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Wei Dai

Publications and source records attributed to Wei Dai.

At least 55 records · Page 3Linked to original sources

Deep Psychovisual Image Representations

Psychovisual models suggest human vision decouples low-level feature extraction from higher cognition by first forming intermediate abstractions. In contrast, deep learning-based vision models routinely extract and aggregate features using homogeneous stacks of spatial layers, rendering their decision-making processes opaque. In this paper, we propose Deep Visual Coding, a learned frequency-domain representation inspired by 1990s image codes that quantised perceptually salient frequencies, which together with complex-valued image representations produces psychovisual-style abstractions. This approach enables the first psychovisual-based deep learning framework, utilizing data-driven spectral filters that learn to encode task-relevant semantic structures within distinct frequency sub-bands. Salience analyses reveal that our psychovisual models extract highly interpretable object parts compared to the amorphous regions produced by regular Convolutional Neural Networks (CNNs). Furthermore, we find that our models are less depth dependent than CNNs for model scaling, since our complex-valued representations and learned abstractions subsume the role of the deep spatial layers. Together, these findings demonstrate that psychovisual coding provides a promising path toward more efficient and transparent vision models.

cs.CV↗

Sharp gradient stability for a class of Hardy-Sobolev-Maz'ya inequalities

In this paper, we proved the sharp gradient stability for a class of Hardy-Sobolev-Maz'ya inequalities with partial (stronger) singular weight and non-radial extremal functions. Our result seems to be the first stability result for non-radial extremal functions. The presence of partial (stronger) singular weight brings substantial new challenges, requiring us to significantly refine the techniques from Deng-Tian 2025, Figalli-Neumayer 2019 and Figalli-Zhang 2022, and introduce some new ideas to handle both the cylindrical symmetry of non-radial extremal functions and the partial (stronger) singular weight structure. Key technical innovations include new compact embedding with strong singularity, non-degeneracy and spectral property of the linearized operator $\mathcal{L}_{v}$ generated by non-radial extremal function $v$ and new refined spectral inequalities, which are crucial for our analysis. Since the extremal function $v$ is non-radial, ODE approach fails, we use binary PDE to prove the spectral property of $\mathcal{L}_{v}$. Surprisingly, the sharp exponent $γ=\max\{2,p\}$ in our sharp gradient stability inequality (1.12) is independent of the partial weight dimension $k$, while the extremal manifold depends on $k$.

math.AP↗

Liouville theorems for $p$-Laplacian equations in convex cones without finite-energy condition

We study the anisotropic Finsler $p$-Laplacian equation \begin{equation*} \left\{ \begin{aligned} &-Δ^{H}_{p}u=f(u) \quad\,\,\, &{\rm{in}} \,\, \mathcal{C}, &{\bf{a}}(\nabla u)\cdot ν=0 \quad\,\,\, &{\rm{on}} \,\, \partial\mathcal{C}, \end{aligned} \right. \end{equation*} where $N\geq3$, $1<p<N$, $\mathcal{C}\subseteq\mathbb{R}^{N}$ is an open convex cone and $Δ^{H}_{p}$ is the anisotropic Finsler $p$-Laplacian operator. If $f(u)$ is nonnegative and subcritical, we prove that every bounded nonnegative solution in $\mathcal{C}$ is identically zero. In particular, for $f(u)=u^{q}$ with $0<q<p^*-1$, we establish a pointwise decay estimate in $\mathcal{C}$ via the doubling argument and blowing-up method and prove that all nonnegative solutions must be zero without the boundedness assumption. Our results are the subcritical counterpart of the classification result for the critical case in \cite{CFR}, and extend the Liouville type theorems in $\mathbb{R}^{N}$ for the standard $p$-Laplacian in \cite{SZ} and for the anisotropic $p$-Laplacian in \cite{CFV, CHN} to general convex cones $\mathcal{C}$. In the critical case $f(u)=u^{p^*-1} $ and typical case $H(ξ)=|ξ|$, for $\frac{N+1}{3}<p<N$, we classified the positive solutions of the critical $p$-Laplacian equation in convex cones $\mathcal{C}$ without finite-energy assumption. This extends the classification result of \cite{Ou} in $\mathbb{R}^{N}$ to general convex cones $\mathcal{C}$, and removes the finite-energy assumption in \cite{CFR} in the typical case $H(ξ)=|ξ|$.

