arXiv subjects

Jiacheng Sun

Publications and source records attributed to Jiacheng Sun.

At least 19 recordsLinked to original sources

arXiv2026

Can LLMs Reliably Grade Olympiad Proofs? A Study of Mathematical Verification with LLMs

Large Language Models (LLMs) have made remarkable progress on solving competition-level mathematics, yet their ability to verify natural-language mathematical proofs remains relatively underexplored. This gap is especially pronounced for Olympiad-level proofs, which require meticulous assessment of each claim in a long reasoning chain. Current proof verification thus primarily relies on expert inspection, which is costly to scale. In this paper, we present a systematic study of LLM-based verification in this setting. Specifically, we introduce a human-curated dataset of USAMO 2025 candidate solutions with expert grading, and conduct a broad evaluation of existing LLM verifiers across frontier models. We also propose TROJAN, an iterative self-critique pipeline for generating high-fidelity adversarial proofs at scale. Our comprehensive evaluation covers 20 models spanning seven metrics, two prompt styles, three inference methods, and three prompt templates, showing that state-of-the-art models still leave considerable room for improvement. To narrow this gap, we propose MABGrader, a Multi-Armed Bandit framework that reframes grading as arm selection over the discrete score space. MABGrader outperforms the SOTA ProofGrader by 26.4% in Quadratic Weighted Kappa and reduces grading error by 14%. Code and dataset are available at https://github.com/aziksh-ospanov/TROJAN.

cs.AI↗

arXiv2026

Classification of Hom--Lie structures on finite-dimensional simple Lie algebras

We classify the Hom--Lie structures on finite-dimensional simple Lie algebras over an algebraically closed field of characteristic different from $2$ and $3$. Except for the three-dimensional simple Lie algebra and the Zassenhaus algebras, every such structure is a scalar multiple of the identity. In the two exceptional cases, we determine the full Hom--Lie space: it has dimension six for the three-dimensional algebra, while for a Zassenhaus algebra it consists precisely of the multiplication operators arising from the corresponding divided-power algebra. This proves a conjecture of Makhlouf and Zusmanovich.

math.RA↗

arXiv2026

Generative End-to-end Ad Retrieval at Douyin

Generative retrieval reformulates recommendation as the generation of discrete item tokens. However, scaling this paradigm to real-world recommender systems reveals two critical bottlenecks: 1) Representation collapse, where the item tokenizer converges to degenerate results under continuous distribution shifts, fundamentally hindering stable end-to-end adaptation. 2) Item collisions, where the massive candidate pool causes distinct items to share identical token sequences, compromising the final retrieval precision. Crucially, these bottlenecks are inherently coupled: expanding codebook capacity to mitigate collisions inevitably exacerbates collapse. To address them simultaneously, we propose GEAR, an end-to-end framework that jointly optimizes the tokenizer, generator, and reranker. To mitigate representation collapse, we introduce BasisVQ, which re-parameterizes the codebook via an orthogonal basis to enable global gradient sharing and rigid spatial rotation of the latent space, effectively stabilizing gradient dynamics without ad-hoc heuristics. We further extend it to prefix-aware BasisRQ, substantially enhancing the codebook's expressiveness with the same asymptotic time complexity. To resolve item collisions, GEAR integrates a context-conditioned reranking head into the generative process, efficiently disambiguating colliding items with minimal computational overhead. By unifying stable tokenization and joint reranking within an end-to-end generative framework, GEAR establishes a fully differentiable and scalable paradigm. It currently serves hundreds of millions of daily active users on Douyin Ads, yielding substantial empirical improvements in extensive online A/B tests.

cs.IR↗

arXiv2026

Experimental certification of multipartite Bell correlations using only few-body symmetric correlations

