arXiv subjects

Chenyang Zhang

Publications and source records attributed to Chenyang Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Jacap: Robust KV Cache Eviction via Jacobian-Based Nonlinear Information Capacity Preservation

Key-value (KV) cache eviction is essential for scaling long-context inference in Large Language Models. However, existing policies predominantly rely on empirical heuristics, lacking a rigorous characterization of token utility under the inherently nonlinear softmax attention mechanism. In this work, we rethink KV cache eviction through the lens of local information geometry, modeling the attention process as a nonlinear Gaussian communication channel. By performing a first-order Taylor expansion of the attention mapping, we derive the Jacobian Information Capacity, a novel objective that explicitly captures query relevance, softmax sensitivity, and structural diversity. Guided by this theory, we introduce Jacap, a capacity-aware eviction method that utilizes softmax-aware importance weighting and statistical leverage scores for subset selection. Extensive experiments across diverse architectures and benchmarks demonstrate that \textsc{Jacap} delivers superior performance in most scenarios, particularly in high-compression regimes.

cs.CL↗

arXiv2026

Extremal problems for cancellative and locally thin hypergraphs

We study Tur\'an-type extremal problems for cancellative and locally thin uniform hypergraphs. An $r$-uniform hypergraph is $t$-cancellative if $(\cup_{i=1}^t A_i)\cup B\ne (\cup_{i=1}^t A_i)\cup C$ whenever $A_1,\ldots,A_t,B,C$ are distinct edges. Let $C_t(n,r)$ denote the maximum number of edges in such a hypergraph on $n$ vertices. For all fixed integers $t,k\ge2$, we prove that $C_{2(t-1)}(n,tk)=(1+o(1))\frac{\binom{n}{k}}{\binom{tk-1}{k-1}}$ as $n\to\infty$. In the case $t=2$, this shows that F\"uredi's 2012 upper bound for $C_2(n,2k)$ is asymptotically sharp. The lower bound uses locally sparse induced packings, while the upper bound follows from double counting and a matching argument. More generally, for integers $s\ge t\ge1$, an $r$-uniform hypergraph is locally $(s,t)$-thin if among any $s$ distinct edges, at least $t$ contain a vertex that lies in none of the other $s-1$ edges. This notion includes cancellative hypergraphs as special cases. We establish general upper and lower bounds for the corresponding extremal numbers and determine their polynomial order of growth under suitable divisibility assumptions.

math.CO↗

arXiv2026

Baseline-Relative Counterfactual Refinement for Bit-Aware Visual Token Communication

Generative visual-token communication reduces transmission load by sending only selected discrete tokens and reconstructing missing content at the receiver. However, existing token-selection criteria based on local uncertainty, importance, or diversity do not directly determine whether changing the current selection improves the final reconstruction under the same packet budget. To address this problem, we propose Gated Counterfactual Refinement for Communication (GCR-C), a rollout-style correction layer over Local-MDL. GCR-C constructs a compact diversified candidate set, evaluates each candidate through matched full-budget Local-MDL continuation, and replaces the baseline action only when a positive baseline-relative reconstruction gain is obtained. Experiments on CIFAR-10, STL-10, a coded 5G-LDPC link, and a limited high-resolution Kodak transfer show that GCR-C consistently improves reconstruction quality at active low- and medium-rate operating points without increasing the realized packet rate, while remaining effective across changes in dataset, channel condition, resolution, token grid, and tokenizer. The results also reveal a clear quality--computation tradeoff due to the additional encoder-side counterfactual evaluation.

cs.AI↗

arXiv2026

CrossAtlas: Evaluating Projection Techniques for Spatial Referencing in Cross-Reality Collaboration

Cross-reality collaboration increasingly connects immersive and desktop users within synchronized workspaces, yet little is known about how bidirectional projection techniques between immersive 3D layouts and desktop 2D views influence communication. Spatial referencing depends on shared spatial understanding, but different mappings preserve and distort geometric relationships in different ways, altering perceived adjacency, orientation, and coverage across collaborators' views. We present CrossAtlas, a synchronized PC-VR collaboration platform that integrates multiple bidirectional projection techniques, including three planar projection variants and equirectangular, a spherical projection variant, across layouts of varying curvature. In a controlled study with 24 dyads, collaborators completed spatial referencing tasks under different projection-layout conditions while we collected performance and subjective measures. Our results show that projection choice strongly shaped collaboration, with the spherical variant often outperforming planar projections and remaining robust across object layouts.

