Daily Papers

Reinforcement learning can align visual generators with reward signals beyond their pretraining objectives, but existing score-function methods typically introduce stochasticity by perturbing the reverse denoising trajectory, leading to costly rollout-based optimization. We instead ask whether stochastic exploration can be introduced inside the generator while preserving its original sampler. Routing Policy Optimization (RPO) answers this question by turning attention routing into a stochastic exploration action. At a few selected denoising levels, each query block keeps its own block and samples further key blocks in proportion to the generator's native attention mass, or keeps dense attention. The sampled route perturbs the velocity of that transition, and a Gaussian likelihood around the dense velocity scores the perturbation with a score-function objective. RPO further uses a controlled two-rollout estimator: two rollouts share the same prompt, initial latent, routed denoising levels, and dense anchor layers, differing only in their sampled attention routes. Their reward difference provides an advantage signal for the routed transitions. Because the likelihood differentiates the dense velocity itself, the learned updates remain effective after routing is removed. At inference, RPO restores dense attention and retains the original deterministic sampler. Experiments on text-to-image and text-to-video generation show that RPO improves generation quality while achieving nearly 4x higher training efficiency than Flow-GRPO-style methods. Please see our project page at https://velox-world.com/rpo for visual results.

We introduce a novel framework for efficient sampling from complex, unnormalised target distributions by exploiting multiscale dynamics. Traditional score-based sampling methods either rely on learned approximations of the score function or involve computationally expensive nested Markov chain Monte Carlo (MCMC) loops. In contrast, the proposed approach leverages stochastic averaging within a slow-fast system of stochastic differential equations (SDEs) to estimate intermediate scores along a diffusion path without training or inner-loop MCMC. Two algorithms are developed under this framework: MultALMC, which uses multiscale annealed Langevin dynamics, and MultCDiff, based on multiscale controlled diffusions for the reverse-time Ornstein-Uhlenbeck process. Both overdamped and underdamped variants are considered, with theoretical guarantees of convergence to the desired diffusion path. The framework is extended to handle heavy-tailed target distributions using Student's t-based noise models and tailored fast-process dynamics. Empirical results across synthetic and real-world benchmarks, including multimodal and high-dimensional distributions, demonstrate that the proposed methods are competitive with existing samplers in terms of accuracy and efficiency, without the need for learned models.

Many biological processes involve numerous coupled degrees of freedom, yet free-energy estimation is often restricted to one-dimensional profiles to mitigate the high computational cost of multidimensional sampling. In this work, we extend Fokker--Planck Score Learning (FPSL) to efficiently reconstruct two-dimensional free-energy landscapes from non-equilibrium molecular dynamics simulations using different types of collective variables. We show that explicitly modeling orthogonal degrees of freedom reveals insights hidden in one-dimensional projections at negligible computational overhead. Additionally, exploiting symmetries in the underlying landscape enhances reconstruction accuracy, while regularization techniques ensure numerical robustness in sparsely sampled regions. We validate our approach on three distinct systems: the conformational dynamics of alanine dipeptide, as well as coarse-grained and all-atom models of solute permeation through lipid bilayers. We demonstrate that, because FPSL learns a smooth score function rather than histogram-based densities, it overcomes the exponential scaling of grid-based methods, establishing it as a data-efficient and scalable tool for multidimensional free-energy estimation.

In applications of diffusion models, controllable generation is of practical significance, but is also challenging. Current methods for controllable generation primarily focus on modifying the score function of diffusion models, while Mean Reverting (MR) Diffusion directly modifies the structure of the stochastic differential equation (SDE), making the incorporation of image conditions simpler and more natural. However, current training-free fast samplers are not directly applicable to MR Diffusion. And thus MR Diffusion requires hundreds of NFEs (number of function evaluations) to obtain high-quality samples. In this paper, we propose a new algorithm named MRS (MR Sampler) to reduce the sampling NFEs of MR Diffusion. We solve the reverse-time SDE and the probability flow ordinary differential equation (PF-ODE) associated with MR Diffusion, and derive semi-analytical solutions. The solutions consist of an analytical function and an integral parameterized by a neural network. Based on this solution, we can generate high-quality samples in fewer steps. Our approach does not require training and supports all mainstream parameterizations, including noise prediction, data prediction and velocity prediction. Extensive experiments demonstrate that MR Sampler maintains high sampling quality with a speedup of 10 to 20 times across ten different image restoration tasks. Our algorithm accelerates the sampling procedure of MR Diffusion, making it more practical in controllable generation.

We argue that inventory management presents unique opportunities for the reliable application of deep reinforcement learning (DRL). To enable this, we emphasize and test two complementary techniques. The first is Hindsight Differentiable Policy Optimization (HDPO), which uses pathwise gradients from offline counterfactual simulations to directly and efficiently optimize policy performance. Unlike standard policy gradient methods that rely on high-variance score-function estimators, HDPO computes gradients by differentiating through the known system dynamics. Via extensive benchmarking, we show that HDPO recovers near-optimal policies in settings with known or bounded optima, is more robust than variants of the REINFORCE algorithm, and significantly outperforms generalized newsvendor heuristics on problems using real time series data. Our second technique aligns neural policy architectures with the topology of the inventory network. We exploit Graph Neural Networks (GNNs) as a natural inductive bias for encoding supply chain structure, demonstrate that they can represent optimal and near-optimal policies in two theoretical settings, and empirically show that they reduce data requirements across six diverse inventory problems. A key obstacle to progress in this area is the lack of standardized benchmark problems. To address this gap, we open-source a suite of benchmark environments, along with our full codebase, to promote transparency and reproducibility. All resources are available at github.com/MatiasAlvo/Neural_inventory_control.

Conformal prediction is a powerful framework for constructing prediction sets with valid coverage guarantees in multi-class classification. However, existing methods often rely on a single score function, which can limit their efficiency and informativeness. We propose a novel approach that combines multiple score functions to improve the performance of conformal predictors by identifying optimal weights that minimize prediction set size. Our theoretical analysis establishes a connection between the weighted score functions and subgraph classes of functions studied in Vapnik-Chervonenkis theory, providing a rigorous mathematical basis for understanding the effectiveness of the proposed method. Experiments demonstrate that our approach consistently outperforms single-score conformal predictors while maintaining valid coverage, offering a principled and data-driven way to enhance the efficiency and practicality of conformal prediction in classification tasks.

Recent controllable generation approaches such as FreeControl and Diffusion Self-guidance bring fine-grained spatial and appearance control to text-to-image (T2I) diffusion models without training auxiliary modules. However, these methods optimize the latent embedding for each type of score function with longer diffusion steps, making the generation process time-consuming and limiting their flexibility and use. This work presents Ctrl-X, a simple framework for T2I diffusion controlling structure and appearance without additional training or guidance. Ctrl-X designs feed-forward structure control to enable the structure alignment with a structure image and semantic-aware appearance transfer to facilitate the appearance transfer from a user-input image. Extensive qualitative and quantitative experiments illustrate the superior performance of Ctrl-X on various condition inputs and model checkpoints. In particular, Ctrl-X supports novel structure and appearance control with arbitrary condition images of any modality, exhibits superior image quality and appearance transfer compared to existing works, and provides instant plug-and-play functionality to any T2I and text-to-video (T2V) diffusion model. See our project page for an overview of the results: https://genforce.github.io/ctrl-x

Recent advances in one-step generative models typically follow a two-stage process: first training a teacher diffusion model and then distilling it into a one-step student model. This distillation process traditionally relies on both the teacher model's score function to compute the distillation loss and its weights for student initialization. In this paper, we explore whether one-step generative models can be trained directly without this distillation process. First, we show that the teacher's score function is not essential and propose a family of distillation methods that achieve competitive results without relying on score estimation. Next, we demonstrate that initialization from teacher weights is indispensable in successful training. Surprisingly, we find that this benefit is not due to improved ``input-output" mapping but rather the learned feature representations, which dominate distillation quality. Our findings provide a better understanding of the role of initialization in one-step model training and its impact on distillation quality.

Consistency Models (CM) (Song et al., 2023) accelerate score-based diffusion model sampling at the cost of sample quality but lack a natural way to trade-off quality for speed. To address this limitation, we propose Consistency Trajectory Model (CTM), a generalization encompassing CM and score-based models as special cases. CTM trains a single neural network that can -- in a single forward pass -- output scores (i.e., gradients of log-density) and enables unrestricted traversal between any initial and final time along the Probability Flow Ordinary Differential Equation (ODE) in a diffusion process. CTM enables the efficient combination of adversarial training and denoising score matching loss to enhance performance and achieves new state-of-the-art FIDs for single-step diffusion model sampling on CIFAR-10 (FID 1.73) and ImageNet at 64x64 resolution (FID 1.92). CTM also enables a new family of sampling schemes, both deterministic and stochastic, involving long jumps along the ODE solution trajectories. It consistently improves sample quality as computational budgets increase, avoiding the degradation seen in CM. Furthermore, unlike CM, CTM's access to the score function can streamline the adoption of established controllable/conditional generation methods from the diffusion community. This access also enables the computation of likelihood. The code is available at https://github.com/sony/ctm.

Self-supervised contrastive learning (CL) has achieved state-of-the-art performance in representation learning by minimizing the distance between positive pairs while maximizing that of negative ones. Recently, it has been verified that the model learns better representation with diversely augmented positive pairs because they enable the model to be more view-invariant. However, only a few studies on CL have considered the difference between augmented views, and have not gone beyond the hand-crafted findings. In this paper, we first observe that the score-matching function can measure how much data has changed from the original through augmentation. With the observed property, every pair in CL can be weighted adaptively by the difference of score values, resulting in boosting the performance of the existing CL method. We show the generality of our method, referred to as ScoreCL, by consistently improving various CL methods, SimCLR, SimSiam, W-MSE, and VICReg, up to 3%p in k-NN evaluation on CIFAR-10, CIFAR-100, and ImageNet-100. Moreover, we have conducted exhaustive experiments and ablations, including results on diverse downstream tasks, comparison with possible baselines, and improvement when used with other proposed augmentation methods. We hope our exploration will inspire more research in exploiting the score matching for CL.

Single image-to-3D generation is pivotal for crafting controllable 3D assets. Given its underconstrained nature, we leverage geometric priors from a 3D novel view generation diffusion model and appearance priors from a 2D image generation method to guide the optimization process. We note that a disparity exists between the training datasets of 2D and 3D diffusion models, leading to their outputs showing marked differences in appearance. Specifically, 2D models tend to deliver more detailed visuals, whereas 3D models produce consistent yet over-smooth results across different views. Hence, we optimize a set of 3D Gaussians using 3D priors in spatial domain to ensure geometric consistency, while exploiting 2D priors in the frequency domain through Fourier transform for higher visual quality. This 2D-3D hybrid Fourier Score Distillation objective function (dubbed hy-FSD), can be integrated into existing 3D generation methods, yielding significant performance improvements. With this technique, we further develop an image-to-3D generation pipeline to create high-quality 3D objects within one minute, named Fourier123. Extensive experiments demonstrate that Fourier123 excels in efficient generation with rapid convergence speed and visual-friendly generation results.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

In this research, we compare four different evaluation methods in coevolution on the Majority Function problem. The size of the problem is selected such that evaluation against all possible test cases is feasible. Two measures are used for the comparisons, i.e., the objective fitness derived from evaluating solutions against all test cases, and the objective fitness correlation (OFC), which is defined as the correlation coefficient between subjective and objective fitness. The results of our experiments suggest that a combination of average score and weighted informativeness may provide a more accurate evaluation in coevolution. In order to confirm this difference, a series of t-tests on the preference between each pair of the evaluation methods is performed. The resulting significance is affirmative, and the tests for two quality measures show similar preference on four evaluation methods. %This study is the first time OFC is actually computed on a real problem. Experiments on Majority Function problems with larger sizes and Parity problems are in progress, and their results will be added in the final version.

