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Tao Luo

Publications and source records attributed to Tao Luo.

At least 19 recordsLinked to original sources
arXiv2026

Multi-dimensional centered rarefaction waves of gas dynamics with vacuum states

We establish the local-in-time structural stability of two centered rarefaction waves bounding a vacuum region for the two-dimensional isentropic Euler equations with $p(ρ)=kρ^γ$, for $γ\in(1,1.3]\cup\{\frac75,\frac53\}$. For general sufficiently small perturbations of the planar Riemann data, allowing nonzero vorticity, we construct an entropy solution that is continuous for positive time and whose five regions are separated by four characteristic surfaces. The conservative solution has uniform spatial $W^{2,\infty}$ bounds on each time slice of the central region in coordinates $(x_1/t,x_2)$; for $γ=7/5,5/3$, we also obtain spacetime $W^{2,\infty}$ regularity in $(t,x_1/t,x_2)$. The proof develops characteristic geometry directly for the symmetric first-order Euler system and uses two overlapping characteristic charts to separate matching with the exterior flow from estimates uniform up to vacuum. Fixed commutators without sound-speed weights exhibit a first-order null structure, while subtraction of explicit approximate solutions produces damping that cancels the leading antidamping bulk terms in the energy identity. An explicit analysis of the initial-slice ODEs identifies fractional powers and logarithmic terms at zero sound speed. The logarithmic coefficients couple vorticity to tangential variation of the initial data, revealing an obstruction to higher spatial regularity even when the powers of the sound speed have integer exponents. This analysis determines the finite approximation order used to close the energy and geometric estimates in the stated range. These ingredients provide the geometric and energy framework for the forthcoming second paper of this series, which will use finite evolving profiles to treat the full range $γ\in(1,\frac53]$.

math.AP↗
arXiv2026

Cavity collapse and kinetic energy concentration in three-dimensional free-boundary Euler flow

We construct smooth axisymmetric solutions of the three-dimensional incompressible free-boundary Euler equations in bounded domains for which a tubular cavity collapses onto a circle at a finite time $T$. The velocity has a single-valued potential, and the construction applies without surface tension and with any fixed positive surface tension. Both boundary components remain embedded and disjoint before collapse, while the outer boundary converges smoothly. The terminal outer meridional domain may be any smooth bounded simply connected domain whose closure is separated from the rotation axis; the interior point generating the collapse circle and the positive concentrated energy may be prescribed independently. We prove a sharp collapse law with radius asymptotic to an explicit multiple of $(T-t)^{1/2}|\log(T-t)|^{-1/4}$, determine curvature blow-up asymptotics, and show that kinetic energy concentrates uniformly on the circle. For a canonical reflection symmetric family, we identify a common cylindrical spacetime limit and sharp velocity and pressure profiles. At every fixed spatial point in the region enclosed by the limiting outer boundary and away from the collapse circle, the velocity tends to zero while the pressure tends to positive infinity. For this family, we characterize the topology of the limiting material map and prove its optimal $1/2$-Hölder regularity and sharp $W^{1,p}$ threshold $1\le p<2$, with first derivatives in weak $L^2$ but not in $L^2$. These canonical solutions admit weak continuations that preserve mass and momentum and whose total energy drops at collapse by exactly the concentrated kinetic energy.

math.AP↗
arXiv2026

UniSGR-V2: Stepwise Target-Side Feature Anticipation and Crossing for Generative Recommendation