cs.HC↗

arXiv2026

ToolVerse: Unlocking Massive Environments and Long-Horizon Tasks for Agentic Reinforcement Learning

While LLM agents demonstrate strong reasoning abilities in compact and well-defined scenarios, they struggle to maintain robustness and effectiveness when faced with large-scale, diverse, and dynamic real-world environments that demand seamless tool integration. To address this gap, we introduce ToolVerse, a comprehensive framework that scales up agentic RL environments and enables agents to perform complex long-horizon reasoning in Tool-Integrated Reasoning (TIR) tasks. First, ToolVerse automatically builds the massive executable agent training environments from nearly 400 real-world Model Context Protocols (MCPs) that contain about 4500 tools. Second, we propose a task design strategy based on a tool dependency graph, utilizing Dynamic Unlocking Sampling Algorithm to generate long-horizon tasks, and produce GUST (Graph Unlocking Sampling Tasks) dataset. Third, to alleviate the credit assigment problem in long-horizon agentic RL, we propose a fine-grained Turn-Aware Relative Advantage algorithm. We conduct extensive Agentic RL training using ToolVerse and evaluate our framework on serveral agentic benchmarks. Experimental results demonstrate that our framework significantly strengthens LLMs' capabilities in long-horizon tool use, achieving a marked performance boost and showcasing robust reasoning within dynamic environments.

cs.AI↗

arXiv2026

EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments

Pretraining scaling laws reveal that model capability improves predictably with data and compute. But learning from real world environments after deployment remains far less understood. Analyzing roughly 38,000 hours of agent interaction with the environment across 134 real world tasks, we find, to the best of our knowledge, the first evidence that overall performance during environment learning follows a log-sigmoid scaling law with remarkably high precision, reaching R^2 = 0.998. Across model generations, we also find that agent learning speed roughly doubles every three months. This discovery stems from EdgeBench, a suite of 134 real world tasks with ultra-long horizons, spanning scientific discovery, software engineering, combinatorial optimization, professional knowledge work, formal mathematics, and interactive games. Each task sustains at least 12 hours of continuous agent operation under rich, multilevel feedback, and is built through substantial expert effort. We publicly release 51 tasks and our full evaluation framework to accelerate the study of how agents learn from real world experience.

cs.CL↗

arXiv2026

Towards Reliable and Robust LLM Planning: Symbolic Feedback-Driven Iterative Self-Refinement Framework

Large language models (LLMs) have attracted widespread attention from academia and industry, yet their deployment raises critical security concerns regarding robustness and reliability. Planning, a core component of intelligent behavior, remains challenging for LLMs, which often produce infeasible or incorrect solutions in long-horizon decision-making tasks due to inherent complexity. In this paper, we propose a symbolic feedback-driven iterative self-refinement framework to enhance the robustness and reliability of LLMs in long-horizon planning. Specifically, a natural language prompting mechanism is introduced to map logical symbols into natural language descriptions, enabling LLMs to better capture task constraints and semantics. We further design a symbolic verifier that identifies errors and converts them into corrective instructions interpretable by the LLM, thereby guiding self-refinement. In addition, we leverage a plan recognizer to infer goal reachability, facilitating more effective guidance toward desired goals. Empirical results demonstrate that the proposed framework consistently improves both feasibility and correctness in long-horizon planning tasks. This highlights its effectiveness in enhancing the reliability of LLM-based planning and potential to enable more trustworthy AI systems.

cs.AI↗

arXiv2026

Bridging Vision and Language Concepts through Optimal Transport Semantic Flow

Concept Bottleneck Models (CBMs) promise transparent reasoning by predicting through human-interpretable concepts, yet their effectiveness fundamentally depends on how well visual and textual representations are aligned or matched. Existing vision-language CBMs often rely on pre-aligned encoders or global cosine similarity, which obscures fine-grained concept localization and fails to reflect true semantic geometry. In this work, we rethink concept alignment as a dynamic cross-modal transport process instead of static projection and propose the Optimal Transport Flow Concept Bottleneck Model (OTF-CBM). It first learns a data-driven semantic cost via Inverse Optimal Transport to measure cross-modal distances, and then performs unbalanced optimal-transport-based flow matching to model semantic transitions between visual patches and textual concepts. With velocity-based concept activation, OTF-CBM captures interpretable geometric relations without ODE integration. Experiments further show that OTF-CBM achieves superior classification accuracy and concept faithfulness, offering a new geometric and dynamical perspective for interpretable cross-modal reasoning.

