Papers

Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting comprehensive parameter exploration and transient analysis. This paper introduces a deep learning-based pseudo-analytical probability solution (PAPS) that, via a single training process, simultaneously resolves transient FPE solutions for arbitrary multi-modal initial distributions, system parameters, and time points. The core idea is to unify initial, transient, and stationary distributions via Gaussian mixture distributions (GMDs) and develop a constraint-preserving autoencoder that bijectively maps constrained GMD parameters to unconstrained, low-dimensional latent representations. In this representation space, the panoramic transient dynamics across varying initial conditions and system parameters can be modeled by a single evolution network. Extensive experiments on paradigmatic systems demonstrate that the proposed PAPS maintains high accuracy while achieving inference speeds four orders of magnitude faster than GPU-accelerated Monte Carlo simulations. This efficiency leap enables previously intractable real-time parameter sweeps and systematic investigations of stochastic bifurcations. By decoupling representation learning from physics-informed transient dynamics, our work establishes a scalable paradigm for probabilistic modeling of multi-dimensional, parameterized stochastic systems.

Large Language Models (LLMs) internalize vast world knowledge as parametric memory, yet inevitably inherit the staleness and errors of their source corpora. Consequently, ensuring the reliability and malleability of these internal representations is imperative for trustworthy real-world deployment. Knowledge editing offers a pivotal paradigm for surgically modifying memory without retraining. However, while recent editors demonstrate high success rates on standard benchmarks, it remains questionable whether current evaluation frameworks that rely on assessing output under specific prompting conditions can reliably authenticate genuine memory modification. In this work, we introduce a simple diagnostic framework that subjects models to discriminative self-assessment under in-context learning (ICL) settings that better reflect real-world application environments, specifically designed to scrutinize the subtle behavioral nuances induced by memory modifications. This probing reveals a pervasive phenomenon of Surface Compliance, where editors achieve high benchmark scores by merely mimicking target outputs without structurally overwriting internal beliefs. Moreover, we find that recursive modifications accumulate representational residues, triggering cognitive instability and permanently diminishing the reversibility of the model's memory state. These insights underscore the risks of current editing paradigms and highlight the pivotal role of robust memory modification in building trustworthy, long-term sustainable LLM systems. Code is available at https://github.com/XiaojieGu/SA-MCQ.

We investigate the data distribution valuation problem, which aims to quantify the values of data distributions from their samples. This is a recently proposed problem that is related to but different from classical data valuation and can be applied to various applications. For this problem, we develop a novel framework called Generalized Bayes Valuation that utilizes generalized Bayesian inference with a loss constructed from transferability measures. This framework allows us to solve, in a unified way, seemingly unrelated practical problems, such as annotator evaluation and data augmentation. Using the Bayesian principles, we further improve and enhance the applicability of our framework by extending it to the continuous data stream setting. Our experiment results confirm the effectiveness and efficiency of our framework in different real-world scenarios.

Understanding how training shapes the geometry of recurrent network dynamics is a central problem in time-series modeling. We study the emergence of low-dimensional dominant manifolds in the training of Reservoir Computing (RC) networks for temporal forecasting tasks. For a general linear continuous-time reservoir in the infinite-data limit, we show that the training data generate an invariant subspace of the trained reservoir, whose dimension equals the number of dominant modes. We then specialize to a simplified diagonal linear reservoir, where we link the dominant eigenvalues and eigenvectors to the spectrum of a backward Dynamic Mode Decomposition matrix, which yields a finite-dimensional approximation of the backward-time Koopman operator of the system generating the training data. We illustrate the emergence of these dominant modes during training in simulation, and discuss how the analysis may be extended to nonlinear RC via tangent dynamics and differential p-dominance.