This paper proposes a novel framework for the use of eye movement patterns for biometric applications. Eye movements contain abundant information about cognitive brain functions, neural pathways, etc. In the proposed method, eye movement data is classified into fixations and saccades. Features extracted from fixations and saccades are used by a Gaussian Radial Basis Function Network (GRBFN) based method for biometric authentication. A score fusion approach is adopted to classify the data in the output layer. In the evaluation stage, the algorithm has been tested using two types of stimuli: random dot following on a screen and text reading. The results indicate the strength of eye movement pattern as a biometric modality. The algorithm has been evaluated on BioEye 2015 database and found to outperform all the other methods. Eye movements are generated by a complex oculomotor plant which is very hard to spoof by mechanical replicas. Use of eye movement dynamics along with iris recognition technology may lead to a robust counterfeit-resistant person identification system.

Diffusion models offer powerful generative capabilities for robot trajectory planning, yet their practical deployment on robots is hindered by a critical bottleneck: a reliance on imitation learning from expert demonstrations. This paradigm is often impractical for specialized robots where data is scarce and creates an inefficient, theoretically suboptimal training pipeline. To overcome this, we introduce PegasusFlow, a hierarchical rolling-denoising framework that enables direct and parallel sampling of trajectory score gradients from environmental interaction, completely bypassing the need for expert data. Our core innovation is a novel sampling algorithm, Weighted Basis Function Optimization (WBFO), which leverages spline basis representations to achieve superior sample efficiency and faster convergence compared to traditional methods like MPPI. The framework is embedded within a scalable, asynchronous parallel simulation architecture that supports massively parallel rollouts for efficient data collection. Extensive experiments on trajectory optimization and robotic navigation tasks demonstrate that our approach, particularly Action-Value WBFO (AVWBFO) combined with a reinforcement learning warm-start, significantly outperforms baselines. In a challenging barrier-crossing task, our method achieved a 100% success rate and was 18% faster than the next-best method, validating its effectiveness for complex terrain locomotion planning. https://masteryip.github.io/pegasusflow.github.io/

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

In an era marked by the rapid scaling of foundation models, autonomous driving technologies are approaching a transformative threshold where end-to-end autonomous driving (E2E-AD) emerges due to its potential of scaling up in the data-driven manner. However, existing E2E-AD methods are mostly evaluated under the open-loop log-replay manner with L2 errors and collision rate as metrics (e.g., in nuScenes), which could not fully reflect the driving performance of algorithms as recently acknowledged in the community. For those E2E-AD methods evaluated under the closed-loop protocol, they are tested in fixed routes (e.g., Town05Long and Longest6 in CARLA) with the driving score as metrics, which is known for high variance due to the unsmoothed metric function and large randomness in the long route. Besides, these methods usually collect their own data for training, which makes algorithm-level fair comparison infeasible. To fulfill the paramount need of comprehensive, realistic, and fair testing environments for Full Self-Driving (FSD), we present Bench2Drive, the first benchmark for evaluating E2E-AD systems' multiple abilities in a closed-loop manner. Bench2Drive's official training data consists of 2 million fully annotated frames, collected from 13638 short clips uniformly distributed under 44 interactive scenarios (cut-in, overtaking, detour, etc), 23 weathers (sunny, foggy, rainy, etc), and 12 towns (urban, village, university, etc) in CARLA v2. Its evaluation protocol requires E2E-AD models to pass 44 interactive scenarios under different locations and weathers which sums up to 220 routes and thus provides a comprehensive and disentangled assessment about their driving capability under different situations. We implement state-of-the-art E2E-AD models and evaluate them in Bench2Drive, providing insights regarding current status and future directions.

Large models based on the Transformer architecture are susceptible to extreme-token phenomena, such as attention sinks and value-state drains. These issues, which degrade model performance, quantization fidelity, and interpretability, arise from a problematic mutual reinforcement mechanism where the model learns an inefficient 'no-op' behavior by focusing attention on tokens with near-zero value states. In this paper, we propose Value-State Gated Attention (VGA), a simple, dedicated, and stable architectural mechanism for performing 'no-op' attention efficiently by directly breaking this cycle. VGA introduces a learnable, data-dependent gate, computed directly from the value vectors (V), to modulate the output. Through a theoretical analysis of the underlying gradients, we show that gating the value-state with a function of itself is more effective at decoupling value and attention score updates than prior methods that gate on input embeddings. This creates a direct regulatory pathway that allows the model to suppress a token's contribution based on its emergent value representation. Our experiments demonstrate that VGA significantly mitigates the formation of attention sinks and stabilizes value-state norms, leading to improved performance, robust quantization fidelity, and enhanced model interpretability.

Plasma modeling is central to the design of nuclear fusion reactors, yet simulating collisional plasma kinetics from first principles remains a formidable computational challenge: the Vlasov-Maxwell-Landau (VML) system describes six-dimensional phase-space transport under self-consistent electromagnetic fields together with the nonlinear, nonlocal Landau collision operator. A recent deterministic particle method for the full VML system estimates the velocity score function via the blob method, a kernel-based approximation with O(n^2) cost. In this work, we replace the blob score estimator with score-based transport modeling (SBTM), in which a neural network is trained on-the-fly via implicit score matching at O(n) cost. We prove that the approximated collision operator preserves momentum and kinetic energy, and dissipates an estimated entropy. We also characterize the unique global steady state of the VML system and its electrostatic reduction, providing the ground truth for numerical validation. On three canonical benchmarks -- Landau damping, two-stream instability, and Weibel instability -- SBTM is more accurate than the blob method, achieves correct long-time relaxation to Maxwellian equilibrium where the blob method fails, and delivers 50% faster runtime with 4times lower peak memory.

There is a long history, as well as a recent explosion of interest, in statistical and generative modeling approaches based on score functions -- derivatives of the log-likelihood of a distribution. In seminal works, Hyv\"arinen proposed vanilla score matching as a way to learn distributions from data by computing an estimate of the score function of the underlying ground truth, and established connections between this method and established techniques like Contrastive Divergence and Pseudolikelihood estimation. It is by now well-known that vanilla score matching has significant difficulties learning multimodal distributions. Although there are various ways to overcome this difficulty, the following question has remained unanswered -- is there a natural way to sample multimodal distributions using just the vanilla score? Inspired by a long line of related experimental works, we prove that the Langevin diffusion with early stopping, initialized at the empirical distribution, and run on a score function estimated from data successfully generates natural multimodal distributions (mixtures of log-concave distributions).

We deal with the combinatorial problem of learning directed acyclic graph (DAG) structure from observational data adhering to a linear structural equation model (SEM). Leveraging advances in differentiable, nonconvex characterizations of acyclicity, recent efforts have advocated a continuous constrained optimization paradigm to efficiently explore the space of DAGs. Most existing methods employ lasso-type score functions to guide this search, which (i) require expensive penalty parameter retuning when the unknown SEM noise variances change across problem instances; and (ii) implicitly rely on limiting homoscedasticity assumptions. In this work, we propose a new convex score function for sparsity-aware learning of linear DAGs, which incorporates concomitant estimation of scale and thus effectively decouples the sparsity parameter from the exogenous noise levels. Regularization via a smooth, nonconvex acyclicity penalty term yields CoLiDE (Concomitant Linear DAG Estimation), a regression-based criterion amenable to efficient gradient computation and closed-form estimation of noise variances in heteroscedastic scenarios. Our algorithm outperforms state-of-the-art methods without incurring added complexity, especially when the DAGs are larger and the noise level profile is heterogeneous. We also find CoLiDE exhibits enhanced stability manifested via reduced standard deviations in several domain-specific metrics, underscoring the robustness of our novel linear DAG estimator.

Accelerating the sampling speed of diffusion models remains a significant challenge. Recent score distillation methods distill a heavy teacher model into an one-step student generator, which is optimized by calculating the difference between the two score functions on the samples generated by the student model. However, there is a score mismatch issue in the early stage of the distillation process, because existing methods mainly focus on using the endpoint of pre-trained diffusion models as teacher models, overlooking the importance of the convergence trajectory between the student generator and the teacher model. To address this issue, we extend the score distillation process by introducing the entire convergence trajectory of teacher models and propose Distribution Backtracking Distillation (DisBack) for distilling student generators. DisBask is composed of two stages: Degradation Recording and Distribution Backtracking. Degradation Recording is designed to obtain the convergence trajectory of teacher models, which records the degradation path from the trained teacher model to the untrained initial student generator. The degradation path implicitly represents the intermediate distributions of teacher models. Then Distribution Backtracking trains a student generator to backtrack the intermediate distributions for approximating the convergence trajectory of teacher models. Extensive experiments show that DisBack achieves faster and better convergence than the existing distillation method and accomplishes comparable generation performance. Notably, DisBack is easy to implement and can be generalized to existing distillation methods to boost performance. Our code is publicly available on https://github.com/SYZhang0805/DisBack.

Recently, there has been extensive research interest in training deep networks to denoise images without clean reference. However, the representative approaches such as Noise2Noise, Noise2Void, Stein's unbiased risk estimator (SURE), etc. seem to differ from one another and it is difficult to find the coherent mathematical structure. To address this, here we present a novel approach, called Noise2Score, which reveals a missing link in order to unite these seemingly different approaches. Specifically, we show that image denoising problems without clean images can be addressed by finding the mode of the posterior distribution and that the Tweedie's formula offers an explicit solution through the score function (i.e. the gradient of log likelihood). Our method then uses the recent finding that the score function can be stably estimated from the noisy images using the amortized residual denoising autoencoder, the method of which is closely related to Noise2Noise or Nose2Void. Our Noise2Score approach is so universal that the same network training can be used to remove noises from images that are corrupted by any exponential family distributions and noise parameters. Using extensive experiments with Gaussian, Poisson, and Gamma noises, we show that Noise2Score significantly outperforms the state-of-the-art self-supervised denoising methods in the benchmark data set such as (C)BSD68, Set12, and Kodak, etc.

Many NLP tasks, such as summarization and extractive question answering, reduce to retrieving relevant content from documents under two constraints: coverage, retaining enough pertinent information to achieve some goal, and conciseness, removing as much irrelevant information as possible. Conformal prediction methods have been used to guarantee coverage, and must be optimized for conciseness through design of a score function. State-of-the-art scoring functions use hand-engineered LLM prompts asking the model to rate the importance of content, but manual prompt engineering is labor-intensive and task-specific. We introduce the Conformal Relevance framework which uses in-context learning example curation and ensembling to create a score function which maintains coverage while improving conciseness with minimal manual input. We demonstrate this framework's application on seven NLP tasks, and also theoretically study the impact of diversity for ensembled conformal scores, giving a complementarity condition that characterizes when ensembling improves worst-case sentence scores, and a saturation bound on ensemble improvement.