Semantic-ID-based generative recommendation unifies retrieval and ranking through autoregressive decoding but differs structurally from discriminative models, which can directly access rich target-item side features. The attributes are compressed into a finite codebook during quantization, while the target item remains undetermined during decoding and its features cannot be looked up. This target-side feature vacuum weakens generation at each semantic-ID level through high conditional entropy and cascading errors, and final ranking through missing target-side feature crossing. Existing methods interact with candidate representations or generate discrete attribute tokens, but none reconstructs a continuous target-side representation inside decoding to support both stepwise generation and ranking. We propose TacGR (Stepwise Target-Side Feature Anticipation and Crossing for Generative Recommendation). Before decoding each codeword, TacGR anticipates a continuous target-side feature vector and crosses it with the semantic prefix and user behavior sequence inside the decoder. The crossed representation conditions current-level generation and is directly used for ranking. Continuous-vector regression risks a learnable target collapsing with its prediction and prediction noise propagating into generation through attention. TacGR addresses these challenges with a semantic-anchoring auxiliary tower and a unidirectional visibility mask, respectively. For extremely long industrial behavior histories, it introduces gated convolutional denoising to suppress noise and adapts the pyramid memory funnel to reduce inference cost. Offline experiments on a large-scale Lazada dataset show significant gains over OneRec, UniRec, and UniSGR. Online A/B testing improves IPV, Order, and GMV by 0.79%, 5.55%, and 3.09%, respectively.

cs.IR↗
arXiv2026

A SAV Neural Network Method for Allen--Cahn and Cahn--Hilliard Equations

Phase-field equations are fundamental examples of gradient-flow systems and require numerical solvers that preserve intrinsic energy dissipation. In this work, we propose a neural network-based method that combines an SAV time discretization with a mesh-free neural representation. We establish the unconditional energy stability of the underlying SAV semi-discretization, quantify the energy defect caused by solver residuals, and derive a conditional high-probability error estimate for the Allen--Cahn equation. Numerical experiments show that our approach consistently exhibits energy-stable behavior, while outperforming existing neural network-based solvers.

math.NA↗
arXiv2026

Efficient Dataset Distillation for Pre-Trained Self-Supervised Models via Statistical Flow Matching

Dataset distillation seeks to synthesize a compact surrogate dataset that enables performance comparable to training on the original dataset for downstream tasks. For the scenario where pre-trained self-supervised models serve as priors, traditional Linear Gradient Matching optimizes synthetic images by encouraging them to mimic the gradient updates induced by real images on the linear probe. However, this batch-level formulation requires loading thousands of real images and applying multiple differentiable augmentations to synthetic images at each distillation step, leading to substantial computational and memory overheads. In this paper, we revisit the linear gradient and theoretically derive that it is essentially a local relative distribution directed from target class centers toward non-target class centers, which we term flow. This property causes suboptimality and instability, often necessitating expensive multiple augmentations to compensate. To address this, we introduce Statistical Flow Matching, an optimal, stable, and efficient supervised learning framework that optimizes synthetic images by aligning global statistical flows in the original data. Our approach loads raw statistics only once and performs a single augmentation pass on the synthetic data, achieving performance comparable to or better than the state-of-the-art method with 10x less GPU memory usage and 4x faster distillation time. Moreover, increasing the number of augmentations for our method yields further performance gains while incurring lower additional cost. Our code is publicly available at https://github.com/einsteinxia/SFM.

cs.CV↗
arXiv2026

Fyan: A Human--AI Harness with Semantic Auditing for Document-Level Formalization

We present FYAN, a human--AI harness for document-level mathematical formalization. Rather than treating theorems in isolation, FYAN coordinates an end-to-end workflow spanning specification, proof planning, logical review, Lean proof construction, knowledge curation, and validation, with support for independent supervision and human guidance. A central component is evidence-grounded semantic auditing, which assesses whether formal statements faithfully preserve their informal specifications. A language model constructs structured evidence over local correspondences, omissions, scope, and logical relations, while a deterministic validator checks this evidence and produces reproducible judgments. When a substantive but admissible deviation is accepted, FYAN requires an explicit proof-transfer obligation connecting the formal statement back to a source-facing interpretation. With the same model (DeepSeek-V4.1-Flash) in every stage, FYAN proves 86 of 143 FormalTCS theorems under a strict Lean check, against 69 for a general agent harness, and raises the natural-language proof score from 0.501 to 0.851. On ConsistencyCheck, its semantic audit catches more inconsistent statements than a direct LLM judge, both on labels verified against the source (recall 0.777 vs. 0.636) and on the original labels (0.873 vs. 0.820), and localizes each mismatch it reports to a specific hypothesis, conclusion, or scope. FYAN also built ODENumLib, a 9,355-line Lean library for the numerical analysis of ordinary differential equation.