Large Language Models (LLMs) achieve strong program repair performance but often suffer from over-editing, where excessive modifications overwrite correct code and hinder bug localization. We systematically quantify its impact and introduce precise repair task, which maximizes reuse of correct code while fixing only buggy parts. Building on this insight, we propose PRepair, a framework that mitigates over-editing and improves repair accuracy. PRepair has two components: Self-Breaking, which generates diverse buggy programs via controlled bug injection and min-max sampling, and Self-Repairing, which trains models with Edit-Aware Group Relative Policy Optimization (EA-GRPO) using an edit-aware reward to encourage minimal yet correct edits. Experiments show that PRepair improves repair precision by up to 31.4% under $\mathrm{fix}_1@1$, a metric that jointly considers repair correctness and extent, and significantly increases decoding throughput when combined with speculative editing, demonstrating its potential for precise and practical code repair.

Scanning Electron Microscopy (SEM) is indispensable in modern materials science, enabling high-resolution imaging across a wide range of structural, chemical, and functional investigations. However, SEM imaging remains constrained by task-specific models and labor-intensive acquisition processes that limit its scalability across diverse applications. Here, we introduce the first foundation model for SEM images, pretrained on a large corpus of multi-instrument, multi-condition scientific micrographs, enabling generalization across diverse material systems and imaging conditions. Leveraging a self-supervised transformer architecture, our model learns rich and transferable representations that can be fine-tuned or adapted to a wide range of downstream tasks. As a compelling demonstration, we focus on defocus-to-focus image translation-an essential yet underexplored challenge in automated microscopy pipelines. Our method not only restores focused detail from defocused inputs without paired supervision but also outperforms state-of-the-art techniques across multiple evaluation metrics. This work lays the groundwork for a new class of adaptable SEM models, accelerating materials discovery by bridging foundational representation learning with real-world imaging needs.

Landslides represent a major geohazard with severe impacts on human life, infrastructure, and ecosystems, underscoring the need for accurate and timely detection approaches to support disaster risk reduction. This study proposes a modular, multi-model framework that fuses Sentinel-2 optical imagery with Sentinel-1 Synthetic Aperture Radar (SAR) data, for robust landslide detection. The methodology leverages multi-encoder vision transformers, where each data modality is processed through separate lightweight pretrained encoders, achieving strong performance in landslide detection. In addition, the integration of multiple models, particularly the combination of neural networks and gradient boosting models (LightGBM and XGBoost), demonstrates the power of ensemble learning to further enhance accuracy and robustness. Derived spectral indices, such as NDVI, are integrated alongside original bands to enhance sensitivity to vegetation and surface changes. The proposed methodology achieves a state-of-the-art F1 score of 0.919 on landslide detection, addressing a patch-based classification task rather than pixel-level segmentation and operating without pre-event Sentinel-2 data, highlighting its effectiveness in a non-classical change detection setting. It also demonstrated top performance in a machine learning competition, achieving a strong balance between precision and recall and highlighting the advantages of explicitly leveraging the complementary strengths of optical and radar data. The conducted experiments and research also emphasize scalability and operational applicability, enabling flexible configurations with optical-only, SAR-only, or combined inputs, and offering a transferable framework for broader natural hazard monitoring and environmental change applications. Full training and inference code can be found in https://github.com/IoannisNasios/sentinel-landslide-cls.

Generation of graphs constrained by a specified graph edit distance from a source graph is important in applications such as cheminformatics, network anomaly synthesis, and structured data augmentation. Despite the growing demand for such constrained generative models in areas including molecule design and network perturbation analysis, the neural architectures required to provably generate graphs within a bounded graph edit distance remain largely unexplored. In addition, existing graph generative models are predominantly data-driven and depend heavily on the availability and quality of training data, which may result in generated graphs that do not satisfy the desired edit distance constraints. In this paper, we address these challenges by theoretically characterizing ReLU neural networks capable of generating graphs within a prescribed graph edit distance from a given graph. In particular, we show the existence of constant depth and O(n^2 d) size ReLU networks that deterministically generate graphs within edit distance d from a given input graph with n vertices, eliminating reliance on training data while guaranteeing validity of the generated graphs. Experimental evaluations demonstrate that the proposed network successfully generates valid graphs for instances with up to 1400 vertices and edit distance bounds up to 140, whereas baseline generative models fail to generate graphs with the desired edit distance. These results provide a theoretical foundation for constructing compact generative models with guaranteed validity.