We introduce iterative reasoning through energy diffusion (IRED), a novel framework for learning to reason for a variety of tasks by formulating reasoning and decision-making problems with energy-based optimization. IRED learns energy functions to represent the constraints between input conditions and desired outputs. After training, IRED adapts the number of optimization steps during inference based on problem difficulty, enabling it to solve problems outside its training distribution -- such as more complex Sudoku puzzles, matrix completion with large value magnitudes, and pathfinding in larger graphs. Key to our method's success is two novel techniques: learning a sequence of annealed energy landscapes for easier inference and a combination of score function and energy landscape supervision for faster and more stable training. Our experiments show that IRED outperforms existing methods in continuous-space reasoning, discrete-space reasoning, and planning tasks, particularly in more challenging scenarios. Code and visualizations at https://energy-based-model.github.io/ired/

Diffusion models have emerged as a powerful tool rivaling GANs in generating high-quality samples with improved fidelity, flexibility, and robustness. A key component of these models is to learn the score function through score matching. Despite empirical success on various tasks, it remains unclear whether gradient-based algorithms can learn the score function with a provable accuracy. As a first step toward answering this question, this paper establishes a mathematical framework for analyzing score estimation using neural networks trained by gradient descent. Our analysis covers both the optimization and the generalization aspects of the learning procedure. In particular, we propose a parametric form to formulate the denoising score-matching problem as a regression with noisy labels. Compared to the standard supervised learning setup, the score-matching problem introduces distinct challenges, including unbounded input, vector-valued output, and an additional time variable, preventing existing techniques from being applied directly. In this paper, we show that with proper designs, the evolution of neural networks during training can be accurately modeled by a series of kernel regression tasks. Furthermore, by applying an early-stopping rule for gradient descent and leveraging recent developments in neural tangent kernels, we establish the first generalization error (sample complexity) bounds for learning the score function with neural networks, despite the presence of noise in the observations. Our analysis is grounded in a novel parametric form of the neural network and an innovative connection between score matching and regression analysis, facilitating the application of advanced statistical and optimization techniques.

Curriculum Learning is the presentation of samples to the machine learning model in a meaningful order instead of a random order. The main challenge of Curriculum Learning is determining how to rank these samples. The ranking of the samples is expressed by the scoring function. In this study, scoring functions were compared using data set features, using the model to be trained, and using another model and their ensemble versions. Experiments were performed for 4 images and 4 text datasets. No significant differences were found between scoring functions for text datasets, but significant improvements were obtained in scoring functions created using transfer learning compared to classical model training and other scoring functions for image datasets. It shows that different new scoring functions are waiting to be found for text classification tasks.

Large Language Models (LLMs) are increasingly deployed in high-stakes domains such as science, law, and healthcare, where accurate expressions of uncertainty are essential for reliability and trust. However, current LLMs are often observed to generate incorrect answers with high confidence, a phenomenon known as "overconfidence". Recent efforts have focused on calibrating LLMs' verbalized confidence: i.e., their expressions of confidence in text form, such as "I am 80% confident that...". Existing approaches either rely on prompt engineering or fine-tuning with heuristically generated uncertainty estimates, both of which have limited effectiveness and generalizability. Motivated by the notion of proper scoring rules for calibration in classical machine learning models, we introduce ConfTuner, a simple and efficient fine-tuning method that introduces minimal overhead and does not require ground-truth confidence scores or proxy confidence estimates. ConfTuner relies on a new loss function, tokenized Brier score, which we theoretically prove to be a proper scoring rule, intuitively meaning that it "correctly incentivizes the model to report its true probability of being correct". ConfTuner improves calibration across diverse reasoning tasks and generalizes to black-box models such as GPT-4o. Our results further show that better-calibrated confidence enables downstream gains in self-correction and model cascade, advancing the development of trustworthy LLM systems. The code is available at https://github.com/liushiliushi/ConfTuner.

Score-based generative models (SGMs) sample from a target distribution by iteratively transforming noise using the score function of the perturbed target. For any finite training set, this score function can be evaluated in closed form, but the resulting SGM memorizes its training data and does not generate novel samples. In practice, one approximates the score by training a neural network via score-matching. The error in this approximation promotes generalization, but neural SGMs are costly to train and sample, and the effective regularization this error provides is not well-understood theoretically. In this work, we instead explicitly smooth the closed-form score to obtain an SGM that generates novel samples without training. We analyze our model and propose an efficient nearest-neighbor-based estimator of its score function. Using this estimator, our method achieves competitive sampling times while running on consumer-grade CPUs.

Many existing conditional score-based data generation methods utilize Bayes' theorem to decompose the gradients of a log posterior density into a mixture of scores. These methods facilitate the training procedure of conditional score models, as a mixture of scores can be separately estimated using a score model and a classifier. However, our analysis indicates that the training objectives for the classifier in these methods may lead to a serious score mismatch issue, which corresponds to the situation that the estimated scores deviate from the true ones. Such an issue causes the samples to be misled by the deviated scores during the diffusion process, resulting in a degraded sampling quality. To resolve it, we formulate a novel training objective, called Denoising Likelihood Score Matching (DLSM) loss, for the classifier to match the gradients of the true log likelihood density. Our experimental evidence shows that the proposed method outperforms the previous methods on both Cifar-10 and Cifar-100 benchmarks noticeably in terms of several key evaluation metrics. We thus conclude that, by adopting DLSM, the conditional scores can be accurately modeled, and the effect of the score mismatch issue is alleviated.

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.

We consider the problem of subset selection where one is given multiple rankings of items and the goal is to select the highest ``quality'' subset. Score functions from the multiwinner voting literature have been used to aggregate rankings into quality scores for subsets. We study this setting of subset selection problems when, in addition, rankings may contain systemic or unconscious biases toward a group of items. For a general model of input rankings and biases, we show that requiring the selected subset to satisfy group fairness constraints can improve the quality of the selection with respect to unbiased rankings. Importantly, we show that for fairness constraints to be effective, different multiwinner score functions may require a drastically different number of rankings: While for some functions, fairness constraints need an exponential number of rankings to recover a close-to-optimal solution, for others, this dependency is only polynomial. This result relies on a novel notion of ``smoothness'' of submodular functions in this setting that quantifies how well a function can ``correctly'' assess the quality of items in the presence of bias. The results in this paper can be used to guide the choice of multiwinner score functions for the subset selection setting considered here; we additionally provide a tool to empirically enable this.

Score-based diffusion modeling is a generative machine learning algorithm that can be used to sample from complex distributions. They achieve this by learning a score function, i.e., the gradient of the log-probability density of the data, and reversing a noising process using the same. Once trained, score-based diffusion models not only generate new samples but also enable zero-shot conditioning of the generated samples on observed data. This promises a novel paradigm for data and model fusion, wherein the implicitly learned distributions of pretrained score-based diffusion models can be updated given the availability of online data in a Bayesian formulation. In this article, we apply such a concept to the super-resolution of a high-dimensional dynamical system, given the real-time availability of low-resolution and experimentally observed sparse sensor measurements from multimodal data. Additional analysis on how score-based sampling can be used for uncertainty estimates is also provided. Our experiments are performed for a super-resolution task that generates the ERA5 atmospheric dataset given sparse observations from a coarse-grained representation of the same and/or from unstructured experimental observations of the IGRA radiosonde dataset. We demonstrate accurate recovery of the high dimensional state given multiple sources of low-fidelity measurements. We also discover that the generative model can balance the influence of multiple dataset modalities during spatiotemporal reconstructions.

We discuss methods for modeling eclipsing binary stars using the "physical", "simplified" and "phenomenological" models. There are few realizations of the "physical" Wilson-Devinney (1971) code and its improvements, e.g. Binary Maker, Phoebe. A parameter search using the Monte-Carlo method was realized by Zola et al. (2010), which is efficient in expense of too many evaluations of the test function. We compare existing algorithms of minimization of multi-parametric functions and propose to use a "combined" algorithm, depending on if the Hessian matrix is positively determined. To study methods, a simply fast-computed function resembling the "complete" test function for the physical model. Also we adopt a simplified model of an eclipsing binary at a circular orbit assuming spherical components with an uniform brightness distribution. This model resembles more advanced models in a sense of correlated parameter estimates due to a similar topology of the test function. Such a model may be applied to detached Algol-type systems, where the tidal distortion of components is negligible.

Post-hoc out-of-distribution (OOD) detection has garnered intensive attention in reliable machine learning. Many efforts have been dedicated to deriving score functions based on logits, distances, or rigorous data distribution assumptions to identify low-scoring OOD samples. Nevertheless, these estimate scores may fail to accurately reflect the true data density or impose impractical constraints. To provide a unified perspective on density-based score design, we propose a novel theoretical framework grounded in Bregman divergence, which extends distribution considerations to encompass an exponential family of distributions. Leveraging the conjugation constraint revealed in our theorem, we introduce a ConjNorm method, reframing density function design as a search for the optimal norm coefficient p against the given dataset. In light of the computational challenges of normalization, we devise an unbiased and analytically tractable estimator of the partition function using the Monte Carlo-based importance sampling technique. Extensive experiments across OOD detection benchmarks empirically demonstrate that our proposed ConjNorm has established a new state-of-the-art in a variety of OOD detection setups, outperforming the current best method by up to 13.25% and 28.19% (FPR95) on CIFAR-100 and ImageNet-1K, respectively.

A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This fragmentation of goals causes not only an inconsistent conceptual understanding of explanations but also the practical challenge of not knowing which method to use when. In this work, we begin to address these challenges by unifying eight popular post hoc explanation methods (LIME, C-LIME, KernelSHAP, Occlusion, Vanilla Gradients, Gradients x Input, SmoothGrad, and Integrated Gradients). We show that these methods all perform local function approximation of the black-box model, differing only in the neighbourhood and loss function used to perform the approximation. This unification enables us to (1) state a no free lunch theorem for explanation methods, demonstrating that no method can perform optimally across all neighbourhoods, and (2) provide a guiding principle to choose among methods based on faithfulness to the black-box model. We empirically validate these theoretical results using various real-world datasets, model classes, and prediction tasks. By bringing diverse explanation methods into a common framework, this work (1) advances the conceptual understanding of these methods, revealing their shared local function approximation objective, properties, and relation to one another, and (2) guides the use of these methods in practice, providing a principled approach to choose among methods and paving the way for the creation of new ones.