cs.AI↗
arXiv2026

Hadamard Local Well-Posedness for Compressible Liquids with a Free Surface

We prove local well-posedness in the Hadamard sense for the three-dimensional compressible Euler equations governing a liquid with a free surface and no surface tension. Under the Taylor sign condition and the boundary compatibility conditions, we establish existence, uniqueness, and strong continuous dependence in a hybrid Sobolev class for every $s>3$. The velocity and interface have $H^s$ regularity, while the enthalpy and velocity divergence belong to $H^{s+1/2}$ and $H^{s-1/2}$, respectively. This separation reflects the coupling of a nondegenerate acoustic equation with the free-surface and vorticity dynamics. The proof uses regularization operators that smooth the moving domain and extend the nonlinear compatibility hierarchy, together with $L^2$ and partial $H^2$ distance estimates for solutions on different domains. Regular solutions are constructed by a regularized forward Euler scheme. High-order energy estimates and frequency envelopes then yield strong convergence of smooth approximations and continuity of the data-to-solution map. Integer Sobolev indices are treated using a Lions--Magenes endpoint compatibility condition.

math.AP↗
arXiv2026

Structure-Guided Masked Autoencoders for Ultra-High Resolution Scientific Image Understanding

Self-supervised pre-training with Vision Transformers, including Masked Autoencoders (MAE), is difficult to apply to gigapixel scientific images. Random masking is poorly matched to the structured, multi-scale morphology of scientific data, while uniform tokenization produces prohibitively long sequences that make $O(N^2)$ attention impractical. We propose SGMA, a structure-guided masked autoencoding framework for ultra-high-resolution scientific images. SGMA couples two components: a content-adaptive quadtree tokenizer that compresses gigapixel images into a fixed-length sequence, and a structure-conditioned masking process that biases reconstruction toward spatially informative regions. To stabilize this process across scales, we introduce Damped Accumulation (DA), which aggregates signal-dependent responses across the tree into a structure canvas used to guide masking. The resulting pre-training task preserves fine microstructure while remaining compatible with standard ViT encoders and MAE-style reconstruction. Across electron microscopy, whole-slide optical microscopy, and X-ray CT datasets, SGMA consistently outperforms MAE baselines. It achieves 95.68% Dice on the 8K x 8K x 28K SpringXCT dataset, improving over the same-architecture MAE baseline by +13.00 points, and 83.21% Dice on the 32K^2 WSI PAIP dataset, improving by +16.84 points, while providing up to a 24.8x inference speedup.

cs.CV↗
arXiv2026

Tool-Augmented On-Policy Distillation for LLM Domain Adaptation in Sequence-Based Omics Tasks

Multi-omics sequences contain complex biological patterns, yet deciphering their mechanisms for automated scientific discovery remains challenging. As large language models (LLMs) interpret these sequences, evaluating both predictions and scientific reasoning is critical. However, existing benchmarks for multi-omics sequence tasks rely on classification and regression metrics, neglecting whether models grasp the underlying biological evidence. We introduce OmicsBench, the first reasoning benchmark for multi-omics sequences, comprising 1,160 expert-validated questions across six tasks spanning DNA regulation, RNA processing, and protein function. OmicsBench requires traceable evidence chains, evaluated using instance-specific rubrics developed with domain experts. Evaluating 17 LLMs reveals an inverse relationship: while scientific LLMs outperform general-purpose LLMs in sequence classification accuracy, they fail to provide valid evidence to support their predictions. One plausible interpretation is shortcut learning: specialized models may rely on statistical patterns rather than the biological mechanisms needed for scientific discovery. Motivated by this finding, we introduce tool-augmented on-policy distillation (TA-OPD), a post-training method to align sequence prediction with evidence-grounded biological reasoning. Across five Qwen3.5 models spanning 0.8B to 27B parameters, TA-OPD consistently strengthens biological evidence grounding while improving predictive performance on most tasks. These gains persist across model scales, indicating that stronger sequence reasoning does not arise solely from increased model capacity, but can be improved through evidence-aware training. Together, OmicsBench and TA-OPD provide a framework for diagnosing reasoning failures in multi-omics LLMs and a path toward models whose predictions are better grounded in biologically meaningful evidence.