math.AP↗

Information-theoretic Multimodal Representation Learning for Electrocardiogram Signals

Electrocardiograms (ECGs) are widely used non-invasive measurements of cardiac activity and play a central role in clinical diagnosis. Recent multimodal approaches align ECG signals with clinical reports to incorporate diagnostic semantics, but clinical reports often fail to preserve the rich physiological structure of ECG waveforms, particularly across multiple levels of abstraction ranging from coarse diagnostic categories to fine-grained morphology. To address this limitation, we formulate ECG representation learning from an information-theoretic perspective and derive a tractable objective that jointly preserves signal structure and integrates clinical semantics. Based on this principle, we propose \textbf{MERIT} (Multimodal ECG Representation via Information Theory), a dual-branch pretraining framework combining masked ECG modeling with ECG--text contrastive alignment. Extensive experiments on PTB-XL and additional benchmarks demonstrate consistent improvements over prior methods, including gains exceeding $3%$ F1 on PTB-XL All and $5%$ F1 on SubClass classification. In zero-shot evaluation, MERIT further improves performance by up to $ +2.66\%$ AUC and $ +2.11\%$ F1 on PTB-XL SubClass, while also demonstrating robustness under multiple distribution-shift settings. Moreover, leveraging the learned ECG representations for ECG-conditioned clinical text generation with large language models improves text quality across several metrics, including ROUGE and METEOR. Together, these results demonstrate that MERIT learns more informative and clinically meaningful ECG representations, particularly for fine-grained clinical applications.

cs.LG↗

System-size dependence of the $D^0$--$D_s^+$ flow splitting from early $D_s^+$ formation at $\sqrt{s_{NN}} = 5.36$~TeV

We investigate the elliptic-flow splitting between prompt $D^0$ and $D_s^+$ mesons within a heavy-quark transport framework with sequential hadronization, in which $D_s^+$ forms at $1.2\,T_c$ and $D^0$ at $T_c$. We present predictions for the $p_T$-differential $v_2$ and $D_s^+/D^0$ yield ratio in O--O $0$--$20\%$ collisions at $\sqrt{s_{NN}} = 5.36$~TeV, where preliminary ALICE data are available. The sequential scenario reproduces the observed $v_2(D^0) > v_2(D_s^+)$ ordering and predicts an enhanced $D_s^+/D^0$ ratio at low $p_T$, whereas a simultaneous baseline yields the opposite ordering. Decomposing the hadronic splitting into its partonic components, we show that the $v_2$ ordering is driven by the late-stage flow accumulated by $D^0$-parent charm quarks during the $1.2\,T_c \to T_c$ interval, with hadronic rescattering essential to preserve the signal in small systems. A systematic scan across nine collision configurations spanning O--O and Pb--Pb centralities reveals a universal linear scaling between the hadronic splitting and the partonic flow increment accumulated during this window. This establishes the $D^0$--$D_s^+$ flow splitting as a hadronization chronometer of the QGP at $\sqrt{s_{NN}} = 5.36$~TeV.