cs.CV↗

arXiv2026

SA-LIVO: Efficient LiDAR-Inertial-Visual Odometry with Subspace-Aware Degeneracy Handling

Tightly coupled LiDAR-inertial-visual odometry (LIVO) fuses geometric depth with visual measurements, but its exteroceptive sensors fail independently: LiDAR when scan geometry is under-constrained, vision under poor illumination or texture absence. Existing countermeasures (binary degeneracy detection, covariance inflation, scene-level quality gating) act at the modality level, so a single isotropic gain sends visual residuals into directions LiDAR already constrains well and cannot concentrate them where constraints are deficient. We propose Subspace-Aware LiDAR-inertial-visual odometry (SA-LIVO), whose Subspace-Aware Information Fusion (SAIF) eigendecomposes the joint LiDAR-visual information matrix and gates each eigendirection by a single-threshold linear clamp, attenuating low-amplitude directions while passing well-observed ones at full strength; robust per-residual gating and a scene-level quality factor screen corrupted measurements. LiDAR and visual residuals share one invariant extended Kalman filter (InEKF) loop and linearization point, letting photometric Jacobians be assembled once and reused across iterations. On 29 public-benchmark sequences (HILTI'22, Newer College Dataset (NCD), Oxford Spires), plus additional concurrent-degradation scenarios, SA-LIVO matches the strongest baselines in accuracy and stays bounded where competing systems diverge. On the HILTI'22 subset that every baseline completes, it averages 12.3 ms per frame on a laptop CPU and 26.8 ms on an embedded ARM board without GPU, at 3.6-6.3x lower peak memory.

cs.RO↗

arXiv2026

Semantic-Aware Generative Image Transmission for Resource-Constrained Visual IoT Systems

Resource-constrained visual Internet of Things (IoT) systems, such as edge cameras, unmanned sensing platforms, industrial inspection nodes, and remote monitoring sensors, often need to transmit task-relevant visual evidence over low-rate wireless links to an edge/cloud service. Existing image communication methods usually compress or transmit complete global representations, leaving limited room to exploit receiver-side generative restoration. This paper proposes a semantic-aware generative image transmission framework for edge-assisted visual IoT. The image captured by an IoT visual sensor is encoded into a discrete token grid by a VQ encoder. At the IoT transmitter or nearby gateway, token recoverability, estimated from prediction entropy and local structure complexity, is fused with semantic importance obtained from instance segmentation and category-aware scoring. A spatial dispersal sampler then selects the tokens to be transmitted under a bitrate budget. The transmitter sends only the quantization indices of kept tokens and a binary mask map, while the edge/cloud receiver recovers masked tokens through MaskGIT with Halton sequence scheduling. Experiments on Kodak and VisDrone scenes under AWGN and Rayleigh channels show that the proposed method provides a flexible bitrate-quality tradeoff for narrowband visual IoT links. At 0.074 bpp, it uses 44.6% of the transmitted bits of the 0.167-bpp DeepJSCC/WITT reference while achieving 29.9 dB PSNR. A pseudo-GT downstream detection study on Kodak further shows that semantic-aware masking preserves task-relevant objects better than random masking at both 30% and 50% mask ratios.