Certifying Bell correlations in increasingly larger multipartite quantum systems is challenging because conventional Bell inequalities rely on many-body correlations, which become experimentally demanding to estimate as system size grows. Here we demonstrate that multipartite Bell correlations can be certified using few-body permutation-invariant (PI) correlations with a fixed maximal correlation order. We experimentally test few-body PI Bell correlation witnesses tailored for six- and eight-photon postselected Dicke states. The addition of a few four-body correlators is found to significantly enhance the noise tolerance compared with previously studied two-body witnesses: for instance, for six qubits, the selected witness tolerates a white-noise fraction of $p_c\approx0.301$, compared with $p_c\approx0.048$ for the best two-body PI inequality with the same two settings per party. For six and eight photons respectively, we observe violations of the witness bounds by $32$ and $8.9$ standard deviations, arising from postselected polarisation states with fidelities of $0.933(4)$ and $0.916(11)$ to the corresponding half-excitation Dicke states. The witnesses for the six- and eight-photon cases use the same symmetric two- and four-body correlators, just with different coefficients. These results demonstrate an experimentally accessible approach for certifying multipartite Bell correlations in larger systems without requiring full-body correlation measurements.

quant-ph↗

arXiv2026

Loss-Resilient Quantum Networking with Dicke Entanglement

Multipartite entanglement can endow a quantum network with capabilities unavailable classically, yet their evolution under progressively reduced physical and informational access remains largely unexplored. Here we realize the first eight-photon half-excitation Dicke state, with a fidelity of 0.922(11), and use it to implement two distinct network tasks: open-destination teleportation and quantum telecloning. An unknown state can be teleported from one agent to any of seven remote agents with fidelities of 0.926(7)-0.941(6), while seven approximate clones are distributed with a fidelity of 0.713(3), close to the optimal value of 5/7. The protocol remains above the classical limit under imperfect photon detection, transmission loss and missing information from participating agents, and outperforms the corresponding GHZ benchmarks. As fewer agents contribute, the teleportation fidelity falls through a stepwise hierarchy whose two extremes recover open-destination teleportation and optimal telecloning, connecting both tasks within a single operational framework. These results establish Dicke entanglement as a promising architecture for loss-resilient quantum networks, opening a route towards quantum technologies that retain useful functionality under realistic operating conditions.

quant-ph↗

arXiv2026

AdaFlash: Adaptive Speculative Decoding via On-Policy Distilled Diffusion Drafters

Speculative decoding, in which a lightweight draft model first generates a draft sequence that is then verified by the target model, has become a prevalent paradigm for accelerating large language model inference. Recent work such as DFlash further boosts drafting efficiency by leveraging diffusion drafters, whose parallel denoising mechanism enables draft generation in a single forward pass. In this work, we uncover a central pitfall of diffusion drafters: the global dependency, arising from bidirectional attention and KV injection in diffusion drafters, is a double-edged sword. On one hand, it endows the model with parallel generation and global contextual modeling capabilities; on the other hand, this global dependency introduces high variance at both the domain-level and the token-level: acceptance rates fluctuate substantially across different domains, and the acceptance probability varies across draft positions. To tackle this issue, we propose the AdaFlash framework, comprising two components: (i) an on-policy distillation (OPD) algorithm with reverse-KL divergence tailored for diffusion drafters, which delivers stable convergence and continuously adapts the drafter to the deployment distribution; and (ii) an adaptive length head that dynamically adjusts the candidate length on the fly, substantially lowering the verification cost of the target model. Experiments demonstrate that AdaFlash consistently improves the speedup during deployment, with especially significant gains under high-concurrency, achieving up to 66% higher average throughput than previous state-of-the-art methods. Our code is available at https://github.com/ZinYY/AdaFlash.

cs.LG↗

arXiv2026

Less Uniform Discrete Diffusion is More Powerful and Scalable

Although uniform diffusion language models (UDLMs) represent a promising diffusion paradigm, scaling them remains challenging. We identify the core obstacle as an over-uniform training objective and condition-target confusion during sampling. To address these, we propose Less Uniform Diffusion (LUDI), a novel UDLM framework. Specifically, we (i) introduce a less uniform loss that directs each reverse transition toward the clean token, and (ii) equip the model with per-token time embeddings that supply token-level corruption hints, enabling confidence-based few-step sampling. Experiments across scales show that LUDI yields cleaner supervision and improves few-step generation. We further continue-train a 7B autoregressive model into LUDI-7B, resulting in a UDLM capable of complex reasoning. It achieves a 3-token-per-step speedup over AR decoding and competitive performance compared with masked diffusion baselines, revealing that the full potential of UDLMs for complex generation remains to be unlocked.