State space models (SSMs) have been shown to possess the theoretical capacity to model both star-free sequential tasks and bounded hierarchical structures Sarrof et al. (2024). However, formal expressivity results do not guarantee that gradient-based optimisation will reliably discover the corresponding solutions. Existing benchmarks probe either monotonic state tracking, as in the standard Flip-Flop task, or structural nesting, as in the Dyck languages, but neither isolates reversible semantic state retrieval. We introduce the UNDO Flip-Flop task to fill this gap. By extending the standard Flip-Flop with an UNDO, the task requires a model to maintain an implicit bounded stack and recover historical states under non-monotonic update sequences. We evaluate one-layer and two-layer Mamba-2 under this framework. Both variants fail to acquire the provably expressible stack-based rollback mechanism, converging instead on a local toggle heuristic that inverts the current state rather than retrieving stored history. Under an adversarial retraction pressure test held within the training length distribution, the two-layer model collapses to 41.10% accuracy, which is below random chance. The results confirm systematic rather than incidental failure. Causal ablation shows that the bottleneck lies in retrieval, not storage. These results draw a clear line between what an architecture can in principle represent and what gradient descent reliably learns, a distinction that theoretical expressivity analyses alone cannot capture.

Gray-box RC models are widely used to enable energy-efficient model predictive control (MPC) in buildings. However, estimating RC parameters remains difficult, as conventional optimization-based algorithms are prone to local minima, rely heavily on good initial guesses, and incur high computational cost. To address these issues, we propose the Estimator from Scratch, a novel neural parameter estimation approach that embeds the physical equations into a neural network's training process to estimate RC parameters. To further improve estimation accuracy and eliminate dependence on an initial guess, we extend this approach by pretraining the neural network on data from multiple source buildings, the Pretrained Estimator. We benchmark both methods against a genetic-algorithm-based RC estimator and a fully black-box neural network. All methods are evaluated across eight simulated and three real-world buildings for two RC configurations, for both prediction accuracy and closed-loop MPC performance, the latter only for the simulated buildings. The Pretrained Estimator achieves the best prediction performance among all RC-based methods, particularly with little training data, and yields the lowest and least variable MPC costs across buildings and benchmarks. These results position the Pretrained Estimator as a robust, computationally efficient, and initial-guess-free alternative for RC parameter estimation, with potential to extend to other control-oriented dynamical systems.

Bayesian inference in high-dimensional discrete-input additive noise models is a fundamental challenge in communication systems, as the support of the required joint a posteriori probability (APP) mass function grows exponentially with the number of unknown variables. In this work, we propose a tensor-train (TT) framework for tractable, near-optimal Bayesian inference in discrete-input additive noise models. The central insight is that the joint log-APP mass function admits an exact low-rank representation in the TT format, enabling compact storage and efficient computations. To recover symbol-wise APP marginals, we develop a practical inference procedure that approximates the exponential of the log-posterior using a TT-cross algorithm initialized with a truncated Taylor-series. To demonstrate the generality of the approach, we derive explicit low-rank TT constructions for two canonical communication problems: the linear observation model under additive white Gaussian noise (AWGN), applied to multiple-input multiple-output (MIMO) detection, and soft-decision decoding of binary linear block error correcting codes over the binary-input AWGN channel. Numerical results show near-optimal error-rate performance across a wide range of signal-to-noise ratios while requiring only modest TT ranks. These results highlight the potential of tensor-network methods for efficient Bayesian inference in communication systems.