By learning the gradient of smoothed data distributions, diffusion models can iteratively generate samples from complex distributions. The learned score function enables their generalization capabilities, but how the learned score relates to the score of the underlying data manifold remains largely unclear. Here, we aim to elucidate this relationship by comparing learned neural scores to the scores of two kinds of analytically tractable distributions: Gaussians and Gaussian mixtures. The simplicity of the Gaussian model makes it theoretically attractive, and we show that it admits a closed-form solution and predicts many qualitative aspects of sample generation dynamics. We claim that the learned neural score is dominated by its linear (Gaussian) approximation for moderate to high noise scales, and supply both theoretical and empirical arguments to support this claim. Moreover, the Gaussian approximation empirically works for a larger range of noise scales than naive theory suggests it should, and is preferentially learned early in training. At smaller noise scales, we observe that learned scores are better described by a coarse-grained (Gaussian mixture) approximation of training data than by the score of the training distribution, a finding consistent with generalization. Our findings enable us to precisely predict the initial phase of trained models' sampling trajectories through their Gaussian approximations. We show that this allows the skipping of the first 15-30% of sampling steps while maintaining high sample quality (with a near state-of-the-art FID score of 1.93 on CIFAR-10 unconditional generation). This forms the foundation of a novel hybrid sampling method, termed analytical teleportation, which can seamlessly integrate with and accelerate existing samplers, including DPM-Solver-v3 and UniPC. Our findings suggest ways to improve the design and training of diffusion models.

Accurate identification of software vulnerabilities is crucial for system integrity. Vulnerability datasets, often derived from the National Vulnerability Database (NVD) or directly from GitHub, are essential for training machine learning models to detect these security flaws. However, these datasets frequently suffer from significant noise, typically 40% to 75%, due primarily to the automatic and indiscriminate labeling of all changes in vulnerability-fixing commits (VFCs) as vulnerability-related. This misclassification occurs because not all changes in a commit aimed at fixing vulnerabilities pertain to security threats; many are routine updates like bug fixes or test improvements. This paper introduces the first methodology that uses the Large Language Model (LLM) with a heuristic enhancement to automatically identify vulnerability-fixing changes from VFCs, achieving an F1-score of 0.82. VulSifter was applied to a large-scale study, where we conducted a crawl of 127,063 repositories on GitHub, resulting in the acquisition of 5,352,105 commits. VulSifter involves utilizing an LLM to comprehend code semantics and contextual information, while applying heuristics to filter out unrelated changes. We then developed CleanVul, a high-quality dataset comprising 8,198 functions using our LLM heuristic enhancement approach, demonstrating Correctness (90.6%) comparable to established datasets such as SVEN and PrimeVul. To evaluate the CleanVul dataset, we conducted experiments focusing on fine-tuning various LLMs on CleanVul and other high-quality datasets. Evaluation results reveal that LLMs fine-tuned on CleanVul not only exhibit enhanced accuracy but also superior generalization capabilities compared to those trained on uncleaned datasets. Specifically, models trained on CleanVul and tested on PrimeVul achieve accuracy higher than those trained and tested exclusively on PrimeVul.

Fine-tuning pre-trained language models (PLMs), e.g., SciBERT, generally requires large numbers of annotated data to achieve state-of-the-art performance on a range of NLP tasks in the scientific domain. However, obtaining the fine-tune data for scientific NLP task is still challenging and expensive. Inspired by recent advancement in prompt learning, in this paper, we propose the Mix Prompt Tuning (MPT), which is a semi-supervised method to alleviate the dependence on annotated data and improve the performance of multi-granularity academic function recognition tasks with a small number of labeled examples. Specifically, the proposed method provides multi-perspective representations by combining manual prompt templates with automatically learned continuous prompt templates to help the given academic function recognition task take full advantage of knowledge in PLMs. Based on these prompt templates and the fine-tuned PLM, a large number of pseudo labels are assigned to the unlabeled examples. Finally, we fine-tune the PLM using the pseudo training set. We evaluate our method on three academic function recognition tasks of different granularity including the citation function, the abstract sentence function, and the keyword function, with datasets from computer science domain and biomedical domain. Extensive experiments demonstrate the effectiveness of our method and statistically significant improvements against strong baselines. In particular, it achieves an average increase of 5% in Macro-F1 score compared with fine-tuning, and 6% in Macro-F1 score compared with other semi-supervised method under low-resource settings. In addition, MPT is a general method that can be easily applied to other low-resource scientific classification tasks.

The rapid growth of scientific submissions has pushed traditional peer review toward its scalability limits, motivating the exploration of large language models (LLMs) as intelligent automated evaluation assistants. Although recent studies show that LLMs can generate fluent critiques and approximate reviewer scores, their reliability, robustness, and security as decision-support systems remain insufficiently understood. This survey offers a systems-level analysis of LLM-based scientific peer review, focusing on two core evaluative functions: critique generation and score prediction. We present a structured taxonomy of modeling approaches (including prompt-based, supervised, retrieval-augmented, and alignment-optimized approaches), and synthesize empirical findings across existing benchmarks. We analyze dataset constraints, evaluation shortcomings, and domain concentration biases that limit current assessment practices. Beyond performance metrics, we identify emerging robustness risks, including prompt injection, data poisoning, retrieval vulnerabilities, and reward hacking, which expose automated review pipelines to strategic manipulation. From a data mining perspective, we outline key open challenges in modeling subjective disagreement and cross-domain generalization. By reframing automated peer review as a high-stakes, multi-objective decision problem, this survey provides a roadmap for developing robust, transparent, and trustworthy AI-assisted scientific evaluation systems.

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small L^2 error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in epsilon-accuracy can be done in tilde Oleft(d log (1/delta){epsilon}right) steps: 1) the variance-delta Gaussian perturbation of any data distribution; 2) data distributions with 1/delta-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

Recent advancements in 3D scene editing have been propelled by the rapid development of generative models. Existing methods typically utilize generative models to perform text-guided editing on 3D representations, such as 3D Gaussian Splatting (3DGS). However, these methods are often limited to texture modifications and fail when addressing geometric changes, such as editing a character's head to turn around. Moreover, such methods lack accurate control over the spatial position of editing results, as language struggles to precisely describe the extent of edits. To overcome these limitations, we introduce DYG, an effective 3D drag-based editing method for 3D Gaussian Splatting. It enables users to conveniently specify the desired editing region and the desired dragging direction through the input of 3D masks and pairs of control points, thereby enabling precise control over the extent of editing. DYG integrates the strengths of the implicit triplane representation to establish the geometric scaffold of the editing results, effectively overcoming suboptimal editing outcomes caused by the sparsity of 3DGS in the desired editing regions. Additionally, we incorporate a drag-based Latent Diffusion Model into our method through the proposed Drag-SDS loss function, enabling flexible, multi-view consistent, and fine-grained editing. Extensive experiments demonstrate that DYG conducts effective drag-based editing guided by control point prompts, surpassing other baselines in terms of editing effect and quality, both qualitatively and quantitatively. Visit our project page at https://quyans.github.io/Drag-Your-Gaussian.

We propose a Monte Carlo sampler from the reverse diffusion process. Unlike the practice of diffusion models, where the intermediary updates -- the score functions -- are learned with a neural network, we transform the score matching problem into a mean estimation one. By estimating the means of the regularized posterior distributions, we derive a novel Monte Carlo sampling algorithm called reverse diffusion Monte Carlo (rdMC), which is distinct from the Markov chain Monte Carlo (MCMC) methods. We determine the sample size from the error tolerance and the properties of the posterior distribution to yield an algorithm that can approximately sample the target distribution with any desired accuracy. Additionally, we demonstrate and prove under suitable conditions that sampling with rdMC can be significantly faster than that with MCMC. For multi-modal target distributions such as those in Gaussian mixture models, rdMC greatly improves over the Langevin-style MCMC sampling methods both theoretically and in practice. The proposed rdMC method offers a new perspective and solution beyond classical MCMC algorithms for the challenging complex distributions.

We introduce BM25S, an efficient Python-based implementation of BM25 that only depends on Numpy and Scipy. BM25S achieves up to a 500x speedup compared to the most popular Python-based framework by eagerly computing BM25 scores during indexing and storing them into sparse matrices. It also achieves considerable speedups compared to highly optimized Java-based implementations, which are used by popular commercial products. Finally, BM25S reproduces the exact implementation of five BM25 variants based on Kamphuis et al. (2020) by extending eager scoring to non-sparse variants using a novel score shifting method. The code can be found at https://github.com/xhluca/bm25s

Neural Posterior Estimation methods for simulation-based inference can be ill-suited for dealing with posterior distributions obtained by conditioning on multiple observations, as they tend to require a large number of simulator calls to learn accurate approximations. In contrast, Neural Likelihood Estimation methods can handle multiple observations at inference time after learning from individual observations, but they rely on standard inference methods, such as MCMC or variational inference, which come with certain performance drawbacks. We introduce a new method based on conditional score modeling that enjoys the benefits of both approaches. We model the scores of the (diffused) posterior distributions induced by individual observations, and introduce a way of combining the learned scores to approximately sample from the target posterior distribution. Our approach is sample-efficient, can naturally aggregate multiple observations at inference time, and avoids the drawbacks of standard inference methods.

Identifying cirrhosis is key to correctly assess the health of the liver. However, the gold standard diagnosis of the cirrhosis needs a medical intervention to obtain the histological confirmation, e.g. the METAVIR score, as the radiological presentation can be equivocal. In this work, we propose to leverage transfer learning from large datasets annotated by radiologists, which we consider as a weak annotation, to predict the histological score available on a small annex dataset. To this end, we propose to compare different pretraining methods, namely weakly-supervised and self-supervised ones, to improve the prediction of the cirrhosis. Finally, we introduce a loss function combining both supervised and self-supervised frameworks for pretraining. This method outperforms the baseline classification of the METAVIR score, reaching an AUC of 0.84 and a balanced accuracy of 0.75, compared to 0.77 and 0.72 for a baseline classifier.

Large Language Models (LLMs) exhibit remarkable capabilities but are susceptible to adversarial prompts that exploit vulnerabilities to produce unsafe or biased outputs. Existing red-teaming methods often face scalability challenges, resource-intensive requirements, or limited diversity in attack strategies. We propose RainbowPlus, a novel red-teaming framework rooted in evolutionary computation, enhancing adversarial prompt generation through an adaptive quality-diversity (QD) search that extends classical evolutionary algorithms like MAP-Elites with innovations tailored for language models. By employing a multi-element archive to store diverse high-quality prompts and a comprehensive fitness function to evaluate multiple prompts concurrently, RainbowPlus overcomes the constraints of single-prompt archives and pairwise comparisons in prior QD methods like Rainbow Teaming. Experiments comparing RainbowPlus to QD methods across six benchmark datasets and four open-source LLMs demonstrate superior attack success rate (ASR) and diversity (Diverse-Score approx 0.84), generating up to 100 times more unique prompts (e.g., 10,418 vs. 100 for Ministral-8B-Instruct-2410). Against nine state-of-the-art methods on the HarmBench dataset with twelve LLMs (ten open-source, two closed-source), RainbowPlus achieves an average ASR of 81.1%, surpassing AutoDAN-Turbo by 3.9%, and is 9 times faster (1.45 vs. 13.50 hours). Our open-source implementation fosters further advancements in LLM safety, offering a scalable tool for vulnerability assessment. Code and resources are publicly available at https://github.com/knoveleng/rainbowplus, supporting reproducibility and future research in LLM red-teaming.