cs.CL↗

arXiv2026

Matrices as graded BiHom-algebras and decompositions

We present matrices as graded regular BiHom-associative algebras and study several features of their decompositions. More precisely, we introduce a notion of connection in the support of the grading and use it to construct a family of canonical graded ideals. We show that, under suitable assumptions, including $Σ$-multiplicativity, maximal length and triviality of the centre, the matrix regular BiHom-associative algebra decomposes into a direct sum of graded simple ideals. We further extend our results to general graded regular BiHom-associative algebras over arbitrary base fields. As applications, we reinterpret classical gradings on matrix algebras such as those induced by Pauli matrices and the $\mathbb{Z}_n \times \mathbb{Z}_n$-grading in terms of our setting.

math.RA↗

arXiv2026

Unveiling the Scaling Potential of Drain Merge through Active (DMtA) in CFETs: Breaking the Super-Via Bottlenecks and Unlocking New PPA Boosters

Drain merge (DM), a super via vertically connecting the common S/D terminals of stacked n/pFETs in Complementary FETs (CFETs), blocks further parasitic optimization and cell scaling. For the first time, this work systematically investigates the state-of-the-art Drain Merge through Active (DMtA), a revolutionary technology reported recently with the DM embedded in the active region, through a comprehensive DTCO framework spanning process integration, contact-configuration-dependent (CTCD) compact modeling, standardcell design, RO evaluation and block-level PPA benchmark on a 32-bit RISC-V Ibex core. By reducing DM parasitics and enabling DM-width optimization, DMtA improves RO frequency by 11.7% over its conventional Drain Merge through field (DMtF) counterpart. Active widening and Area Borrowing, the latter first reported in [8] and exploiting spatial slack in adjacent cells to further enlarge the nanosheet width (WNS), increase the maximum Ibex-core frequency by up to 34.8%. More importantly, DMtA also enables the once GAA-exclusive Hyper-cells on CFETs by merging the active regions across adjacent cell rows, providing a further 8.7% frequency gain. A post-routing floating-output-pin-aware optimization further removes redundant S/D contacts (CTs) and reduces power by 5.3%. Finally, DMtA facilitates more area-efficient 2.5T cell scaling by preserving single-row cell compatibility, reducing post-PR core area by 25.7%.

cond-mat.mes-hall↗

arXiv2026

Any-Order GPT as Masked Diffusion Model: Decoupling Formulation and Architecture

Efficiently scaling Large Language Models (LLMs) necessitates exploring alternatives to dominant autoregressive (AR) methods, with Masked Diffusion Models (MDMs) emerging as candidates. However, comparing AR (typically decoder-only) and MDM (often encoder-only) paradigms is confounded by differing architectures, obscuring true algorithmic and efficiency trade-offs. This research decouples these factors by evaluating MDMs within a decoder-only framework to: (1) Equitably compare MDM (as Any-Order AR) and standard AR paradigms through discrepancies on orders. (2) Investigate MDM architectural impacts on computational efficiency. We show decoder-only MDMs, despite a larger modeling space, can achieve significant inference speedups ($\sim25\times$) and comparable perplexity with techniques like temperature annealing, offering a path to reduced inference compute. This work provides insights for developing more computationally efficient foundation models by disentangling core modeling choices from architectural influences. Code is available at https://github.com/scxue/AO-GPT-MDM.

cs.LG↗

arXiv2026

Bridging Object Detection and Segmentation with Polygon Detection Transformers

Box detection and mask segmentation are two dominant paradigms for foreground representation: boxes are efficient but too coarse for object shapes, while masks are accurate but over-modeled for compact geometry. To bridge this gap, we present a Polygon Detection Transformer (Poly-DETR) built upon Polar Representation, where object queries regress a starting point and its fixed number of radial distances to directly construct the contour-approximating polygon. This formulation can be integrated into most DETR-like detectors by linear extension, since box is a degenerate case of Polar Representation with four rays. Furthermore, we propose two simple but necessary designs, Polar Deformable Attention and Position-Aware Training Scheme, to align feature sampling and polygon supervision. As a DETR-oriented advancement of Polar Representation, Poly-DETR outperforms existing polar-based methods by 4.7 mAP on MS COCO. Moreover, we explore the application regimes of polygon detection in geometry-driven domains, including remote sensing, medical imaging, and autonomous driving. In particular, Poly-DETR shows stronger scalability than its mask-based counterpart in high-resolution scenarios. Additional experiments show that, owing to its Transformer structure, Poly-DETR can be naturally extended to recent DETR variants equipped with foundation-model priors.