cs.LG↗
arXiv2026

Local Well-posedness of Free Boundary Problems for the Euler--Monge--Ampère Equations

We study the free-boundary Euler--Monge--Ampère system as a conservative relaxation of ideal incompressible fluid motion. The force is determined on the actual fluid domain by a Monge--Ampère equation coupled to a nonlinear boundary condition. For each fixed relaxation parameter, we establish local well-posedness for uniformly convex initial domains of class $C^{2,α}$, densities in $C^{1,α}$, and arbitrary initial velocities in $C^{2,α}$. The solution retains these spatial regularities, and the force potential belongs to $C^{3,α}$ up to the moving boundary. Within uniformly bounded data families, the solution depends continuously on the initial data at every lower Hölder exponent.

math.AP↗
arXiv2026

PhysBrain 1.5: From Vision-Language Models to Physical Foundation Models

We present PhysBrain 1.5, a unified model for understanding physical environments, generating actions, and predicting future states. Motivated by the physical loop of observation, interaction, and environmental change, we bring these capabilities into a common learning framework. Starting from a general vision--language model, we encode language responses, end-effector motion, and dense visual targets as discrete sequences and jointly optimize them with autoregressive next-token prediction. Pre-training draws its embodied supervision entirely from human interaction videos, using task-centered episodes to pair semantic and spatial context with recovered motion and subsequent observations. We then adapt the model through supervised fine-tuning on a mixture of human demonstrations, robot trajectories, and simulated experience. Across 28 embodied understanding benchmarks, our 8B model achieves an average score of 72.5, setting a new open-source state of the art and performing on par with leading proprietary models such as GPT-6-Astra and Gemini 3.6 Flash. It achieves the best open-source results on 14 benchmarks while retaining general multimodal capabilities. Beyond these understanding evaluations, qualitative examples show the model's ability to produce end-effector trajectories and predict future scenes through spatially aligned RGB, depth, and robot-mask outputs.

cs.CV↗
arXiv2026

LazFormer: Scaling Transformers for Industrial Recommendation via Transferable Generative Pre-training

Transformers have shown promising performance in LLMs due to their outstanding scalability, several studies have investigated the scalability of Transformers for industrial recommendation. They typically rely on a single ranking model to optimize both sparse and dense parameters from scratch, resulting in substantial computational resource consumption and slow convergence. Fortunately, the pre-training models offer an effective solution to the above issues by providing favorable initialization of both sparse and dense parameters for the subsequent ranking. However, they still face two major limitations: (1) Since the input features used in pre-training and ranking are usually inconsistent, directly transferring dense parameters from pre-training to ranking may lead to negative transfer. (2) Multi-epoch training during the ranking process may result in the overfitting of sparse parameters, while freezing the sparse parameters limits their adaptability to the ranking objectives. To this end, we propose a Scaling Transformer for Industrial Recommendation via Transferable Generative Pre-training, termed LazFormer. Specifically, we first present a generative pre-training module to autoregressively generate sequential features, providing favorable initialization of both sparse and dense parameters for the subsequent ranking. To solve the negative transfer of dense parameters, we propose a transferable residual adapter that injects additional ranking-specific features into ranking in a residual manner. Moreover, a request-aware ranking module integrates long-sequence compression, hybrid sparse attention, and a request-aware paradigm to efficiently model users' long sequences. Besides, we further propose an asymmetric multi-epoch training strategy that resets sparse parameters while continuously accumulating dense parameters across epochs, alleviating the overfitting of sparse parameters.