hep-ph↗

SAMRI: Segment Any MRI

Summary: SAMRI is an MRI-specialized adaptation of the Segment Anything Model achieving superior whole-body MRI segmentation, particularly for small and clinically critical structures, through box and point prompts for rapid annotation. Purpose: Existing SAM adaptations treat MRI as a generic modality, overlooking variable tissue contrast, intensity inhomogeneity, and clinically important small structures. We propose an MRI-specialized foundation model with strong whole-body segmentation and zero-shot generalization for direct use on any MRI annotation task. Methods: SAMRI fine-tunes only the mask decoder of SAM (ViT-B/16), keeping encoders frozen to preserve pretrained representations and eliminate redundant passes-reducing training time by 94%, trainable parameters by 96%, and FLOPs by ~99% versus full-model retraining. Training used 1.1 million 2D slice-mask pairs from 30 datasets spanning 47 targets, T1/T2/FLAIR/DWI contrasts, and whole-body anatomy, with focal-Dice loss and bounding-box (with optional point) prompts. Sizes were stratified by mask area (small: <0.5%; medium: 0.5-3.5%; large: >3.5%), and significance assessed by the Wilcoxon signed-rank test. Results: SAMRI with box+point prompts achieved mean DSC 0.87 +/- 0.11 across 47 targets, outperforming MedSAM (0.74 +/- 0.24) by 17.6% (p < 0.05), with largest gains for small (+42.4%) and medium (+26.9%) structures. On six zero-shot datasets, SAMRI achieved mean DSC 0.85, outperforming baselines. Inference requires only ~4.5 GB VRAM through an interactive interface on standard hardware. Conclusion: Decoder-only fine-tuning on a large, MRI-specific corpus delivers superior whole-body segmentation with strong zero-shot generalization, particularly for small and clinically salient structures. Public code, pretrained models, and an interactive interface make SAMRI deployable for MRI segmentation research and clinical workflows.

eess.IV↗

CasualSynth: Generating Structurally Sound Synthetic Data

Large Language Models (LLMs) generate realistic synthetic data but offer no guarantee that their outputs respect the causal mechanisms governing the target domain. We introduce CausalSynth, a framework that decouples causal structure generation from semantic realization, yielding synthetic data that is both causally valid and linguistically rich. The framework operates in three phases. First, a Structural Causal Model (SCM) - a tuple of structural equations defined over a directed acyclic graph (DAG) generates causal skeletons, i.e., variable assignments that satisfy the Global Markov Property of the governing DAG, via ancestral sampling. Second, an LLM acts as a constrained \emph{realizer}, a conditional translator that maps each skeleton to a high-dimensional observation such as a clinical note or a transaction log. Third, an Iterative Consistency Verification module detects structural violations through deterministic extraction and feeds targeted corrections back to the LLM, forming a closed-loop refinement process. We identify the Semantic Backdoor problem the systematic tendency of LLMs to override imposed causal facts with pre-training priors -- and prove that our iterative mechanism reduces the resulting selection bias relative to standard rejection sampling. On three causal benchmarks (ASIA, ALARM, and MIMIC-Struct), CausalSynth preserved conditional independencies with false-positive rates near the nominal $α=0.05$ level and achieved realizability rates above 96% with 70B-parameter LLM backbones. The framework additionally supports principled interventional and counterfactual generation through noise retention and graph mutilation.

cs.LG↗

Differentially Private Motif-Preserving Multi-modal Hashing

Cross-modal hashing enables efficient retrieval by encoding images and text into compact binary codes. State-of-the-art methods rely on semantic similarity graphs derived from user interactions for supervision, yet these graphs encode sensitive behavioral patterns vulnerable to link reconstruction attacks. Existing privacy-preserving approaches fail on graph-structured data: Differentially Private SGD destroys relational motifs by treating samples independently, while graph synthesis methods suffer from unbounded local sensitivity in scale-free networks, hub nodes cause single-edge modifications to alter triangle counts by $\mathcal{O}(N)$, necessitating prohibitive noise injection. We term this phenomenon Hubness Explosion. We propose DMP-MH, a Sanitize-then-Distill framework that decouples privacy from representation learning. Our approach first bounds sensitivity by deterministically clipping node degrees, capping the $L_2$-sensitivity of triangle motifs independently of dataset size. A sanitized synthetic graph is then generated via Noisy Mirror Descent under $(ε,δ)$-Edge Differential Privacy. Finally, dual-stream hashing networks distill this topology using a holistic structural loss that enforces cross-modal alignment. Evaluated on MIRFlickr-25K and NUS-WIDE under a strict inductive protocol, DMP-MH outperforms private baselines by up to 11.4 mAP points while retaining up to 92.5% of non-private performance.

cs.IR↗

Identity-Decoupled Anonymization for Visual Evidence in Multi-modal Retrieval-Augmented Generation