cs.CV↗

arXiv2026

An Erd\H{o}s Matching Conjecture for Vector Spaces

We study a vector-space analogue of the Erd\H{o}s Matching Conjecture. Let $m_q(n,k,s)$ denote the maximum cardinality of a family of $k$-dimensional subspaces of an $n$-dimensional vector space over $\mathbb F_q$ with no $s+1$ members whose sum is direct. Two natural constructions provide lower bounds. The first consists of all $k$-subspaces contained in a fixed $((s+1)k-1)$-dimensional subspace; the second consists of all $k$-subspaces that intersect a fixed $s$-dimensional subspace nontrivially. These constructions motivate the following vector-space analogue of the Erd\H{o}s Matching Conjecture: for all $n\ge (s+1)k$, $$m_q(n,k,s)=\max\left\{\genfrac{[}{]}{0pt}{}{(s+1)k-1}{k}_q,~\genfrac{[}{]}{0pt}{}{n}{k}_q-q^{ks}\genfrac{[}{]}{0pt}{}{n-s}{k}_q\right\}.$$ We prove this conjecture when $k=2$, when $n=(s+1)k$, and when $n$ is sufficiently large. In particular, the case $k=2$ may be viewed as a vector-space analogue of the Erd\H{o}s--Gallai theorem. In the large-$n$ range, we also prove a Hilton--Milner-type stability theorem, determining the largest nontrivial families with this property. Finally, we connect this problem with $t$-cover-free families in vector spaces and determine their extremal number up to a lower-order term, extending a recent result of Shan and Zhou for the special case $t=2$. The proofs combine Lov\'asz's minimax theorem for matroid matchings, a high-dimensional Hoffman bound for uniform hypergraphs, and packing-design arguments in vector spaces.

math.CO↗

arXiv2026

Synergistic Dual-Branch Adaptation for Multi-modal Generalized Category Discovery

Generalized Category Discovery (GCD) aims to classify old categories and discover new ones from unlabeled data. Recent multi-modal approaches introduce retrieved or synthesized texts into a dual-branch architecture to provide semantic cues complementary to visual features. However, the cross-modal synergy in existing dual-branch methods remains coarse and incomplete: the two modalities are encoded independently with the bias and noise in the derived text left unaddressed during encoding, and existing mutual learning strategies operate only on global class-level anchors, lacking fine-grained relational supervision. To address these limitations, we propose the Synergistic Dual-Branch Adaptation (SDBA) framework, which serves as a plug-and-play enhancement compatible with existing dual-branch methods such as GET and TextGCD. SDBA comprises two components: the cross-modal synergistic adapter inserts lightweight adapters into both branches and further injects visual information into the text adapter at each encoder layer to enhance text feature learning during encoding; the neighborhood mutual learning module enforces consistent local neighborhood distributions between the two branches via bidirectional KL divergence, providing fine-grained relational supervision for both old and new classes. Extensive experiments on six benchmarks demonstrate state-of-the-art performance, and consistent improvements on different baselines validate the broad scalability of the proposed framework.

cs.CV↗

arXiv2026

Mixed Torsion on Right Triangles and the P\'olya--Szeg\H{o} Monotonicity Problem for Regular Polygons

Motivated by the polygonal P\'olya--Szeg\H{o} conjecture for torsional rigidity, we study two monotonicity problems for torsional rigidity. The first concerns a mixed torsion problem on fixed-area right triangles, with a Dirichlet condition on one leg and Neumann conditions on the other leg and on the hypotenuse. We prove that the mixed torsional rigidity strictly increases as the ratio of the Neumann leg to the Dirichlet leg increases. The proof uses a Hadamard shape derivative, a Pohozaev-type identity, and a monotonicity result for the mixed torsion function. We also prove a similar result for the mixed ground state of Laplacian. The second concerns regular polygons. If $P_N$ denotes the regular $N$-gon of area $\pi$, we prove, by a purely analytic Schwarz--Christoffel/Bergman analytic-content argument, that \[ T^D(P_{N+1})>T^D(P_N),\qquad N\ge3, \] where $T^D$ is the Dirichlet torsional rigidity. We also obtain the asymptotic expansion \[ T^D(P_N)=\frac{\pi}{8}-\frac{\pi\zeta(3)}{N^3} +\frac{\pi^5}{45N^4}+O(N^{-5}). \]

math.AP↗

arXiv2026

Looped Transformers with Layer Normalization Provably Learn the Power Method

Transformers have achieved remarkable success across a wide range of applications, and a growing body of work suggests that part of their strength comes from their ability to learn and execute algorithmic procedures. However, our understanding of how transformers learn such algorithms remains limited, especially in the presence of layer normalization (LN). In this work, we study principal component prediction as a concrete testbed for understanding the training dynamics of transformers with LN. We prove that a looped linear transformer with LN, trained by gradient descent, converges to a solution that implements the power method, with each self-attention layer performing one power iteration. Notably, the model is trained only for principal component prediction, rather than being explicitly supervised to implement the power method. Our finding thus reveals an "algorithmic implicit bias" of looped transformers with LN: principal-component prediction can in principle be achieved by many mechanisms, yet gradient descent selects one that realizes the power method. We further provide a concrete comparison between transformers with and without LN: even with layerwise guidance from power iterations, a transformer without LN cannot exactly learn the power method, whereas the corresponding transformer with LN can, leading to a provable performance gap in principal component prediction. Our results provide, to our knowledge, the first theoretical analysis of the training dynamics of looped and single-layer transformers with LN, and shed light on the role of LN in transformer models.

