creation time and never migrates it. FlatCake streams coalesced SSD reads directly into a bounded GPU window via GPUDirect Storage and decouples DRAM and SSD request queues to prevent head-of-line blocking. On a production Claude Code trace with DeepSeek-V4-Flash, FlatCake sustains a 94% cache hit rate as load increases (versus 64% for Mooncake), eliminates Mooncake's $6.5\times$--$6.7\times$ SSD read amplification, and reduces peak-load mean TTFT by $1.6\times$ while improving total token throughput by $1.6\times$. Across 8K--128K contexts on Llama-3.1-70B, FlatCake further reduces mean TTFT by up to $2.4\times$ over Mooncake and $1.8\times$ over Mooncake-GDS.

cs.DC↗

arXiv2026

RARE: Response-Aware Rational Equilibrium in Pricing Games

We study a pricing game in markets with budget-constrained buyers, where each seller offers a single good at a price she sets, and each buyer chooses a utility-maximizing bundle subject to her budget. We consider both the rivalrous setting, such as markets for physical goods, and the non-rivalrous setting, such as markets for datasets. Pure Nash equilibria often fail to exist in this game. However, Nash equilibrium assumes that the other sellers keep their prices fixed when one seller deviates, whereas in practice, sellers harmed by a price change may respond, for example, by matching the new price. We propose a new equilibrium notion called Response-Aware Rational Equilibrium (RARE). At a RARE, every deviation by a seller can be deterred by a response from the other sellers, in which no responder earns less than she did right after the deviation. Every Nash equilibrium is a RARE. Assuming that buyers' purchases (among their optimal choices) change continuously with prices, we show that a RARE always exists for rivalrous goods, and for non-rivalrous goods when buyers have equal budgets. Moreover, the RARE that we construct extracts the buyers' entire budget. For non-rivalrous goods with unequal budgets, we show that an approximate RARE exists, where a deviating seller can increase her revenue by a factor of at most $b_{\mathrm{avg}}/b_{\min}$, the ratio of the average budget to the minimum budget. Our proof uses two nested applications of the KKM lemma. We also study a natural dynamic in which sellers repeatedly raise their prices to earn the revenue that they could guarantee themselves by deviating, and show that it reaches an approximate RARE, with additive error $δ$, within $\lfloor B/δ\rfloor$ rounds, where $B$ is the buyers' total budget. The main results of this paper are formally verified in the Lean 4 proof assistant (https://github.com/sharmaeklavya2/dm-rare).

cs.GT↗

arXiv2026

Morita equivalent blocks with an endotrivial source that are not globally isotypic

Let $(K,\mathcal{O},k)$ be a large enough $2$-modular system. We construct two nilpotent block algebras of finite groups which are isomorphic as $\mathcal{O}$-algebras and are Morita equivalent via a bimodule with an endotrivial source of $\mathcal{O}$-rank $3$, but which are not globally isotypic. Hence they are not $2$-permutation equivalent and not splendidly Rickard equivalent. These results separate Morita equivalences with endopermutation source from $p$-permutation equivalences and splendid Rickard equivalences, and also separate almost global isotypies from global isotypies.

math.RT↗

arXiv2026

The refined Broué conjecture for RoCK blocks of double covers of symmetric and alternating groups

Recently, Kleshchev and Livesey proved the existence of RoCK $p$-blocks for double covers of symmetric and alternating groups over large enough coefficient rings. They proved that these RoCK blocks of double covers are Morita equivalent to standard ``local" blocks via bimodules with endopermutation source. Based on this, Kleshchev and Livesey proved that RoCK blocks are splendidly Rickard equivalent to their Brauer correspondents. The analogous result for blocks of symmetric groups, a theorem of Chuang and Kessar, was an important step in Chuang and Rouquier ultimately proving Broué's abelian defect group conjecture for symmetric groups. In this paper we show that the Morita and splendid Rickard equivalences constructed by Kleshchev and Livesey descend to the ring $\mathbb{Z}_p$ of $p$-adic integers, hence prove Kessar and Linckelmann's refinement of Broué's abelian defect group conjecture for these RoCK blocks.