cs.IR↗
arXiv2026

MIMA: Multi-Interest Recommendation via Multi-Positive Exclusive Assignment

Multi-interest recommendation represents each user with multiple interest vectors for fine-grained candidate matching, yet it often suffers from interest collapse, where the learned interests converge to similar representations. We highlight the prevailing single-positive paradigm as one important factor behind this issue. Since each instance provides only one positive item, intents are optimized independently, potentially causing the same best-matching interest to be repeatedly updated toward different positives while leaving the others under-supervised. Moreover, existing methods rarely model how strongly a user activates each interest, leaving scores from different interest channels incomparable at inference. To address these problems, we propose MIMA, a Multi-Interest recommendation framework built on Multi-positive exclusive Assignment. MIMA groups items co-occurring within the same request into a positive set, generates complementary interests with a causal Transformer decoder, and exclusively assigns each positive to supervise a distinct interest via Hungarian matching, so that interest differentiation emerges from the training objective itself rather than auxiliary regularization. A lightweight routing module further estimates user-interest activation probabilities to calibrate scores across interest channels. Experiments on three public datasets and an industrial dataset show that MIMA consistently outperforms state-of-the-art baselines, and an online A/B test yields significant business gains.

cs.IR↗
arXiv2026

An Efficient Out-of-Core Tomographic Imaging Framework for Edge Devices

Computed Tomography (CT) is an essential 3D imaging technology widely used in medical diagnostics and scientific research. However, performing CT imaging on edge devices is challenging due to limitations in computational power, memory capacity, and energy budget. This paper presents an efficient CT reconstruction framework, called edgeFBP, designed for Nvidia Jetson System-on-Chip (SoC) devices. edgeFBP adopts an end-to-end pipeline design for efficient out-of-core image reconstruction under tight power and memory constraints. edgeFBP utilizes a mixed-precision strategy leveraging half-precision Tensor Cores (TCs) to accelerate the bottleneck back-projection (BP) kernel. edgeFBP achieves a 1.83x speedup over the widely used RTK library on Jetson Nano and a 2.56x speedup on Jetson AGX. Under a strict 25-Watt power budget, edgeFBP on Jetson Nano achieves up to 5-48x higher energy efficiency than an Nvidia DGX A100, enabling datacenter-scale imaging on constrained edge devices.

cs.DC↗
arXiv2026

STAR-Pro: Stage-Wise Token Adaptive Reduction with Progressive Refinement for Efficient Large Vision-Language Models

Large vision-language models (LVLMs) achieve strong multimodal understanding, but the hundreds to thousands of visual tokens they process impose substantial computational overhead, motivating training-free visual token pruning. In this work, we conduct two complementary analyses of visual token pruning. First, we measure the feature-space coverage of tokens retained before cross-modal fusion and find that aggressive pruning discards substantial visual information. Second, we track text-to-visual attention across decoder layers and find that the visual tokens considered important change substantially with depth, making one-shot pruning decisions unreliable. Together, these findings show that effective pruning should preserve broad visual coverage before fusion and progressively refine the retained tokens as cross-modal evidence evolves during fusion. We therefore propose STAR-Pro (STage-Wise Adaptive Token Reduction with Progressive Refinement), a training-free two-stage framework. Its Adaptive Stage applies pivoted QR to construct an over-budget feature-coverage candidate pool, while its Progressive Stage uses evolving text-to-visual attention at selected decoder layers to prune a nested survivor set under a target layer-average token budget. Extensive experiments across seven LVLMs spanning multiple architectures and 18 image and video benchmarks demonstrate the effectiveness of STAR-Pro under aggressive pruning. On LLaVA-Video-7B, STAR-Pro reduces visual tokens by 90.5%, retains 92.7% of baseline performance, and achieves a $2.24\times$ measured inference speedup. Code is available at https://github.com/EasonAI-5589/starpro.