The integration of Large Language Models (LLMs) into healthcare holds significant potential to enhance diagnostic accuracy and support medical treatment planning. These AI-driven systems can analyze vast datasets, assisting clinicians in identifying diseases, recommending treatments, and predicting patient outcomes. This study evaluates the performance of a range of contemporary LLMs, including both open-source and closed-source models, on the 2024 Portuguese National Exam for medical specialty access (PNA), a standardized medical knowledge assessment. Our results highlight considerable variation in accuracy and cost-effectiveness, with several models demonstrating performance exceeding human benchmarks for medical students on this specific task. We identify leading models based on a combined score of accuracy and cost, discuss the implications of reasoning methodologies like Chain-of-Thought, and underscore the potential for LLMs to function as valuable complementary tools aiding medical professionals in complex clinical decision-making.

First-order logic (FOL) can represent the logical entailment semantics of natural language (NL) sentences, but determining natural language entailment using FOL remains a challenge. To address this, we propose the Entailment-Preserving FOL representations (EPF) task and introduce reference-free evaluation metrics for EPF, the Entailment-Preserving Rate (EPR) family. In EPF, one should generate FOL representations from multi-premise natural language entailment data (e.g. EntailmentBank) so that the automatic prover's result preserves the entailment labels. Experiments show that existing methods for NL-to-FOL translation struggle in EPF. To this extent, we propose a training method specialized for the task, iterative learning-to-rank, which directly optimizes the model's EPR score through a novel scoring function and a learning-to-rank objective. Our method achieves a 1.8-2.7% improvement in EPR and a 17.4-20.6% increase in EPR@16 compared to diverse baselines in three datasets. Further analyses reveal that iterative learning-to-rank effectively suppresses the arbitrariness of FOL representation by reducing the diversity of predicate signatures, and maintains strong performance across diverse inference types and out-of-domain data.

Diffusion Probabilistic Models (DPMs) have achieved considerable success in generation tasks. As sampling from DPMs is equivalent to solving diffusion SDE or ODE which is time-consuming, numerous fast sampling methods built upon improved differential equation solvers are proposed. The majority of such techniques consider solving the diffusion ODE due to its superior efficiency. However, stochastic sampling could offer additional advantages in generating diverse and high-quality data. In this work, we engage in a comprehensive analysis of stochastic sampling from two aspects: variance-controlled diffusion SDE and linear multi-step SDE solver. Based on our analysis, we propose SA-Solver, which is an improved efficient stochastic Adams method for solving diffusion SDE to generate data with high quality. Our experiments show that SA-Solver achieves: 1) improved or comparable performance compared with the existing state-of-the-art sampling methods for few-step sampling; 2) SOTA FID scores on substantial benchmark datasets under a suitable number of function evaluations (NFEs).

Diffusion models have achieved remarkable progress in various domains with an intriguing ability to produce new data that do not exist in the training set. In this work, we study the hypothesis that such creativity arises from the neural network backbone learning a smoothed version of the empirical score function, which guides the denoising dynamics to generate data points that interpolate the training data. Focusing mainly on settings where the training set lies uniformly in a one-dimensional subspace, we elucidate the interplay between score smoothing and the denoising dynamics with analytical solutions and numerical experiments, demonstrating how smoothing the score function can cause the denoised data samples to interpolate the training set along the subspace. Moreover, we present theoretical and empirical evidence that learning score functions with neural networks - either with or without explicit regularization - can naturally achieve a similar effect, including when the data belong to simple nonlinear manifolds.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

Recent research has leveraged large language model multi-agent systems for complex problem-solving while trying to reduce the manual effort required to build them, driving the development of automated agent workflow optimization methods. However, existing methods remain inflexible due to representational limitations, a lack of adaptability, and poor scalability when relying on discrete optimization techniques. We address these challenges with ScoreFlow, a simple yet high-performance framework that leverages efficient gradient-based optimization in a continuous space. ScoreFlow incorporates Score-DPO, a novel variant of the direct preference optimization method that accounts for quantitative feedback. Across six benchmarks spanning question answering, coding, and mathematical reasoning, ScoreFlow achieves an 8.2% improvement over existing baselines. Moreover, it empowers smaller models to outperform larger ones with lower inference costs. Project: https://github.com/Gen-Verse/ScoreFlow

Existing Score-Based Models (SBMs) can be categorized into constrained SBMs (CSBMs) or unconstrained SBMs (USBMs) according to their parameterization approaches. CSBMs model probability density functions as Boltzmann distributions, and assign their predictions as the negative gradients of some scalar-valued energy functions. On the other hand, USBMs employ flexible architectures capable of directly estimating scores without the need to explicitly model energy functions. In this paper, we demonstrate that the architectural constraints of CSBMs may limit their modeling ability. In addition, we show that USBMs' inability to preserve the property of conservativeness may lead to degraded performance in practice. To address the above issues, we propose Quasi-Conservative Score-Based Models (QCSBMs) for keeping the advantages of both CSBMs and USBMs. Our theoretical derivations demonstrate that the training objective of QCSBMs can be efficiently integrated into the training processes by leveraging the Hutchinson's trace estimator. In addition, our experimental results on the CIFAR-10, CIFAR-100, ImageNet, and SVHN datasets validate the effectiveness of QCSBMs. Finally, we justify the advantage of QCSBMs using an example of a one-layered autoencoder.

Estimating the performance difficulty of a musical score is crucial in music education for adequately designing the learning curriculum of the students. Although the Music Information Retrieval community has recently shown interest in this task, existing approaches mainly use machine-readable scores, leaving the broader case of sheet music images unaddressed. Based on previous works involving sheet music images, we use a mid-level representation, bootleg score, describing notehead positions relative to staff lines coupled with a transformer model. This architecture is adapted to our task by introducing an encoding scheme that reduces the encoded sequence length to one-eighth of the original size. In terms of evaluation, we consider five datasets -- more than 7500 scores with up to 9 difficulty levels -- , two of them particularly compiled for this work. The results obtained when pretraining the scheme on the IMSLP corpus and fine-tuning it on the considered datasets prove the proposal's validity, achieving the best-performing model with a balanced accuracy of 40.34\% and a mean square error of 1.33. Finally, we provide access to our code, data, and models for transparency and reproducibility.

Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the denoising diffusion model in the function space which also allows us to naturally handle irregularly-sampled observations. The forward process gradually adds noise to functions, preserving their continuity, while the learned reverse process removes the noise and returns functions as new samples. To this end, we define suitable noise sources and introduce novel denoising and score-matching models. We show how our method can be used for multivariate probabilistic forecasting and imputation, and how our model can be interpreted as a neural process.

We made a comparative analysis of numerical methods for multidimensional optimization. The main parameter is a number of computations of the test function to reach necessary accuracy, as it is computationally "slow". For complex functions, analytic differentiation by many parameters can cause problems associated with a significant complication of the program and thus slowing its operation. For comparison, we used the methods: "brute force" (or minimization on a regular grid), Monte Carlo, steepest descent, conjugate gradients, Brent's method (golden section search), parabolic interpolation etc. The Monte-Carlo method was applied to the eclipsing binary system AM Leo.

What do auto-encoders learn about the underlying data generating distribution? Recent work suggests that some auto-encoder variants do a good job of capturing the local manifold structure of data. This paper clarifies some of these previous observations by showing that minimizing a particular form of regularized reconstruction error yields a reconstruction function that locally characterizes the shape of the data generating density. We show that the auto-encoder captures the score (derivative of the log-density with respect to the input). It contradicts previous interpretations of reconstruction error as an energy function. Unlike previous results, the theorems provided here are completely generic and do not depend on the parametrization of the auto-encoder: they show what the auto-encoder would tend to if given enough capacity and examples. These results are for a contractive training criterion we show to be similar to the denoising auto-encoder training criterion with small corruption noise, but with contraction applied on the whole reconstruction function rather than just encoder. Similarly to score matching, one can consider the proposed training criterion as a convenient alternative to maximum likelihood because it does not involve a partition function. Finally, we show how an approximate Metropolis-Hastings MCMC can be setup to recover samples from the estimated distribution, and this is confirmed in sampling experiments.

GossipSub is a new peer-to-peer communication protocol designed to counter attacks from misbehaving peers by controlling what information is sent and to whom, via a score function computed by each peer that captures positive and negative behaviors of its neighbors. The score function depends on several parameters (weights, caps, thresholds) that can be configured by applications using GossipSub. The specification for GossipSub is written in English and its resilience to attacks from misbehaving peers is supported empirically by emulation testing using an implementation in Golang. In this work we take a foundational approach to understanding the resilience of GossipSub to attacks from misbehaving peers. We build the first formal model of GossipSub, using the ACL2s theorem prover. Our model is officially endorsed by the GossipSub developers. It can simulate GossipSub networks of arbitrary size and topology, with arbitrarily configured peers, and can be used to prove and disprove theorems about the protocol. We formalize fundamental security properties stating that the score function is fair, penalizes bad behavior, and rewards good behavior. We prove that the score function is always fair, but can be configured in ways that either penalize good behavior or ignore bad behavior. Using our model, we run GossipSub with the specific configurations for two popular real-world applications: the FileCoin and Eth2.0 blockchains. We show that all properties hold for FileCoin. However, given any Eth2.0 network (of any topology and size) with any number of potentially misbehaving peers, we can synthesize attacks where these peers are able to continuously misbehave by never forwarding topic messages, while maintaining positive scores so that they are never pruned from the network by GossipSub.

In this paper we introduce the SCoRe (Submodular Combinatorial Representation Learning) framework, a novel approach in representation learning that addresses inter-class bias and intra-class variance. SCoRe provides a new combinatorial viewpoint to representation learning, by introducing a family of loss functions based on set-based submodular information measures. We develop two novel combinatorial formulations for loss functions, using the Total Information and Total Correlation, that naturally minimize intra-class variance and inter-class bias. Several commonly used metric/contrastive learning loss functions like supervised contrastive loss, orthogonal projection loss, and N-pairs loss, are all instances of SCoRe, thereby underlining the versatility and applicability of SCoRe in a broad spectrum of learning scenarios. Novel objectives in SCoRe naturally model class-imbalance with up to 7.6\% improvement in classification on CIFAR-10-LT, CIFAR-100-LT, MedMNIST, 2.1% on ImageNet-LT, and 19.4% in object detection on IDD and LVIS (v1.0), demonstrating its effectiveness over existing approaches.

We propose a new score-based model with one-step sampling. Previously, score-based models were burdened with heavy computations due to iterative sampling. For substituting the iterative process, we train a standalone generator to compress all the time steps with the gradient backpropagated from the score network. In order to produce meaningful gradients for the generator, the score network is trained to simultaneously match the real data distribution and mismatch the fake data distribution. This model has the following advantages: 1) For sampling, it generates a fake image with only one step forward. 2) For training, it only needs 10 diffusion steps.3) Compared with consistency model, it is free of the ill-posed problem caused by consistency loss. On the popular CIFAR-10 dataset, our model outperforms Consistency Model and Denoising Score Matching, which demonstrates the potential of the framework. We further provide more examples on the MINIST and LSUN datasets. The code is available on GitHub.