math.RT↗

arXiv2026

The Broué invariant of a Morita equivalence with an endopermutation source

A perfect isometry $I$ (introduced by Broué) between two blocks $b$ and $c$ is a frequent phenomenon in the block theory of finite groups. It maps an irreducible character $ψ$ of $c$ to $\pm$ an irreducible character of $b$. Broué proved that the ratio of the codegrees of $ψ$ and $I(ψ)$ is a rational number with $p$-value zero and that its class in $\mathbb{F}_p$ is independent of $ψ$. This element is called the Broué invariant of $I$ by Boltje. The goal of this paper is to show that if $I$ comes from a Morita equivalence with an endopermutation source $V$, then, up to a sign, the Broué invariant of $I$ is determined by local data of $b$ and $c$. Therefore, up to a sign, it is independent of the endopermutation-source Morita equivalence. Moreover, we show that the sign factor is given by the reduction of the rank of $V$ modulo $p$. As a corollary, we obtain that the Isaacs--Navarro refinement of the Alperin--McKay conjecture holds for inertial blocks.

math.RT↗

arXiv2026

Schwarz lemmas and rigidity of $\bar\partial_b$-harmonic maps

We prove Schwarz lemmas for $\bar\partial_b$-harmonic maps from complete pseudo-Hermitian manifolds into K"ahler manifolds of negative curvature. For maps of bounded generalized dilatation we bound the full and the horizontal differential. For CR maps a coupled Bochner identity yields rank-dependent horizontal estimates and a bound for the Reeb differential. On Sasakian sources and complex hyperbolic targets we classify the maps attaining the horizontal bound, bound the deviation from equality in integral form by the deficit at one point, and prove compactness of almost extremal sequences. As an application, a Siu-type divergence identity yields foliation, pluriharmonicity and rank rigidity under volume growth conditions.

math.DG↗

arXiv2026

Parabolic induction for Takiff algebras and character formulas in Chari's category $\widetilde{\mathcal{O}}$

Let $\mathfrak{g}$ be a finite-dimensional complex semisimple Lie algebra, and let $\mathcal{C}_N\mathfrak{g}=\mathfrak{g}\otimes (\mathbb{C}[t]/t^{N+1}\mathbb{C}[t])$ denote the $N$-th Takiff algebra of $\mathfrak{g}$. We introduce a notion of parabolic subalgebras of $\mathcal{C}_N\mathfrak{g}$ and classify them in terms of $(N+2)$-partitions of a simple root system of $\mathfrak{g}$. We then study the corresponding parabolically induced $\mathcal{C}_N\mathfrak{g}$-modules and establish a necessary and sufficient criterion for their irreducibility, extending Jantzen's criterion for parabolically induced $\mathfrak{g}$-modules. As an application, we derive character formulas for almost all irreducible Harish-Chandra modules in Chari's category $\widetilde{\mathcal{O}}$ over the (centerless) affine Lie algebra associated with $\mathfrak{g}$. In particular, when $\mathfrak{g}=\mathfrak{sl}_3(\mathbb{C})$, we obtain explicit character formulas for all irreducible Harish-Chandra modules in this category.

math.RT↗

arXiv2026

Right Answers, Costly Models: The Efficiency Gap in LLM-based Optimization Modeling

Optimization modeling formulates real-world decision problems as mathematical programs that solvers can use to find optimal decisions. Large language models (LLMs) can automate this process, but the resulting correct formulations can require substantial time and memory to construct and solve, limiting practical scalability. Therefore, we systematically investigate whether LLMs can identify problem structure from natural-language descriptions and apply suitable optimization modeling techniques to generate mathematical models and solver code that solve the problems correctly and efficiently. To this end, we first curate OptTips, a knowledge base of 50 expert modeling techniques in eight families. Using this knowledge, we develop OptDachshund, a multi-agent framework that transforms problems from existing optimization benchmarks into new tasks for evaluating LLMs' use of modeling techniques. It constructs conventional and expert mathematical models with solver code for the same task and data, providing baselines for correctness and computational cost. The resulting EfficientOpt benchmark contains 561 expert-reviewed tasks with paired reference implementations. Evaluation of 11 representative LLMs reveals an efficiency gap on correctly solved tasks with comparable measurements: for every LLM, most generated programs take longer to solve than their expert counterparts. Within the comparable reference-size subset, 57\% of programs with correct objective values and fewer variables and linear constraints have longer recorded solver times. Case studies show that different modeling techniques can achieve the same optimal value at similar recorded cost. Faster solving may not reduce execution time if the code takes longer to prepare data and build the model. LLM optimization modeling should therefore be evaluated for both correctness and computational efficiency.