cs.CV↗

arXiv2026

Exploring More to Solve More: Boosting Diversity in Text Diffusion Models via Entropy-Based Guidance

Although diffusion models have revolutionized continuous domains like image synthesis through high quality generations and controllable guidance mechanisms, bringing this controllability to the discrete, sequential nature of text remains an open challenge. Meanwhile, current sampling strategies and guidance methods adjust token likelihoods without capturing the broader semantic landscape, leading to a suboptimal balance between fidelity and diversity. In this work, we introduce a novel training-free Semantic-Aware Kernel Entropy (SAKE) guidance method. Our method computes the order-2 Rényi entropy over a kernel Gram matrix that captures both cross-token semantic interactions and relative token positions. By linearizing this objective in the embedding space, we derive a tractable guidance signal that dynamically adjusts the sampling distribution, flattening it to encourage exploration during redundancy and sharpening it for fidelity when diverse. Empirical experiments demonstrate that our approach achieves a superior Pareto frontier between fidelity and diversity, and improves multi-sample performance on reasoning-intensive tasks, such as code and mathematics generation, compared to temperature scaling and discrete guidance baselines.

cs.CL↗

arXiv2026

ViewMask-1-to-3: Multi-View Consistent Image Generation via Multimodal Discrete Diffusion Models

Motivated by discrete diffusion's success in language-vision modeling, we explore its potential for multi-view generation, a task dominated by continuous approaches. We introduce ViewMask-1-to-3, formulating multi-view generation as a discrete sequence modeling problem where each viewpoint is represented as visual tokens from MAGVIT-v2. Through discrete diffusion via masked token prediction, our approach enables progressive multi-view generation via iterative token unmasking, unifying language and vision in a shared token space. Importantly, simple random masking combined with self-attention naturally encourages cross-view consistency without specialized architectures or 3D geometric priors. Our method outperforms the baseline on the GSO and 3D-FUTURE benchmarks, ranking first on average across standard image metrics, and achieving a 10.6% higher IoU than continuous diffusion models on 3D-FUTURE. Furthermore, the proposed framework can be naturally extended to support text-to-image generation and multimodal understanding, highlighting its potential toward a more unified paradigm for multimodal understanding and generation.

cs.CV↗

arXiv2026

HERMES: Towards Efficient and Verifiable Mathematical Reasoning in LLMs

Informal mathematics has been central to modern large language model (LLM) reasoning, offering flexibility and efficient construction of arguments. However, purely informal reasoning is prone to logical gaps and subtle errors that are difficult to detect and correct. In contrast, formal theorem proving provides rigorous, verifiable mathematical reasoning, where each inference step is checked by a trusted compiler, but lacks the exploratory freedom of informal problem-solving. This mismatch leaves current LLM-based math agents without a principled way to combine the strengths of both paradigms. In this work, we introduce Hermes, the first tool-assisted agent that explicitly interleaves informal reasoning with formally verified proofs in Lean. The framework performs intermediate formal checking to prevent reasoning drift and a memory module for proof continuity across multi-step reasoning chains, enabling both exploration and verification. We evaluate Hermes on four challenging mathematical reasoning benchmarks using LLMs of varying parameter scales, from small models to state-of-the-art systems. Across all settings, Hermes reliably improves the reasoning accuracy of base models while substantially reducing reasoning token usage and computational cost compared to reward-based approaches. On difficult datasets such as AIME and HARDMath2, Hermes@1 achieves up to a 40% accuracy improvement while using 80% fewer total inference FLOPs. When scaled at test time, Hermes@5 boosts accuracy further by 20%. The implementation and codebase are publicly available at https://github.com/aziksh-ospanov/HERMES.

cs.AI↗

arXiv2026

Metasurface Holography on a Relative-Phase Manifold for Stable and High Fidelity Tweezer-Array Generation