cs.CV↗
arXiv2026

Scalable High-Fidelity Macromolecular Docking for GPU-Accelerated Supercomputers

Flexible macromolecular docking offers high-fidelity predictions of biomolecular interactions, but remains prohibitively expensive at scale. Among existing approaches, LightDock leverages Glowworm Swarm Optimization (GSO) for accuracy, yet suffers from limited parallelism, irregular computation, and severe load imbalance, preventing efficient execution on GPU supercomputers. We present SparkleDock, a scalable GSO-based docking framework enabling near-real-time flexible docking. We redesign GSO to expose massive fine-grained parallelism at the glowworm-agent level, and restructure the dominant energy scoring computation into a Tensor Core-compatible formulation, enabling efficient execution of irregular pairwise interactions through structured matrix operations. We further introduce a performance-model-driven scheduling for load balancing and out-of-core scaling across GPUs. SparkleDock achieves 9.7 $\times$ and 18.9 $\times$ speedups over LightDock on single A100 and H100 GPU, and delivers over two orders of magnitude acceleration at scale. On 512 GPUs, it reduces docking time from hours to seconds, enabling large-scale, high-fidelity virtual screening previously impractical with flexible docking.

cs.DC↗
arXiv2026

GoQuant: Geometric Orthogonal Residual Projection for Multiplier-Free Power-of-Two Transformer Quantization

The deployment of Large Language Models (LLMs) and Vision Transformers (ViTs) on edge devices is significantly constrained by memory capacity and the critical timing bottlenecks introduced by dense Multiply--Accumulate (MAC) arrays. In the ultra-low-bit regime, logarithmic Power-of-Two (PoT) quantization provides a hardware-efficient alternative by replacing general multiplications in the dominant dot-product computation with bit-shift operations. However, its non-uniform exponential lattice inherently suffers from a \textbf{Low Angular Resolution Regime}, a structural limitation that becomes particularly pronounced below 4-bit precision and can substantially degrade the representation of high-dimensional feature manifolds. To address this geometric limitation, we propose Geometric Orthogonal Residual Projection Quantization (GoQuant), an algorithm--hardware co-design framework for multiplier-reduced low-bit inference. By formulating quantization as a dual-basis geometric projection, GoQuant constructs a higher-resolution residual lattice while retaining a shift-and-add inner-product structure. Its analytical solver further avoids computationally intensive gradient-based or iterative search procedures. The data-free Geometric-Only (GEO) mode quantizes LLaMA-2-7B in only 0.47 minutes, while the Activation-Refined (REF) mode completes full-model quantization in approximately \textbf{4.4 minutes}.

cs.LG↗
arXiv2026

Classification of finite-time blow-up mechanisms for the incompressible free-boundary Euler equations with surface tension

We establish a blow-up criterion for strong solutions of the three-dimensional incompressible Euler equations with surface tension in a bounded domain with a closed moving free boundary. The criterion is formulated at the $H^3\times H^4$ regularity level of the Shatah--Zeng local well-posedness theory and imposes \textit{no} assumptions of symmetry, periodicity, graph structure, or simple connectedness. If the maximal existence time $T<\infty$, then at least one of the following four mechanisms must occur: (i) first self-intersection of the free boundary; (ii) loss of mean curvature regularity in $H^{\frac{3}{2}}$, or loss of boundary regularity in $H^{2+\varepsilon}$ for any sufficiently small fixed $\varepsilon>0$; (iii) loss of $H^{\frac{5}{2}}$ regularity of the normal boundary velocity; or (iv) $L^1_tL^\infty$ blow-up of the interior velocity gradient. For simply connected domains, the interior alternative admits a refinement involving only the $L^1_tL^\infty$-norm of the vorticity, and this refinement recovers exactly the classical Beale--Kato--Majda criterion in the fixed-boundary case. For irrotational flows in the simply connected free-boundary setting, the criterion reduces to the three boundary mechanisms.

math.AP↗