Multi-modal retrieval-augmented generation (MRAG) systems retrieve visual evidence from large image corpora to ground the responses of large multi-modal models, yet the retrieved images frequently contain human faces whose identities constitute sensitive personal information. Existing anonymization techniques that destroy the non-identity visual cues that downstream reasoning depends on or fail to provide principled privacy guarantees. We propose Identity-Decoupled MRAG, a framework that interposes a generative anonymization module between retrieval and generation. Our approach consists of three components: (i)a disentangled variational encoder that factorizes each face into an identity code and a spatially-structured attribute code, regularized by a mutual-information penalty and a gradient-based independence term; (ii)a manifold-aware rejection sampler that replaces the identity code with a synthetic one guaranteed to be both distinct from the original and realistic; and (iii)a conditional latent diffusion generator that synthesizes the anonymized face from the replacement identity and the preserved attributes, distilled into a latent consistency model for low-latency deployment. Privacy is enforced through a multi-oracle ensemble of face recognition models with a hinge-based loss that halts optimization once identity similarity drops below the impostor-regime threshold.

cs.CV↗

PuzzleWorld: A Benchmark for Multimodal, Open-Ended Reasoning in Puzzlehunts

Puzzlehunts are a genre of complex, multi-step puzzles lacking well-defined problem definitions. In contrast to conventional reasoning benchmarks consisting of tasks with clear instructions and constrained environments, puzzlehunts requires discovering the underlying problem structure from multimodal evidence and iterative reasoning, mirroring real-world domains such as scientific discovery, exploratory data analysis, or investigative problem-solving. Despite progress in foundation models, their performance on open-ended settings remains largely untested. We introduce PuzzleWorld, a comprehensive benchmark of 667 puzzlehunt-style problems designed to assess step-by-step, open-ended, and creative multimodal reasoning. Each puzzle is annotated with the final solution, detailed reasoning traces, and cognitive skill labels, enabling holistic benchmarking and fine-grained diagnostic analysis. Most state-of-the-art models achieve only 1-4% final answer accuracy. On PuzzleWorld, the best model solves only 18% of puzzles and reaches 40% stepwise accuracy, matching human puzzle novices but falling significantly behind puzzle enthusiasts. To demonstrate the value of our reasoning annotations, we show that fine-tuning a small model on reasoning traces boosts stepwise accuracy from 4% to 11%, which translates to improvements in downstream visual reasoning tasks. Our detailed error analysis reveals that current models exhibit myopic reasoning, are bottlenecked by the limitations of language-based inference, and lack sketching capabilities crucial for visual and spatial reasoning. We release PuzzleWorld at https://github.com/MIT-MI/PuzzleWorld to support future work on building more general, open-ended, and creative reasoning systems.

cs.CL↗

SmellNet: A Large-scale Dataset for Real-world Smell Recognition

The ability of AI to sense and identify various substances based on their smell alone can have profound impacts on allergen detection (e.g. smelling gluten or peanuts in a cake), monitoring the manufacturing process, and sensing hormones that indicate emotional states, stress levels, and diseases. Despite these broad impacts, there are few standardized datasets, and therefore little progress, for training and evaluating AI systems' ability to `smell' in the real-world. In this paper, we use small gas and chemical sensors to create SmellNet, a comparatively large dataset for sensor-based machine olfaction that digitizes a diverse range of smells in the natural world. SmellNet contains about 828,000 time-series data points across 50 substances, spanning nuts, spices, herbs, fruits, and vegetables, and 43 mixtures among them with fixed ingredient volumetric ratios, with 68 hours of data collected. Using SmellNet, we developed ScentFormer, a Transformer-based architecture combining temporal differencing and sliding-window augmentation for smell data. For the SmellNet-Base classification tasks, ScentFormer achieves 63.3% Top-1 accuracy with GC-MS supervision, and for the SmellNet-Mixture distribution prediction tasks, ScentFormer achieves 50.2% Top-1@0.1 on the test-seen split. ScentFormer's ability to generalize across conditions and capture transient chemical dynamics demonstrates the promise of temporal modeling in sensor-based olfactory AI. SmellNet and ScentFormer lay the groundwork for sensor-based olfactory applications across healthcare, food and beverage, environmental monitoring, manufacturing, and entertainment.