We present a new holographic approach for generating large scale, polarization resolved optical tweezer arrays. By analyzing the ideal Jones fields that realize a target pattern, we identify that the fundamental degrees of freedom are the relative phases of the individual tweezers, rather than the full spatial phase profile. Leveraging this insight, we formulate a reverse projection optimization that adjusts only a small set of phase parameters to approximate the ideal operator within the physical constraints of a metasurface. This produces significantly higher fidelity and robustness than Gerchberg_Saxton type algorithms. Experimentally, we demonstrate H, V, L, and R polarized tweezer arrays using a single layer metasurface. A key advantage of our method is its phase stability, yielding strong resistance to optical aberrations and enabling coherent global phase modulation such as forming vortex tweezer lattice, without degrading trap quality. This framework provides a conceptually clear and experimentally powerful route for scalable optical field synthesis.

physics.optics↗

arXiv2026

The Structural Origin of Attention Sink: Variance Discrepancy, Super Neurons, and Dimension Disparity

Despite the prevalence of the attention sink phenomenon in Large Language Models (LLMs), where initial tokens disproportionately monopolize attention scores, its structural origins remain elusive. This work provides a \textit{mechanistic explanation} for this phenomenon. First, we trace its root to the value aggregation process inherent in self-attention, which induces a systematic variance discrepancy. We further demonstrate that this discrepancy is drastically amplified by the activation of super neurons within Feed-Forward Network (FFN) layers. Specifically, the channel-sparse down-projections trigger a dimension disparity of the first-token representation, necessitating the formation of attention sinks as a structural anchor. Then, we validate this causal chain through two controlled interventions: (i) isolating the aggregation effect via attention mask modifications and (ii) amplifying the variance of targeted token representations. Both interventions can replicate attention sinks at arbitrary positions. Our mechanistic understanding offers a foundation for the systematic control of sink formation. Finally, as a proof of concept, we propose \textit{head-wise RMSNorm}, an architectural modification that stabilizes value aggregation outputs during pre-training. Our experiments demonstrate that restoring statistical parity across positions significantly accelerates convergence.

cs.LG↗

arXiv2026

Variational Autoencoding Discrete Diffusion with Enhanced Dimensional Correlations Modeling

Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively unmasking multiple dimensions from an all-masked input, but their performance can degrade when using few denoising steps due to limited modeling of inter-dimensional dependencies. In this paper, we propose Variational Autoencoding Discrete Diffusion (VADD), a novel framework that enhances discrete diffusion with latent variable modeling to implicitly capture correlations among dimensions. By introducing an auxiliary recognition model, VADD enables stable training via variational lower bounds maximization and amortized inference over the training set. Our approach retains the efficiency of traditional MDMs while significantly improving sample quality, especially when the number of denoising steps is small. Empirical results on 2D toy data, pixel-level image generation, and text generation demonstrate that VADD consistently outperforms MDM baselines in sample quality with few denoising steps.

cs.LG↗

arXiv2026

ICG: Improving Cover Image Generation via MLLM-based Prompting and Personalized Preference Alignment

Recent advances in multimodal large language models (MLLMs) and diffusion models (DMs) have opened new possibilities for AI-generated content. Yet, personalized cover image generation remains underexplored, despite its critical role in boosting user engagement on digital platforms. We propose ICG, a novel framework that integrates MLLM-based prompting with personalized preference alignment to generate high-quality, contextually relevant covers. ICG extracts semantic features from item titles and reference images via meta tokens, refines them with user embeddings, and injects the resulting personalized context into the diffusion model. To address the lack of labeled supervision, we adopt a multi-reward learning strategy that combines public aesthetic and relevance rewards with a personalized preference model trained from user behavior. Unlike prior pipelines relying on handcrafted prompts and disjointed modules, ICG employs an adapter to bridge MLLMs and diffusion models for end-to-end training. Experiments demonstrate that ICG significantly improves image quality, semantic fidelity, and personalization, leading to stronger user appeal and offline recommendation accuracy in downstream tasks. As a plug-and-play adapter bridging MLLMs and diffusion models, ICG is compatible with common checkpoints and requires no ground-truth labels during optimization.

cs.CL↗