cs.LG↗

arXiv2026

What is Missing from AI Post-Training AI: An Empirical Analysis

Large language model (LLM) agents can now post-train an LLM end-to-end, raising the prospect of recursive self-improvement (RSI). Yet this progress is measured by aggregate benchmark scores, which cannot tell whether an agent executes a fixed plan well or strategically revises the plan when it fails. We separate these two capabilities: execution-level capability, iterating within an established training strategy, and strategy-level capability, revising that strategy as experimental evidence accumulates. Analyzing 1,338 post-training trajectories of frontier agents, we find that agents reliably execute post-training but lock into a default strategy, which follows the agent rather than the task, and only 2.1% of transitions between adjacent training runs ever change strategy. We then test whether the agent lacks experience, reasoning, or the decision to switch. (1) Experience improves execution but not the strategy. (2) Additional reasoning compute yields front-loaded gains on easier tasks but refines, rather than revises, the committed strategy. (3) Human review before training changes which strategy the agent locks into, not whether it locks in, whereas a single mid-run instruction outperforms the agent's own continuation by up to 17.44 points under the same budget. In conclusion, what the agent lacks is the decision to reopen a committed strategy and try another one. Realizing RSI therefore calls for interaction protocols and training signals that make strategy revision an explicit, rewarded decision.

cs.AI↗

arXiv2026

Does Native 3D Texture Generation Necessarily Require 3D Assets for Training?

Native 3D texture generation synthesizes colors directly in 3D space for a given geometry, conditioned on multi-view reference images. It is generally believed that training such models requires large-scale, high-quality real 3D asset data, whose acquisition remains a long-standing and challenging problem. In this work, we propose Tex-Zero, demonstrating that a high-fidelity native 3D texture generation framework can be trained without 3D assets. Our key observation is that only high-quality and fine-grained color information is essential for 3D texture training, while the required geometric information is less critical and can be manually constructed rather than obtained from real 3D assets. This finding makes it possible to transform abundant, high-quality 2D images into effective training samples for 3D texture generation. Specifically, we convert high-quality 2D images into 3D training samples by representing each image as a plane in 3D space and applying patch-wise random rotations and aggregation to construct complex geometric structures. Using these constructed image data, we train the Tex-Zero VAE, which can reconstruct real 3D assets with high quality despite never observing them during training. Building upon the Tex-Zero VAE, we train the Tex-Zero DiT also exclusively on the constructed image data, where the conditioning 2D multi-view images are transformed into planes in 3D space and also encoded by the Tex-Zero VAE, thereby reducing the representation gap and improving generation quality. Extensive experiments show that Tex-Zero generates high-fidelity 3D textures with fine-grained details solely using images as training data, offering a promising perspective on the data paradigm for scaling 3D texture generation.

cs.CV↗

arXiv2026

Instability and Morse Index of Exponentially Subelliptic Harmonic Maps

Let $M$ be a closed manifold with a bracket-generating distribution $H$. We study the Morse index of exponentially subelliptic harmonic maps. After establishing finiteness, we estimate the index through two test spaces. The extrinsic one averages the index form over projected ambient parallel frames, reducing the estimate to a trace identity involving an extrinsic scalar with a quartic exponential term. The intrinsic one uses parallel sections of the pullback bundle, on which the index form descends to a coupled quadratic form that is exact when a global parallel frame exists. The bounds apply to round spheres, products of spheres, and convex hypersurfaces. On a closed Heisenberg nilmanifold, the intrinsic reduction yields a spectral formula for the index.