Estimating truncated density models is difficult, as these models have intractable normalising constants and hard to satisfy boundary conditions. Score matching can be adapted to solve the truncated density estimation problem, but requires a continuous weighting function which takes zero at the boundary and is positive elsewhere. Evaluation of such a weighting function (and its gradient) often requires a closed-form expression of the truncation boundary and finding a solution to a complicated optimisation problem. In this paper, we propose approximate Stein classes, which in turn leads to a relaxed Stein identity for truncated density estimation. We develop a novel discrepancy measure, truncated kernelised Stein discrepancy (TKSD), which does not require fixing a weighting function in advance, and can be evaluated using only samples on the boundary. We estimate a truncated density model by minimising the Lagrangian dual of TKSD. Finally, experiments show the accuracy of our method to be an improvement over previous works even without the explicit functional form of the boundary.

Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from lookahead heuristics such as strong branching, and linear programming (LP) bound improvement for cut selection. Training and evaluation of the learned models often focus on local score accuracy. We show that such local score-based methods can lead to search trees exponentially larger than optimal tree sizes, by identifying two sources of this gap. The first is that these widely used expert signals can be misaligned with overall tree size. LP bound improvement can select a root cut set that yields an exponentially larger strong branching tree than selecting cuts by a simple proxy score, and strong branching itself can be exponentially suboptimal (Dey et al., 2024). The second is that small discrepancies can be amplified by the branch-and-bound recursion. An arbitrarily small perturbation of the right-hand sides in a root cut set can change the minimum tree size from a single node to exponentially many. For branching, arbitrarily small score discrepancies, and differences only in tie-breaking, can produce trees of exponentially different sizes, and even a small number of decision differences along a trajectory can incur exponential growth. These results show that branch-and-cut policies trained and learned using local expert scores do not guarantee small trees, thus motivating the study of data-driven methods that produce policies better aligned with tree size rather than only accuracy on expert scores.

Diffusion models have emerged as the principal paradigm for generative modeling across various domains. During training, they learn the score function, which in turn is used to generate samples at inference. They raise a basic yet unsolved question: which score do they actually learn? In principle, a diffusion model that matches the empirical score in the entire data space would simply reproduce the training data, failing to generate novel samples. Recent work addresses this question by arguing that diffusion models underfit the empirical score due to training-time inductive biases. In this work, we refine this perspective, introducing the notion of selective underfitting: instead of underfitting the score everywhere, better diffusion models more accurately approximate the score in certain regions of input space, while underfitting it in others. We characterize these regions and design empirical interventions to validate our perspective. Our results establish that selective underfitting is essential for understanding diffusion models, yielding new, testable insights into their generalization and generative performance.

The crux of effective out-of-distribution (OOD) detection lies in acquiring a robust in-distribution (ID) representation, distinct from OOD samples. While previous methods predominantly leaned on recognition-based techniques for this purpose, they often resulted in shortcut learning, lacking comprehensive representations. In our study, we conducted a comprehensive analysis, exploring distinct pretraining tasks and employing various OOD score functions. The results highlight that the feature representations pre-trained through reconstruction yield a notable enhancement and narrow the performance gap among various score functions. This suggests that even simple score functions can rival complex ones when leveraging reconstruction-based pretext tasks. Reconstruction-based pretext tasks adapt well to various score functions. As such, it holds promising potential for further expansion. Our OOD detection framework, MOODv2, employs the masked image modeling pretext task. Without bells and whistles, MOODv2 impressively enhances 14.30% AUROC to 95.68% on ImageNet and achieves 99.98% on CIFAR-10.

Diffusion models achieve state-of-the-art performance in various generation tasks. However, their theoretical foundations fall far behind. This paper studies score approximation, estimation, and distribution recovery of diffusion models, when data are supported on an unknown low-dimensional linear subspace. Our result provides sample complexity bounds for distribution estimation using diffusion models. We show that with a properly chosen neural network architecture, the score function can be both accurately approximated and efficiently estimated. Furthermore, the generated distribution based on the estimated score function captures the data geometric structures and converges to a close vicinity of the data distribution. The convergence rate depends on the subspace dimension, indicating that diffusion models can circumvent the curse of data ambient dimensionality.

We present SURE-Score: an approach for learning score-based generative models using training samples corrupted by additive Gaussian noise. When a large training set of clean samples is available, solving inverse problems via score-based (diffusion) generative models trained on the underlying fully-sampled data distribution has recently been shown to outperform end-to-end supervised deep learning. In practice, such a large collection of training data may be prohibitively expensive to acquire in the first place. In this work, we present an approach for approximately learning a score-based generative model of the clean distribution, from noisy training data. We formulate and justify a novel loss function that leverages Stein's unbiased risk estimate to jointly denoise the data and learn the score function via denoising score matching, while using only the noisy samples. We demonstrate the generality of SURE-Score by learning priors and applying posterior sampling to ill-posed inverse problems in two practical applications from different domains: compressive wireless multiple-input multiple-output channel estimation and accelerated 2D multi-coil magnetic resonance imaging reconstruction, where we demonstrate competitive reconstruction performance when learning at signal-to-noise ratio values of 0 and 10 dB, respectively.

We study the problem of optimizing biological sequences, e.g., proteins, DNA, and RNA, to maximize a black-box score function that is only evaluated in an offline dataset. We propose a novel solution, bootstrapped training of score-conditioned generator (BootGen) algorithm. Our algorithm repeats a two-stage process. In the first stage, our algorithm trains the biological sequence generator with rank-based weights to enhance the accuracy of sequence generation based on high scores. The subsequent stage involves bootstrapping, which augments the training dataset with self-generated data labeled by a proxy score function. Our key idea is to align the score-based generation with a proxy score function, which distills the knowledge of the proxy score function to the generator. After training, we aggregate samples from multiple bootstrapped generators and proxies to produce a diverse design. Extensive experiments show that our method outperforms competitive baselines on biological sequential design tasks. We provide reproducible source code: https://github.com/kaist-silab/bootgen{https://github.com/kaist-silab/bootgen}.

Test-time scaling evaluates reasoning LLMs by sampling multiple outputs per prompt, but ranking models in this regime remains underexplored. We formalize dense benchmark ranking under test-time scaling and introduce Scorio, a library that implements statistical ranking methods such as paired-comparison models, item response theory (IRT) models, voting rules, and graph- and spectral-based methods. Across 20 reasoning models on four Olympiad-style math benchmarks (AIME'24, AIME'25, HMMT'25, and BrUMO'25; up to N=80 trials), most full-trial rankings agree closely with the Bayesian gold standard Bayes_{U}@80 (mean Kendall's τ_b = 0.93--0.95), and 19--34 methods recover exactly the same ordering. In the single-trial regime, the best methods reach τ_b approx 0.86. Using greedy decoding as an empirical prior (Bayes_{R_0}@N) reduces variance at N=1 by 16--52%, but can bias rankings when greedy and stochastic sampling disagree. These results identify reliable ranking methods for both high- and low-budget test-time scaling. We release Scorio as an open-source library at https://github.com/mohsenhariri/scorio.

In Machine Learning, a benchmark refers to an ensemble of datasets associated with one or multiple metrics together with a way to aggregate different systems performances. They are instrumental in (i) assessing the progress of new methods along different axes and (ii) selecting the best systems for practical use. This is particularly the case for NLP with the development of large pre-trained models (e.g. GPT, BERT) that are expected to generalize well on a variety of tasks. While the community mainly focused on developing new datasets and metrics, there has been little interest in the aggregation procedure, which is often reduced to a simple average over various performance measures. However, this procedure can be problematic when the metrics are on a different scale, which may lead to spurious conclusions. This paper proposes a new procedure to rank systems based on their performance across different tasks. Motivated by the social choice theory, the final system ordering is obtained through aggregating the rankings induced by each task and is theoretically grounded. We conduct extensive numerical experiments (on over 270k scores) to assess the soundness of our approach both on synthetic and real scores (e.g. GLUE, EXTREM, SEVAL, TAC, FLICKR). In particular, we show that our method yields different conclusions on state-of-the-art systems than the mean-aggregation procedure while being both more reliable and robust.

Reinforcement learning is structurally harder than supervised learning because the policy changes the data distribution it learns from. The resulting fragility is especially visible in large-model training, where the training and rollout systems differ in numerical precision, sampling, and other implementation details. Existing methods manage this fragility by adding hyper-parameters to the training objective, which makes the algorithm more sensitive to its configuration and requires retuning whenever the task, model scale, or distribution mismatch changes. This fragility traces to two concerns that current objectives entangle through hyper-parameters set before training begins: a trust-region concern, that updates should not move the policy too far from its current value, and an off-policy concern, that data from older or different behavior policies should influence the update only to the extent that it remains reliable. Neither concern is a constant to set in advance, and their severity is reflected in the policy-ratio distribution of the current batch. We present a simple yet effective batch-adaptive objective that replaces fixed clipping with the normalized effective sample size of the policy ratios. The same statistic caps the score-function weight and sets the strength of an off-policy regularizer, so the update stays close to the usual on-policy score-function update when ratios are nearly uniform, and tightens automatically when stale or mismatched data cause ratio concentration, while retaining a nonzero learning signal on high-ratio tokens. Experiments across a wide range of settings show that our method matches or exceeds tuned baselines, introducing no new objective hyper-parameters and removing several existing ones. The code is available at https://github.com/FeynRL-project/FeynRL.

We introduce the use of rectified linear units (ReLU) as the classification function in a deep neural network (DNN). Conventionally, ReLU is used as an activation function in DNNs, with Softmax function as their classification function. However, there have been several studies on using a classification function other than Softmax, and this study is an addition to those. We accomplish this by taking the activation of the penultimate layer h_{n - 1} in a neural network, then multiply it by weight parameters theta to get the raw scores o_{i}. Afterwards, we threshold the raw scores o_{i} by 0, i.e. f(o) = max(0, o_{i}), where f(o) is the ReLU function. We provide class predictions y through argmax function, i.e. argmax f(x).

The training of score-based diffusion models (SDMs) is based on score matching. The challenge of score matching is that it includes a computationally expensive Jacobian trace. While several methods have been proposed to avoid this computation, each has drawbacks, such as instability during training and approximating the learning as learning a denoising vector field rather than a true score. We propose a novel score matching variant, local curvature smoothing with Stein's identity (LCSS). The LCSS bypasses the Jacobian trace by applying Stein's identity, enabling regularization effectiveness and efficient computation. We show that LCSS surpasses existing methods in sample generation performance and matches the performance of denoising score matching, widely adopted by most SDMs, in evaluations such as FID, Inception score, and bits per dimension. Furthermore, we show that LCSS enables realistic image generation even at a high resolution of 1024 times 1024.

Score-based diffusion models are a class of generative models whose dynamics is described by stochastic differential equations that map noise into data. While recent works have started to lay down a theoretical foundation for these models, an analytical understanding of the role of the diffusion time T is still lacking. Current best practice advocates for a large T to ensure that the forward dynamics brings the diffusion sufficiently close to a known and simple noise distribution; however, a smaller value of T should be preferred for a better approximation of the score-matching objective and higher computational efficiency. Starting from a variational interpretation of diffusion models, in this work we quantify this trade-off, and suggest a new method to improve quality and efficiency of both training and sampling, by adopting smaller diffusion times. Indeed, we show how an auxiliary model can be used to bridge the gap between the ideal and the simulated forward dynamics, followed by a standard reverse diffusion process. Empirical results support our analysis; for image data, our method is competitive w.r.t. the state-of-the-art, according to standard sample quality metrics and log-likelihood.