Clustering mixed-type tabular data is fundamental for exploratory analysis, yet remains challenging due to misaligned numerical-categorical representations, uneven and context-dependent feature relevance, and disconnected and post-hoc explanation from the clustering process. We propose WISE, a Weight-Informed Self-Explaining framework that unifies representation, feature weighting, clustering, and interpretation in a fully unsupervised and transparent pipeline. WISE introduces Binary Encoding with Padding (BEP) to align heterogeneous features in a unified sparse space, a Leave-One-Feature-Out (LOFO) strategy to sense multiple high-quality and diverse feature-weighting views, and a two-stage weight-aware clustering procedure to aggregate alternative semantic partitions. To ensure intrinsic interpretability, we further develop Discriminative FreqItems (DFI), which yields feature-level explanations that are consistent from instances to clusters with an additive decomposition guarantee. Extensive experiments on six real-world datasets demonstrate that WISE consistently outperforms classical and neural baselines in clustering quality while remaining efficient, and produces faithful, human-interpretable explanations grounded in the same primitives that drive clustering.

Neural network pruning can be formulated as a combinatorial optimization problem, yet most existing approaches rely on greedy heuristics that ignore complex interactions between filters. Formal optimization methods such as Quadratic Unconstrained Binary Optimization (QUBO) provide a principled alternative but have so far underperformed due to oversimplified objective formulations based on metrics like the L1-norm. In this work, we propose a unified Hybrid QUBO framework that bridges heuristic importance estimation with global combinatorial optimization. Our formulation integrates gradient-aware sensitivity metrics - specifically first-order Taylor and second-order Fisher information - into the linear term, while utilizing data-driven activation similarity in the quadratic term. This allows the QUBO objective to jointly capture individual filter relevance and inter-filter functional redundancy. We further introduce a dynamic capacity-driven search to strictly enforce target sparsity without distorting the optimization landscape. Finally, we employ a two-stage pipeline featuring a Tensor-Train (TT) Refinement stage - a gradient-free optimizer that fine-tunes the QUBO-derived solution directly against the true evaluation metric. Experiments on the SIDD image denoising dataset demonstrate that the proposed Hybrid QUBO significantly outperforms both greedy Taylor pruning and traditional L1-based QUBO, with TT Refinement providing further consistent gains at appropriate combinatorial scales. This highlights the potential of hybrid combinatorial formulations for robust, scalable, and interpretable neural network compression.

Auto-bidding services optimize real-time bidding strategies for advertisers under key performance indicator (KPI) constraints such as target return on investment and budget. However, uncertainties such as model prediction errors and feedback latency can cause bidding strategies to deviate from ex-post optimality, leading to inefficient allocation. To address this issue, we propose JD-BP, a Joint generative Decision framework for Bidding and Pricing. Unlike prior methods, JD-BP jointly outputs a bid value and a pricing correction term that acts additively with the payment rule such as GSP. To mitigate adverse effects of historical constraint violations, we design a memory-less Return-to-Go that encourages future value maximizing of bidding actions while the cumulated bias is handled by the pricing correction. Moreover, a trajectory augmentation algorithm is proposed to generate joint bidding-pricing trajectories from a (possibly arbitrary) base bidding policy, enabling efficient plug-and-play deployment of our algorithm from existing RL/generative bidding models. Finally, we employ an Energy-Based Direct Preference Optimization method in conjunction with a cross-attention module to enhance the joint learning performance of bidding and pricing correction. Offline experiments on the AuctionNet dataset demonstrate that JD-BP achieves state-of-the-art performance. Online A/B tests at JD.com confirm its practical effectiveness, showing a 4.70% increase in ad revenue and a 6.48% improvement in target cost.

Patient healthcare utilization consists of irregularly time-stamped events, such as outpatient visits, inpatient admissions, and emergency encounters, forming individualized care trajectories. Modeling these trajectories is crucial for understanding utilization patterns and predicting future care needs, but is challenging due to temporal irregularity and severe class imbalance. In this work, we build on the Transformer Hawkes Process framework to model patient trajectories in continuous time. By combining Transformer-based history encoding with Hawkes process dynamics, the model captures event dependencies and jointly predicts event type and time-to-event. To address extreme imbalance, we introduce an imbalance-aware training strategy using inverse square-root class weighting. This improves sensitivity to rare but clinically important events without altering the data distribution. Experiments on real-world data demonstrate improved performance and provide clinically meaningful insights for identifying high-risk patient populations.