math.DG↗

arXiv2026

ZOCheck: CPU-Shadow Checkpointing for Zeroth-Order LLM Fine-Tuning

Zeroth-order (ZO) optimization is an attractive option for memory-efficient LLM fine-tuning, but its fault tolerance remains underexplored. Unlike first-order training, ZO progress can be represented by lightweight seed-and-scalar step logs, yet naive log-only recovery still incurs replay cost that grows with training progress, and shortcut replay does not preserve the executed floating-point trajectory. We present ZOCheck, a fault-tolerant ZO training system that exploits this replayable structure through a CPU shadow process that continuously replays logged updates, materializes consistent recovery images off the GPU critical path, and persists them asynchronously. ZOCheck therefore combines non-blocking checkpointing during training with fast recovery from a near-current state. We also develop a cost model for choosing the snapshot policy under realistic failure rates. Experiments show that ZOCheck reduces checkpoint overhead by up to 219.7x and recovery latency by 1.55x on average compared with asynchronous full-state checkpointing, translating into up to 21.3x lower end-to-end wasted time across the evaluated failure rates, while preserving exact recovery behavior.

cs.DC↗

arXiv2026

LayerCheck: Adaptive Layer-wise Checkpointing for Large Language Model Post-training

With the rising computational and monetary costs of training large language models (LLMs), checkpointing---periodically storing model states for recovery---becomes essential for fault tolerance. Conventional checkpointing entails a severe trade-off between checkpoint frequency (I/O overhead) and computational recovery (recovery time). State-of-the-art approaches mitigate this cost through pipelining checkpoint I/Os, differential checkpointing, or in-memory persistence, yet none leverage the distinct characteristics of LLM training dynamics, where model weight updates are non-uniformly distributed across transformer layers. This observation implies that saving all weights each time might not be efficient. Inspired by this observation, we present LayerCheck, a layer-wise adaptive checkpointing framework that selectively persists layers whose updates exceed a threshold. This design avoids periodic I/O bursts by distributing layer-wise checkpoint writes over time, resulting in smoother and more balanced I/O profiles. Upon recovery, LayerCheck reconstructs a mixed-timestamp composite model state by aggregating the most recently persisted versions of each layer together with their matching optimizer states. Under a bounded per-layer staleness guard, this introduces a controlled perturbation: under standard Adam assumptions it adds a bounded staleness term, and empirically the post-restart loss deviates from the failure-free trajectory by at most 0.54%. Empirical results on multiple open-source LLMs with different datasets further demonstrate that recovered models preserve the original convergence behavior and accuracy while substantially reducing checkpoint overheads. Specifically, LayerCheck achieves up to 22.6x reduction in total checkpoint size and 1.31x reduction in end-to-end training time compared to state-of-the-art systems, significantly lowering the cost of checkpointing.

cs.DC↗

arXiv2026

Fusion-stable endosplit $p$-permutation resolutions

Let $k$ be a field of characteristic $p>0$, $\mathcal{F}$ a saturated fusion system over a finite $p$-group $P$, and $V$ an indecomposable capped endopermutation $kP$-module. Let $D_k^Ω(P)$ be the subgroup of the Dade group $D_k(P)$ generated by all the relative syzygies. It is known that $V$ has an endosplit $p$-permutation resolution if and only if the Dade class $[V]$ belongs to $D_k^Ω(P)$. We show that the resolution can be chosen to be $\mathcal{F}$-stable if and only if $V$ is $\mathcal{F}$-stable. As an application, we prove the following folklore result: if two blocks of finite groups are Morita equivalent via a bimodule with an endopermutation $kP$-source $V$ such that $[V]\in D_k^Ω(P)$, then these two blocks are splendidly Rickard equivalent.

math.RT↗

arXiv2026

Big categorification on towers of classical groups and wreath product groups

We develop a uniform framework for ``big'' categorification of representation categories of towers of finite classical groups and wreath product groups. We construct actions of symmetric products of Heisenberg categories, quantum in the finite classical group case and degenerate in the wreath product case. These actions lead to categorical actions of suitable symmetric products of Kac--Moody 2-categories, and hence to actions of large Lie algebras on Grothendieck groups. In characteristic zero, the resulting actions control the full graded centers of the group algebras through diagrammatic central elements, and the associated colored weight functions separate all irreducible ordinary characters. We also obtain modular block descriptions for wreath product groups through categorification.

math.RT↗