Music scores are written representations of music and contain rich information about musical components. The visual information on music scores includes notes, rests, staff lines, clefs, dynamics, and articulations. This visual information in music scores contains more semantic information than audio and symbolic representations of music. Previous music score datasets have limited sizes and are mainly designed for optical music recognition (OMR). There is a lack of research on creating a large-scale benchmark dataset for music modeling and generation. In this work, we propose MusicScore, a large-scale music score dataset collected and processed from the International Music Score Library Project (IMSLP). MusicScore consists of image-text pairs, where the image is a page of a music score and the text is the metadata of the music. The metadata of MusicScore is extracted from the general information section of the IMSLP pages. The metadata includes rich information about the composer, instrument, piece style, and genre of the music pieces. MusicScore is curated into small, medium, and large scales of 400, 14k, and 200k image-text pairs with varying diversity, respectively. We build a score generation system based on a UNet diffusion model to generate visually readable music scores conditioned on text descriptions to benchmark the MusicScore dataset for music score generation. MusicScore is released to the public at https://huggingface.co/datasets/ZheqiDAI/MusicScore.

We introduce the first version of KWBench (Knowledge Work Bench), a benchmark for unprompted problem recognition in large language models: can an LLM identify a professional scenario before attempting to solve it. Existing frontier benchmarks have saturated, and most knowledge-work evaluations to date reduce to extraction or task completion against a specification. KWBench targets the step before that: recognizing the governing structure of the situation from raw inputs alone. The benchmark contains 223 tasks sourced from practitioners across acquisitions, contract negotiations, clinical pharmacy, organizational politics, fraud analysis, and incentive design. Each task encodes a formal game-theoretic pattern (principal-agent conflict, signaling, mechanism design failure, strategic omission, coalitional dynamics, strategic interdependence) and carries structured ground truth recording the expert reading of the situation and the anticipated failure modes. Models receive raw data and a task prompt with no indication of problem type. Scoring is a three-tier rubric gated by a mandatory conjunctive check. Mandatory criteria encode the predicted wrong paths. We evaluate 16 models. The best model passes on 27.9% of tasks. The top two models agree on only 31.7% of their passes. Among the top 8, 44 tasks are solved by exactly one model; routing across the top 8 covers 50.7% of the benchmark, nearly double the best single model. Conditional on passing, quality scores converge (approx 83% across models); unconditional scores do not. Same models articulate the relevant game-theoretic concept correctly when asked, then fail to apply it unprompted. We release KWBench to shift how frontier models are evaluated on knowledge work, scoring them on whether they recognize the right problem from the situation alone, not only on how well they execute once the problem has been framed for them.

In order to solve a task using reinforcement learning, it is necessary to first formalise the goal of that task as a reward function. However, for many real-world tasks, it is very difficult to manually specify a reward function that never incentivises undesirable behaviour. As a result, it is increasingly popular to use reward learning algorithms, which attempt to learn a reward function from data. However, the theoretical foundations of reward learning are not yet well-developed. In particular, it is typically not known when a given reward learning algorithm with high probability will learn a reward function that is safe to optimise. This means that reward learning algorithms generally must be evaluated empirically, which is expensive, and that their failure modes are difficult to anticipate in advance. One of the roadblocks to deriving better theoretical guarantees is the lack of good methods for quantifying the difference between reward functions. In this paper we provide a solution to this problem, in the form of a class of pseudometrics on the space of all reward functions that we call STARC (STAndardised Reward Comparison) metrics. We show that STARC metrics induce both an upper and a lower bound on worst-case regret, which implies that our metrics are tight, and that any metric with the same properties must be bilipschitz equivalent to ours. Moreover, we also identify a number of issues with reward metrics proposed by earlier works. Finally, we evaluate our metrics empirically, to demonstrate their practical efficacy. STARC metrics can be used to make both theoretical and empirical analysis of reward learning algorithms both easier and more principled.

As Learning-to-Rank (LTR) approaches primarily seek to improve ranking quality, their output scores are not scale-calibrated by design. This fundamentally limits LTR usage in score-sensitive applications. Though a simple multi-objective approach that combines a regression and a ranking objective can effectively learn scale-calibrated scores, we argue that the two objectives are not necessarily compatible, which makes the trade-off less ideal for either of them. In this paper, we propose a practical regression compatible ranking (RCR) approach that achieves a better trade-off, where the two ranking and regression components are proved to be mutually aligned. Although the same idea applies to ranking with both binary and graded relevance, we mainly focus on binary labels in this paper. We evaluate the proposed approach on several public LTR benchmarks and show that it consistently achieves either best or competitive result in terms of both regression and ranking metrics, and significantly improves the Pareto frontiers in the context of multi-objective optimization. Furthermore, we evaluated the proposed approach on YouTube Search and found that it not only improved the ranking quality of the production pCTR model, but also brought gains to the click prediction accuracy. The proposed approach has been successfully deployed in the YouTube production system.

This article motivates, describes, and presents the PBSCR dataset for studying composer recognition of classical piano music. Our goal was to design a dataset that facilitates large-scale research on composer recognition that is suitable for modern architectures and training practices. To achieve this goal, we utilize the abundance of sheet music images and rich metadata on IMSLP, use a previously proposed feature representation called a bootleg score to encode the location of noteheads relative to staff lines, and present the data in an extremely simple format (2D binary images) to encourage rapid exploration and iteration. The dataset itself contains 40,000 62x64 bootleg score images for a 9-class recognition task, 100,000 62x64 bootleg score images for a 100-class recognition task, and 29,310 unlabeled variable-length bootleg score images for pretraining. The labeled data is presented in a form that mirrors MNIST images, in order to make it extremely easy to visualize, manipulate, and train models in an efficient manner. We include relevant information to connect each bootleg score image with its underlying raw sheet music image, and we scrape, organize, and compile metadata from IMSLP on all piano works to facilitate multimodal research and allow for convenient linking to other datasets. We release baseline results in a supervised and low-shot setting for future works to compare against, and we discuss open research questions that the PBSCR data is especially well suited to facilitate research on.

We introduce a Cascaded Diffusion Model (Cas-DM) that improves a Denoising Diffusion Probabilistic Model (DDPM) by effectively incorporating additional metric functions in training. Metric functions such as the LPIPS loss have been proven highly effective in consistency models derived from the score matching. However, for the diffusion counterparts, the methodology and efficacy of adding extra metric functions remain unclear. One major challenge is the mismatch between the noise predicted by a DDPM at each step and the desired clean image that the metric function works well on. To address this problem, we propose Cas-DM, a network architecture that cascades two network modules to effectively apply metric functions to the diffusion model training. The first module, similar to a standard DDPM, learns to predict the added noise and is unaffected by the metric function. The second cascaded module learns to predict the clean image, thereby facilitating the metric function computation. Experiment results show that the proposed diffusion model backbone enables the effective use of the LPIPS loss, leading to state-of-the-art image quality (FID, sFID, IS) on various established benchmarks.

Real-time score following from sheet images remains chal- lenging because the model must process streaming au- dio while resolving highly repetitive visual patterns un- der strict latency constraints. Recent image-based meth- ods have attempted to use multi-resolution prediction by simultaneously predicting the positions of the active sys- tem, bar, and note. However, their predictions across these different levels of notation are independent, which makes the predictions unstable and introduces unnecessary ex- tra search space for bar- and note-level predictions. Most existing methods also lack mechanisms to recover from score discontinuities, such as repeats, da capo (D.C.), or coda jumps. This paper proposes CODA, to the best of our knowledge, the first real-time score following system that addresses both gaps. CODA explicitly exploits the cascaded structure of music scores: it first selects the ac- tive system, then the active bar within it, and finally the active note within the selected bar. This enforces pre- diction consistency across resolutions. A silence-driven break mode enables recovery from arbitrary score discon- tinuities without requiring knowledge of the repeat struc- ture. Evaluated on the Multimodal Sheet Music Dataset (MSMD) piano benchmarks, CODA achieves state-of-the- art tracking accuracy and discontinuity-recovery perfor- mance under real-time throughput. Code is available at https://github.com/ValleyC/CODA.

In this work, we present Score MUsic Graph (SMUG)-Explain, a framework for generating and visualizing explanations of graph neural networks applied to arbitrary prediction tasks on musical scores. Our system allows the user to visualize the contribution of input notes (and note features) to the network output, directly in the context of the musical score. We provide an interactive interface based on the music notation engraving library Verovio. We showcase the usage of SMUG-Explain on the task of cadence detection in classical music. All code is available on https://github.com/manoskary/SMUG-Explain.

The rapid release of both language models and benchmarks makes it increasingly costly to evaluate every model on every dataset. In practice, models are often evaluated on different samples, making scores difficult to compare across studies. To address this, we propose a framework based on multidimensional Item Response Theory (IRT) that uses anchor items to calibrate new benchmarks to the evaluation suite while holding previously calibrated item parameters fixed. Our approach supports a realistic evaluation setting in which datasets are introduced over time and models are evaluated only on the datasets available at the time of evaluation, while a fixed anchor set for each dataset is used so that results from different evaluation periods can be compared directly. In large-scale experiments on more than 400 models, our framework predicts full-evaluation performance within 2-3 percentage points using only 100 anchor questions per dataset, with Spearman ρgeq 0.9 for ranking preservation, showing that it is possible to extend benchmark suites over time while preserving score comparability, at a constant evaluation cost per new dataset. Code available at https://github.com/eliyahabba/growing-pains

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Automated Essay Score (AES) is proven to be one of the cutting-edge technologies. Scoring techniques are used for various purposes. Reliable scores are calculated based on influential variables. Such variables can be computed by different methods based on the domain. The research is concentrated on the user's understanding of a given topic. The analysis is based on a scoring index by using Large Language Models. The user can then compare and contrast the understanding of a topic that they recently learned. The results are then contributed towards learning analytics and progression is made for enhancing the learning ability. In this research, the focus is on summarizing a PDF document and gauging a user's understanding of its content. The process involves utilizing a Langchain tool to summarize the PDF and extract the essential information. By employing this technique, the research aims to determine how well the user comprehends the summarized content.

The goal of this article is to provide an introduction to the desirability function approach to multi-objective optimization (direct and surrogate model-based), and multi-objective hyperparameter tuning. This work is based on the paper by Kuhn (2016). It presents a `Python` implementation of Kuhn's `R` package `desirability`. The `Python` package `spotdesirability` is available as part of the `sequential parameter optimization` framework. After a brief introduction to the desirability function approach is presented, three examples are given that demonstrate how to use the desirability functions for classical optimization, surrogate-model based optimization, and hyperparameter tuning.