cs.LG↗

arXiv2026

The MiniMax-M2 Series: Mini Activations Unleashing Max Real-World Intelligence

We introduce the MiniMax-M2 series, a family of Mixture-of-Experts language models built around the principle that mini activations can unleash maximum real-world intelligence. The flagship M2 contains 229.9B total parameters with only 9.8B activated per token. Designed end-to-end for agentic deployment, the M2 series rests on three components: (i) agent-driven data pipelines producing large-scale, verifiable trajectories across agentic coding and agentic cowork, each grounded in an executable workspace and an artifact-aligned reward; (ii) Forge, a scalable agent-native RL system that adapts to long-horizon agent trajectories, paired with windowed-FIFO scheduling, prefix-tree merging, inference optimization, and a clean training-inference-agent decoupling that supports both white-box and black-box agents; (iii) the latest M2.7 checkpoint takes an early step toward self-evolution -- autonomously debugging training runs and modifying its own scaffold. Across M2 through M2.7, this combination translates a mini-activation footprint into frontier-tier performance on agentic coding, deep search, office-task, and reasoning benchmarks.

cs.AI↗

arXiv2026

Sharp asymptotic bounds for uniform union-free hypergraphs

An $r$-uniform hypergraph is called $t$-union-free if any two distinct subsets of at most $t$ edges have distinct union. The study of union-free hypergraphs has multiple origins and a long history, dating back to the works of Kautz and Singleton (1964) in coding theory, Bollob\'as and Erd\H{o}s (1976) in combinatorics, and Hwang and S\'os (1987) in group testing. Let $U_t(n,r)$ denote the maximum number of edges in an $n$-vertex $t$-union-free $r$-uniform hypergraph. In this paper, we determine the asymptotic behavior of $U_t(n,r)$, up to a lower order term, for almost all $t\ge 3$ and $r\ge 3$. This significantly advances the understanding of this extremal function, as previously, only the asymptotics of $U_2(n,3)$ and $U_2(n,4)$ were known. As a key ingredient of our proof, we establish the existence of near-optimal locally sparse induced hypergraph packings, which is of independent interest.

math.CO↗

arXiv2026

Transformers Efficiently Perform In-Context Logistic Regression via Normalized Gradient Descent

Transformers have demonstrated remarkable in-context learning (ICL) capabilities. The strong ICL performance of transformers is commonly believed to arise from their ability to implicitly execute certain algorithms on the context, thereby enhancing prediction and generation. In this work, we investigate how transformers with softmax attention perform in-context learning on linear classification data. We first construct a class of multi-layer transformers that can perform in-context logistic regression, with each layer exactly performing one step of normalized gradient descent on an in-context loss. Then, we show that our constructed transformer can be obtained through (i) training a single self-attention layer supervised by one-step gradient descent, and (ii) recurrently applying the trained layer to obtain a looped model. Training convergence guarantees of the self-attention layer and out-of-distribution generalization guarantees of the looped model are provided. Our results advance the theoretical understanding of ICL mechanism by showcasing how softmax transformers can effectively act as in-context learners.

cs.LG↗

arXiv2026

Low-complexity Frequency Domain Equalization for filtered-AFDM over General Physical Channels

Affine frequency division multiplexing (AFDM) has emerged as a promising waveform for high-mobility communications. However, its equalization remains a practical challenge under general physical channels with off-grid delay and Doppler effects. In this paper, we investigate frequency domain equalization for AFDM by considering a practical filtered-AFDM waveform. We analyze the input-output relations of filtered-AFDM across various domains and show that off-grid effects lead to severe inter-symbol interference in the DAFT domain, limiting the effectiveness of DAFT domain equalization. Motivated by the compactness of the frequency domain channel matrix in wideband systems, we propose a low-complexity two-stage frequency domain equalization scheme. Numerical results demonstrate that the proposed approach achieves performance close to full-block LMMSE equalization with significantly reduced computational complexity, and offers clear advantages over time domain equalization in wideband scenarios.

eess.SP↗