Brain-computer interfaces (BCIs) enable direct communication between the brain and external devices, providing critical support for individuals with motor impairments. However, accurate motor imagery (MI) decoding from electroencephalography (EEG) remains challenging due to noise and cross-session variability. This study introduces EEG-MFTNet, a novel deep learning model based on the EEGNet architecture, enhanced with multi-scale temporal convolutions and a Transformer encoder stream. These components are designed to capture both short and long-range temporal dependencies in EEG signals. The model is evaluated on the SHU dataset using a subject-dependent cross-session setup, outperforming baseline models, including EEGNet and its recent derivatives. EEG-MFTNet achieves an average classification accuracy of 58.9% while maintaining low computational complexity and inference latency. The results highlight the model's potential for real-time BCI applications and underscore the importance of architectural innovations in improving MI decoding. This work contributes to the development of more robust and adaptive BCI systems, with implications for assistive technologies and neurorehabilitation.

Mixture of linear regression is well studied in statistics and machine learning, where the data points are generated probabilistically using $k$ linear models. Algorithms like Expectation Maximization (EM) may be used to recover the ground truth regressors for this problem. Recently, in \cite{pal2022learning,ghosh_agnostic} the mixed linear regression problem is studied in the agnostic setting, where no generative model on data is assumed. Rather, given a set of data points, the objective is fit $k$ lines by minimizing a suitable loss function. It is shown that a modification of EM, namely gradient EM converges exponentially to appropriately defined loss minimizer even in the agnostic setting. In this paper, we study the problem of fitting $k$ parametric functions to given set of data points. We adhere to the agnostic setup. However, instead of fitting lines equipped with quadratic loss, we consider any arbitrary parametric function fitting equipped with a strongly convex and smooth loss. This framework encompasses a large class of problems including mixed linear regression (regularized), mixed linear classifiers (mixed logistic regression, mixed Support Vector Machines) and mixed generalized linear regression. We propose and analyze gradient EM for this problem and show that with proper initialization and separation condition, the iterates of gradient EM converge exponentially to appropriately defined population loss minimizers with high probability. This shows the effectiveness of EM type algorithm which converges to optimal solution in the non-generative setup beyond mixture of linear regression.

Contrastive learning has become a standard approach for unsupervised learning from paired data, as demonstrated by CLIP for image-text matching. However, many domains involve more than two modalities and require objectives that capture higher-order dependencies beyond pairwise alignment. Symile extends CLIP to this setting by replacing the dot product with the multilinear inner product (MIP) over modality embeddings. In this work, we show that there is a fragility which ishidden in the multiplicative interaction: a single weakly informative, misaligned, or missing modality can propagate through the objective and distort cross-modal retrieval scores. We propose Gated Symile, a contrastive gating mechanism that adapts modality contributions on an attention-based, per-candidate basis. The gate suppresses unreliable inputs by interpolating embeddings toward learnable neutral directions with an explicit NULL option when reliable cross-modal alignment is unlikely. Across a controlled synthetic benchmark that uncovers this fragility and three real-world trimodal datasets, Gated Symile achieves higher top-1 retrieval accuracy than well-tuned state-of-the-art (sota) baselines. More broadly, our results highlight gating as a step toward robust multimodal contrastive learning beyond two modalities in the presence of noise, misalignment, or missing inputs.

Approaches to bivariate causal discovery based on the minimum description length (MDL) principle approximate the (uncomputable) Kolmogorov complexity of the models in each causal direction, selecting the one with the lower total complexity. The premise is that nature's mechanisms are simpler in their true causal order. Inherently, the description length (complexity) in each direction includes the description of the cause variable and that of the causal mechanism. In this work, we argue that current state-of-the-art MDL-based methods do not correctly address the problem of estimating the description length of the cause variable, effectively leaving the decision to the description length of the causal mechanism. Based on rate-distortion theory, we propose a new way to measure the description length of the cause, corresponding to the minimum rate required to achieve a distortion level representative of the underlying distribution. This distortion level is deduced using rules from histogram-based density estimation, while the rate is computed using the related concept of information dimension, based on an asymptotic approximation. Combining it with a traditional approach for the causal mechanism, we introduce a new bivariate causal discovery method, termed rate-distortion MDL (RDMDL). We show experimentally that RDMDL achieves competitive performance on the Tübingen dataset. All the code and experiments are publicly available at github.com/tiagobrogueira/Causal-Discovery-In-Exchangeable-Data.