cs.AI↗

CircuitSynth: Reliable Synthetic Data Generation

The generation of high-fidelity synthetic data is a cornerstone of modern machine learning, yet Large Language Models (LLMs) frequently suffer from hallucinations, logical inconsistencies, and mode collapse when tasked with structured generation. Existing approaches, such as prompting or retrieval-augmented generation, lack the mechanisms to balance linguistic expressivity with formal guarantees regarding validity and coverage. To address this, we propose CircuitSynth, a novel neuro-symbolic framework that decouples semantic reasoning from surface realization. By distilling the reasoning capabilities of a Teacher LLM into a Probabilistic Sentential Decision Diagram (PSDD), CircuitSynth creates a tractable semantic prior that structurally enforces hard logical constraints. Furthermore, we introduce a convex optimization mechanism to rigorously satisfy soft distributional goals. Empirical evaluations across diverse benchmarks demonstrate that CircuitSynth achieves 100% Schema Validity even in complex logic puzzles where unconstrained baselines fail (12.4%) while significantly outperforming state-of-the-art methods in rare-combination coverage.

cs.CL↗

Constrained Policy Optimization for Provably Fair Order Matching

Automated matching engines execute millions of orders per session, yet systematic asymmetries in latency, order size, and market access compound into persistent execution disparities that erode participant trust. We formulate provably fair order matching as a Constrained Markov Decision Process and propose CPO-FOAM (Constrained Policy Optimization with Feedback-Optimized Adaptive Margins). An inner loop computes an analytic trust-region step on the Fisher information manifold; a PID-controlled outer loop dynamically tightens safety margins, suppressing the sawtooth oscillations endemic to Lagrangian methods under non-stationary dynamics. Group fairness (demographic parity, equalized odds) enters the CMDP cost vector while individual Lipschitz fairness is enforced deterministically via spectral normalization. We prove BIBO stability and that the integral term drives steady-state violations to zero. On LOBSTER NASDAQ data across six market regimes, CPO-FOAM recovers 95.9% of unconstrained throughput at 2.5% constraint violation frequency; on crypto-asset LOB data under MEV injection it captures 98.4% of the reward envelope at 3.2% CVF. The method scales sub-linearly to M=8 constraints, settles on-chain within one Ethereum block, and yields a 2.1X reward improvement on Safety-Gymnasium, confirming domain-agnostic generalization.

cs.GT↗

Enhancing Foundation VLM Robustness to Missing Modality: Scalable Diffusion for Bi-directional Feature Restoration

Vision Language Model (VLM) typically assume complete modality input during inference. However, their effectiveness drops sharply when certain modalities are unavailable or incomplete. Current research on missing modality primarily faces two dilemmas: Prompt-based methods struggle to restore missing yet indispensable features and degrade the generalizability of VLM. Imputation-based approaches, lacking effective guidance, are prone to generating semantically irrelevant noise. Restoring precise semantics while sustaining VLM's generalization remains challenging. Therefore, we propose a general missing modality restoration strategy in this paper. We introduce an enhanced diffusion model as a pluggable mid-stage training module to effectively restore missing features. Our strategy introduces two key innovations: (I) Dynamic Modality Gating, which adaptively leverages conditional features to guide the generation of semantically consistent features; (II) Cross-Modal Mutual Learning mechanism, which bridges the semantic spaces of the dual models to achieve bi-directional alignment. Notably, our strategy maintains the original integrity of the pre-trained VLM, requiring no fine-tuning of the backbone models while significantly boosting resilience to information loss. Zero-shot evaluations across benchmark datasets demonstrate that our approach consistently outperforms existing baselines, establishing it as a robust and scalable extension that ensures VLM reliability across diverse missing rates and conditions. Our code and models will be publicly available.

cs.AI↗

Fine Structures of Berry Curvature and Unquantized Valley Chern Numbers in Valley Photonic Crystals