Interpreting the decisions of complex computer vision models is crucial to establish trust and accountability, especially in safety-critical domains. An established approach to interpretability is generating visual attribution maps that highlight regions of the input most relevant to the model's prediction. However, existing methods face a three-way trade-off. Propagation-based approaches are efficient, but they can be biased and architecture-specific. Meanwhile, perturbation-based methods are causally grounded, yet they are expensive and for vision transformers often yield coarse, patch-level explanations. Learning-based explainers are fast but usually optimize surrogate objectives or distill from heuristic teachers. We propose a learning scheme that instead optimizes deletion and insertion metrics directly. Since these metrics depend on non-differentiable sorting and ranking, we frame them as permutation learning and replace the hard sorting with a differentiable relaxation using Gumbel-Sinkhorn. This enables end-to-end training through attribution-guided perturbations of the target model. During inference, our method produces dense, pixel-level attributions in a single forward pass with optional, few-step gradient refinement. Our experiments demonstrate consistent quantitative improvements and sharper, boundary-aligned explanations, particularly for transformer-based vision models. Code and pretrained models are available at https://github.com/dschinagl/AHA.

This paper presents Text-Guided Backdoor (TGB), an adjustable backdoor attack against multimodal pretrained models that uses natural-word triggers, namely words that can naturally occur in ordinary textual inputs. Most existing backdoor attacks require specific trigger conditions that are typically not satisfied by ordinary inference inputs, thereby limiting their activation in real-world deployments. TGB overcomes this limitation by exploiting naturally occurring words as triggers, enabling stealthy activation without requiring explicit trigger insertion at inference time. This property avoids conspicuous trigger patterns and improves the practicality of TGB. Furthermore, we introduce visual adversarial perturbations on poisoned samples to modulate the model's learning of natural-word triggers, thereby enabling flexible adjustment of TGB attack strength without modifying the poisoned data. Extensive experiments are conducted on downstream tasks built upon multimodal pretrained models, including Composed Image Retrieval (CIR) and Visual Question Answering (VQA). Results demonstrate the effectiveness of TGB across diverse poisoning settings and its ability to flexibly adjust attack success rates, which reveal critical security vulnerabilities in multimodal pretrained models.

Large language model (LLM) agents have demonstrated strong capabilities in complex interactive decision-making tasks. However, existing LLM agents typically rely on increasingly long interaction histories, resulting in high computational cost and limited scalability. In this paper, we propose STEP-HRL, a hierarchical reinforcement learning (HRL) framework that enables step-level learning by conditioning only on single-step transitions rather than full interaction histories. STEP-HRL structures tasks hierarchically, using completed subtasks to represent global progress of overall task. By introducing a local progress module, it also iteratively and selectively summarizes interaction history within each subtask to produce a compact summary of local progress. Together, these components yield augmented step-level transitions for both high-level and low-level policies. Experimental results on ScienceWorld and ALFWorld benchmarks consistently demonstrate that STEP-HRL substantially outperforms baselines in terms of performance and generalization while reducing token usage. Our code is available at https://github.com/TonyStark042/STEP-HRL.

This chapter presents a novel approach to brain-to-speech (BTS) synthesis from intracranial electroencephalography (iEEG) data, emphasizing prosody-aware feature engineering and advanced transformer-based models for high-fidelity speech reconstruction. Driven by the increasing interest in decoding speech directly from brain activity, this work integrates neuroscience, artificial intelligence, and signal processing to generate accurate and natural speech. We introduce a novel pipeline for extracting key prosodic features directly from complex brain iEEG signals, including intonation, pitch, and rhythm. To effectively utilize these crucial features for natural-sounding speech, we employ advanced deep learning models. Furthermore, this chapter introduces a novel transformer encoder architecture specifically designed for brain-to-speech tasks. Unlike conventional models, our architecture integrates the extracted prosodic features to significantly enhance speech reconstruction, resulting in generated speech with improved intelligibility and expressiveness. A detailed evaluation demonstrates superior performance over established baseline methods, such as traditional Griffin-Lim and CNN-based reconstruction, across both quantitative and perceptual metrics. By demonstrating these advancements in feature extraction and transformer-based learning, this chapter contributes to the growing field of AI-driven neuroprosthetics, paving the way for assistive technologies that restore communication for individuals with speech impairments. Finally, we discuss promising future research directions, including the integration of diffusion models and real-time inference systems.

Real-world heterogeneous graphs are inherently noisy and usually not in the optimal graph structures for downstream tasks, which often adversely affects the performance of GRL models in downstream tasks. Although Graph Structure Learning (GSL) methods have been proposed to learn graph structures and downstream tasks simultaneously, existing methods are predominantly designed for homogeneous graphs, while GSL for heterogeneous graphs remains largely unexplored. Two challenges arise in this context. Firstly, the quality of the input graph structure has a more profound impact on GNN-based heterogeneous GRL models compared to their homogeneous counterparts. Secondly, most existing homogenous GRL models encounter memory consumption issues when applied directly to heterogeneous graphs. In this paper, we propose a novel Graph Topology learning Enhanced Heterogeneous Graph Representation Learning framework (ToGRL).ToGRL learns high-quality graph structures and representations for downstream tasks by incorporating task-relevant latent topology information. Specifically, a novel GSL module is first proposed to extract downstream task-related topology information from a raw graph structure and project it into topology embeddings. These embeddings are utilized to construct a new graph with smooth graph signals. This two-stage approach to GSL separates the optimization of the adjacency matrix from node representation learning to reduce memory consumption. Following this, a representation learning module takes the new graph as input to learn embeddings for downstream tasks. ToGRL also leverages prompt tuning to better utilize the knowledge embedded in learned representations, thus enhancing adaptability to downstream tasks. Extensive experiments on five real-world datasets show that our ToGRL outperforms state-of-the-art methods by a large margin.

Conditional discrete generative models struggle to faithfully compose multiple input conditions. To address this, we derive a theoretically-grounded formulation for composing discrete probabilistic generative processes, with masked generation (absorbing diffusion) as a special case. Our formulation enables precise specification of novel combinations and numbers of input conditions that lie outside the training data, with concept weighting enabling emphasis or negation of individual conditions. In synergy with the richly compositional learned vocabulary of VQ-VAE and VQ-GAN, our method attains a $63.4\%$ relative reduction in error rate compared to the previous state-of-the-art, averaged across 3 datasets (positional CLEVR, relational CLEVR and FFHQ), simultaneously obtaining an average absolute FID improvement of $-9.58$. Meanwhile, our method offers a $2.3\times$ to $12\times$ real-time speed-up over comparable methods, and is readily applied to an open pre-trained discrete text-to-image model for fine-grained control of text-to-image generation.

Breath acetone represents a promising non-invasive biomarker for monitoring fat oxidation during exercise. However, its utility is limited by confounding factors, as well as by the fact that significant changes in concentration occur only hours post-exercise, which makes real-time assessment difficult. We performed an untargeted screening for volatile organic compounds (VOCs) that could serve as markers of fat oxidation beyond acetone, and investigated whether breath measurements taken during exercise could predict post-exercise changes in fat oxidation. Nineteen participants completed two 25-min cycling sessions separated by a brief 5-min rest period. VOC emissions were analysed using proton-transfer-reaction time-of-flight mass spectrometry (PTR-TOF-MS) during exercise and after a 90-min recovery period. Blood $\beta$-hydroxybutyrate (BOHB) concentrations served as the reference marker for fat oxidation. Among 773 relevant analytical features detected in the PTR-TOF-MS measurements, only four signals exhibited strong correlations with BOHB ($\rho$ $\geq$ 0.82, p = 0.0002)-all attributable to acetone or its isotopologues or fragments. End-of-exercise measurements of these signals enabled accurate prediction of participants with substantial post-exercise BOHB changes (F1 score $\geq$ 0.83, accuracy = 0.89). Our study did not reveal any novel breath-based biomarkers of fat oxidation, but it confirmed acetone as the key marker. Moreover, our findings suggest that breath acetone measurements during exercise may already enable basic predictions of post-exercise fat oxidation.