Valley photonics has emerged as a promising platform in topological photonic systems, yet the topological nature of valley-dependent phenomena remains unsettled. Theoretically, inter-valley scattering may occur with structural imperfections, and global Chern numbers vanish due to time-reversal symmetry. As a result, valley-dependent topology is locally defined around K(K') points in the half-Brillouin zone (HBZ). While half-integer valley Chern numbers have been widely assumed, their quantization and topological validity remain controversial. Here, we systematically investigate a continuous spectrum of valley photonic crystal designs by evaluating their Berry curvatures, valley Chern numbers, and angular momenta. We show that valley Chern numbers are generically unquan-tized and instead form a continuous spectrum varying with structural parameters. We further reveal previously unexplored fine structures in the Berry curvature distribution in momentum space. The unquantized valley Chern numbers are attributed to inter- and intra-valley cancellation of Berry curvature, highlighting the absence of a protecting mechanism for quantization. Our results call for a reassessment of valley-dependent topology and provide a more rigorous framework for interpreting valley-related photonic phenomena.

physics.optics↗

Visual Set Program Synthesizer

A user pointing their phone at a supermarket shelf and asking "Which soda has the least sugar?" poses a difficult challenge for current visual Al assistants. Such queries require not only object recognition, but explicit set-based reasoning such as filtering, comparison, and aggregation. Standard endto-end MLLMs often fail at these tasks because they lack an explicit mechanism for compositional logic. We propose treating visual reasoning as Visual Program Synthesis, where the model first generates a symbolic program that is executed by a separate engine grounded in visual scenes. We also introduce Set-VQA, a new benchmark designed specifically for evaluating set-based visual reasoning. Experiments show that our approach significantly outperforms state-of-the-art baselines on complex reasoning tasks, producing more systematic and transparent behavior while substantially improving answer accuracy. These results demonstrate that program-driven reasoning provides a principled alternative to black-box visual-language inference.

cs.MM↗

On endomorphism algebras of silting complexes over hereditary abelian categories

Let $\mathcal{E}$ be the class of finite-dimensional algebras isomorphic to endomorphism algebras of silting complexes over hereditary abelian categories. It is proved that the class $\mathcal{E}$ is closed under taking idempotent quotients, idempotent subalgebras and $τ$-reduction. We also show that the proper class consisting of shod algebras is also closed under these operations. In addition, several classic classes of algebras -- including laura, glued, weakly shod algebras -- are proved to be closed under idempotent quotients, thereby generalizing a known result originally established for specific idempotents.

math.RT↗

Mixed order conformally invariant system with exponential growth and nonlocal nonlinear terms in critical dimensions

In this paper, under the extremely mild assumption $u(x)= O(|x|^{K})$ as $|x|\rightarrow+\infty$ for some $K\gg1$ arbitrarily large, we classify solutions of the following mixed order conformally invariant system with exponentially increasing and nonlocal nonlinearities in $\mathbb{R}^{n}$: $$ \left\{ \begin{aligned} (-Δ)^{\frac{1}{2}}u & = e^{pv} \\ (-Δ)^{\frac{n}{2}}v & = \left(\frac{1}{|x|^2}*u^2\right)u^2 \end{aligned} \right. \quad \text{in}\; \mathbb{R}^n, $$ where $n=3,\,4$, $p>0$, $u\geqslant0$, $v(x)=o(|x|^2)$ as $|x|\to\infty$ and $u$ satisfies the finite total mass condition. The finite total mass condition can be deduced from either $u \in L^\frac{2n}{n-1}(\mathbb{R}^n)$ or $u \in \dot{H}^\frac{1}{2}(\mathbb{R}^n)$. This system is closely related to the conformally invariant equations $(-Δ)^{\frac{1}{2}}u=\left(\frac{1}{|x|^{2}}*u^2\right)u$ and $(-Δ)^{\frac{n}{2}}u=(n-1)!e^{nu}$ in $\mathbb{R}^{n}$ with $n=3,4$, which have been quite extensively studied.

math.AP↗