High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as diffusion models and Flow Matching, have shown promising performance, they are fundamentally constrained by their discrete, pixel-based nature. This limitation restricts their applicability in turbulence computing, where data inherently exists in a functional form. To address this gap, we propose Functional Optimal Transport Conditional Flow Matching (FOT-CFM), a generative framework defined directly in infinite-dimensional function space. Unlike conventional approaches defined on fixed grids, FOT-CFM treats physical fields as elements of an infinite-dimensional Hilbert space, and learns resolution-invariant generative dynamics directly at the level of probability measures. By integrating Optimal Transport (OT) theory, we construct deterministic, straight-line probability paths between noise and data measures in Hilbert space. This formulation enables simulation-free training and significantly accelerates the sampling process. We rigorously evaluate the proposed system on a diverse suite of chaotic dynamical systems, including the Navier-Stokes equations, Kolmogorov Flow, and Hasegawa-Wakatani equations, all of which exhibit rich multi-scale turbulent structures. Experimental results demonstrate that FOT-CFM achieves superior fidelity in reproducing high-order turbulent statistics and energy spectra compared to state-of-the-art baselines.

We introduce LudoBench, a benchmark for evaluating LLM strategic reasoning in Ludo, a stochastic multi-agent board game whose dice mechanics, piece capture, safe-square navigation, and home-path progression introduce meaningful planning complexity. LudoBench comprises 480 handcrafted spot scenarios across 12 behaviorally distinct decision categories, each isolating a specific strategic choice. We additionally contribute a fully functional 4-player Ludo simulator supporting Random, Heuristic, Game-Theory, and LLM agents. The game-theory agent uses Expectiminimax search with depth-limited lookahead to provide a principled strategic ceiling beyond greedy heuristics. Evaluating six models spanning four model families, we find that all models agree with the game-theory baseline only 40-46% of the time. Models split into distinct behavioral archetypes: finishers that complete pieces but neglect development, and builders that develop but never finish. Each archetype captures only half of the game theory strategy. Models also display measurable behavioral shifts under history-conditioned grudge framing on identical board states, revealing prompt-sensitivity as a key vulnerability. LudoBench provides a lightweight and interpretable framework for benchmarking LLM strategic reasoning under uncertainty. All code, the spot dataset (480 entries) and model outputs are available at https://anonymous.4open.science/r/LudoBench-5CBF/

We introduce a natural displacement control for minimizer sets of oracle objectives equipped with certified epigraphic information. Formally, we replace the usual local uniform value control of objective perturbations - uncertifiable from finite pointwise information without additional structure - by the strictly weaker requirement of a cylinder-localized vertical epigraphic control, naturally provided by certified envelopes. Under set-based quadratic growth (allowing nonunique minimizers), this yields the classical square-root displacement estimate with optimal exponent 1/2, without any extrinsic assumption.

There is a growing demand for efficient data removal to comply with regulations like the GDPR and to mitigate the influence of biased or corrupted data. This has motivated the field of machine unlearning, which aims to eliminate the influence of specific data subsets without the cost of full retraining. In this work, we propose a statistical framework for machine unlearning with generic loss functions and establish theoretical guarantees. For squared loss, especially, we develop Unlearning Least Squares (ULS) and establish its minimax optimality for estimating the model parameter of remaining data when only the pre-trained estimator, forget samples, and a small subsample of the remaining data are available. Our results reveal that the estimation error decomposes into an oracle term and an unlearning cost determined by the forget proportion and the forget model bias. We further establish asymptotically valid inference procedures without requiring full retraining. Numerical experiments and real-data applications demonstrate that the proposed method achieves performance close to retraining while requiring substantially less data access.