Residual connections are central to modern deep neural networks, enabling stable optimization and efficient information flow across depth. In this work, we propose SCORE (Skip-Connection ODE Recurrent Embedding), a discrete recurrent alternative to classical layer stacking. Instead of composing multiple independent layers, SCORE iteratively applies a single shared neural block using an ODE (Ordinary Differential Equation)-inspired contractive update: ht+1 = (1 - dt) * ht + dt * F(ht) This formulation can be interpreted as a depth-by-iteration refinement process, where the step size dt explicitly controls stability and update magnitude. Unlike continuous Neural ODE approaches, SCORE uses a fixed number of discrete iterations and standard backpropagation without requiring ODE solvers or adjoint methods. We evaluate SCORE across graph neural networks (ESOL molecular solubility), multilayer perceptrons, and Transformer-based language models (nanoGPT). Across architectures, SCORE generally improves convergence speed and often accelerates training. SCORE is reducing parameter count through shared weights. In practice, simple Euler integration provides the best trade-off between computational cost and performance, while higher-order integrators yield marginal gains at increased compute. These results suggest that controlled recurrent depth with contractive residual updates offers a lightweight and effective alternative to classical stacking in deep neural networks.

Diffusion models have shown remarkable performance in generation problems over various domains including images, videos, text, and audio. A practical bottleneck of diffusion models is their sampling speed, due to the repeated evaluation of score estimation networks during the inference. In this work, we propose a novel framework capable of adaptively allocating compute required for the score estimation, thereby reducing the overall sampling time of diffusion models. We observe that the amount of computation required for the score estimation may vary along the time step for which the score is estimated. Based on this observation, we propose an early-exiting scheme, where we skip the subset of parameters in the score estimation network during the inference, based on a time-dependent exit schedule. Using the diffusion models for image synthesis, we show that our method could significantly improve the sampling throughput of the diffusion models without compromising image quality. Furthermore, we also demonstrate that our method seamlessly integrates with various types of solvers for faster sampling, capitalizing on their compatibility to enhance overall efficiency. The source code and our experiments are available at https://github.com/taehong-moon/ee-diffusion

Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by reversing it (thereby going from noise to data). Unfortunately, current score-based models generate data very slowly due to the sheer number of score network evaluations required by numerical SDE solvers. In this work, we aim to accelerate this process by devising a more efficient SDE solver. Existing approaches rely on the Euler-Maruyama (EM) solver, which uses a fixed step size. We found that naively replacing it with other SDE solvers fares poorly - they either result in low-quality samples or become slower than EM. To get around this issue, we carefully devise an SDE solver with adaptive step sizes tailored to score-based generative models piece by piece. Our solver requires only two score function evaluations, rarely rejects samples, and leads to high-quality samples. Our approach generates data 2 to 10 times faster than EM while achieving better or equal sample quality. For high-resolution images, our method leads to significantly higher quality samples than all other methods tested. Our SDE solver has the benefit of requiring no step size tuning.

We propose a computationally efficient inferential procedure for longitudinal function-on-function regression. The method follows a marginal three-step approach: (1) fit massive pointwise longitudinal scalar-on-function regression models, (2) smooth the resulting estimates along the bivariate functional domain, and (3) compute confidence bands using either an analytic approach for Gaussian data or a cluster bootstrap for Gaussian or non-Gaussian data. Simulation studies demonstrate that the proposed method achieves accurate estimation and valid inference, while substantially reducing computational burden compared to existing approaches. Methods are motivated by a physical activity intervention trial in older adults where high-dimensional wearable data were collected longitudinally across multiple visits. Our applications reveal significant increases in physical activity in the morning using interpersonal intervention strategies, but not intrapersonal strategies. The proposed methods are implemented in an R package.

Score-based models can serve as expressive, data-driven priors for scientific inverse problems. In strong gravitational lensing, they enable posterior inference of a background galaxy from its distorted, multiply-imaged observation. Previous work, however, assumes that the lens mass distribution (and thus the forward operator) is known. We relax this assumption by jointly inferring the source and a parametric lens-mass profile, using a sampler based on GibbsDDRM but operating in continuous time. The resulting reconstructions yield residuals consistent with the observational noise, and the marginal posteriors of the lens parameters recover true values without systematic bias. To our knowledge, this is the first successful demonstration of joint source-and-lens inference with a score-based prior.

GossipSub is a popular new peer-to-peer network protocol designed to disseminate messages quickly and efficiently by allowing peers to forward the full content of messages only to a dynamically selected subset of their neighboring peers (mesh neighbors) while gossiping about messages they have seen with the rest. Peers decide which of their neighbors to graft or prune from their mesh locally and periodically using a score for each neighbor. Scores are calculated using a score function that depends on mesh-specific parameters, weights and counters relating to a peer's performance in the network. Since a GossipSub network's performance ultimately depends on the performance of its peers, an important question arises: Is the score calculation mechanism effective in weeding out non-performing or even intentionally misbehaving peers from meshes? We answered this question in the negative in our companion paper by reasoning about GossipSub using our formal, official and executable ACL2s model. Based on our findings, we synthesized and simulated attacks against GossipSub which were confirmed by the developers of GossipSub, FileCoin, and Eth2.0, and publicly disclosed in MITRE CVE-2022-47547. In this paper, we present a detailed description of our model. We discuss design decisions, security properties of GossipSub, reasoning about the security properties in context of our model, attack generation and lessons we learnt when writing it.

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

Aligning large language models (LLMs) to human preferences is challenging in domains where preference data is unavailable. We address the problem of learning reward models for such target domains by leveraging feedback collected from simpler source domains, where human preferences are easier to obtain. Our key insight is that, while domains may differ significantly, human preferences convey domain-agnostic concepts that can be effectively captured by a reward model. We propose \method, a framework that trains domain-invariant reward models by optimizing a dual loss: a domain loss that minimizes the divergence between source and target distribution, and a source loss that optimizes preferences on the source domain. We show \method is a general approach that we evaluate and analyze across 4 distinct settings: (1) Cross-lingual transfer (accuracy: 0.621 rightarrow 0.661), (2) Clean-to-noisy (accuracy: 0.671 rightarrow 0.703), (3) Few-shot-to-full transfer (accuracy: 0.845 rightarrow 0.920), and (4) Simple-to-complex tasks transfer (correlation: 0.508 rightarrow 0.556). Our code, models and data are available at https://github.com/portal-cornell/dial.

Many peer-review venues are using algorithms to assign submissions to reviewers. The crux of such automated approaches is the notion of the "similarity score" -- a numerical estimate of the expertise of a reviewer in reviewing a paper -- and many algorithms have been proposed to compute these scores. However, these algorithms have not been subjected to a principled comparison, making it difficult for stakeholders to choose the algorithm in an evidence-based manner. The key challenge in comparing existing algorithms and developing better algorithms is the lack of publicly available gold-standard data. We address this challenge by collecting a novel dataset of similarity scores that we release to the research community. Our dataset consists of 477 self-reported expertise scores provided by 58 researchers who evaluated their expertise in reviewing papers they have read previously. Using our dataset, we compare several widely used similarity algorithms and offer key insights. First, all algorithms exhibit significant error, with misranking rates between 12%-30% in easier cases and 36%-43% in harder ones. Second, most specialized algorithms are designed to work with titles and abstracts of papers, and in this regime the SPECTER2 algorithm performs best. Interestingly, classical TF-IDF matches SPECTER2 in accuracy when given access to full submission texts. In contrast, off-the-shelf LLMs lag behind specialized approaches.

Constructing prediction sets with coverage guarantees for unobserved outcomes is a core problem in modern statistics. Methods for predictive inference have been developed for a wide range of settings, but usually only consider test data points one at a time. Here we study the problem of distribution-free predictive inference for a batch of multiple test points, aiming to construct prediction sets for functions -- such as the mean or median -- of any number of unobserved test datapoints. This setting includes constructing simultaneous prediction sets with a high probability of coverage, and selecting datapoints satisfying a specified condition while controlling the number of false claims. For the general task of predictive inference on a function of a batch of test points, we introduce a methodology called batch predictive inference (batch PI), and provide a distribution-free coverage guarantee under exchangeability of the calibration and test data. Batch PI requires the quantiles of a rank ordering function defined on certain subsets of ranks. While computing these quantiles is NP-hard in general, we show that it can be done efficiently in many cases of interest, most notably for batch score functions with a compositional structure -- which includes examples of interest such as the mean -- via a dynamic programming algorithm that we develop. Batch PI has advantages over naive approaches (such as partitioning the calibration data or directly extending conformal prediction) in many settings, as it can deliver informative prediction sets even using small calibration sample sizes. We illustrate that our procedures provide informative inference across the use cases mentioned above, through experiments on both simulated data and a drug-target interaction dataset.

This paper studies the original discrete-time denoising diffusion probabilistic model (DDPM) from a probabilistic point of view. We present three main theoretical results. First, we show that the time-dependent score function associated with the forward diffusion process admits a characterization as the backward component of a forward--backward stochastic differential equation (FBSDE). This result provides a structural description of the score function and clarifies how score estimation errors propagate along the reverse-time dynamics. As a by-product, we also obtain a system of semilinear parabolic PDEs for the score function. Second, we use tools from Schrödinger's problem to relate distributional errors arising in reverse time to corresponding errors in forward time. This approach allows us to control the reverse-time sampling error in a systematic way. Third, combining these results, we derive an explicit upper bound for the total variation distance between the sampling distribution of the discrete-time DDPM algorithm and the target data distribution under general finite noise schedules. The resulting bound separates the contributions of the learning error and the time discretization error. Our analysis highlights the intrinsic probabilistic structure underlying discrete-time DDPMs and provides a clearer understanding of the sources of error in their sampling procedure.

This paper revisits the problem of computing empirical cumulative distribution functions (ECDF) efficiently on large, multivariate datasets. Computing an ECDF at one evaluation point requires O(N) operations on a dataset composed of N data points. Therefore, a direct evaluation of ECDFs at N evaluation points requires a quadratic O(N^2) operations, which is prohibitive for large-scale problems. Two fast and exact methods are proposed and compared. The first one is based on fast summation in lexicographical order, with a O(N{log}N) complexity and requires the evaluation points to lie on a regular grid. The second one is based on the divide-and-conquer principle, with a O(Nlog(N)^{(d-1){vee}1}) complexity and requires the evaluation points to coincide with the input points. The two fast algorithms are described and detailed in the general d-dimensional case, and numerical experiments validate their speed and accuracy. Secondly, the paper establishes a direct connection between cumulative distribution functions and kernel density estimation (KDE) for a large class of kernels. This connection paves the way for fast exact algorithms for multivariate kernel density estimation and kernel regression. Numerical tests with the Laplacian kernel validate the speed and accuracy of the proposed algorithms. A broad range of large-scale multivariate density estimation, cumulative distribution estimation, survival function estimation and regression problems can benefit from the proposed numerical methods.

Diffusion models are powerful generative models that simulate the reverse of diffusion processes using score functions to synthesize data from noise. The sampling process of diffusion models can be interpreted as solving the reverse stochastic differential equation (SDE) or the ordinary differential equation (ODE) of the diffusion process, which often requires up to thousands of discretization steps to generate a single image. This has sparked a great interest in developing efficient integration techniques for reverse-S/ODEs. Here, we propose an orthogonal approach to accelerating score-based sampling: Denoising MCMC (DMCMC). DMCMC first uses MCMC to produce samples in the product space of data and variance (or diffusion time). Then, a reverse-S/ODE integrator is used to denoise the MCMC samples. Since MCMC traverses close to the data manifold, the computation cost of producing a clean sample for DMCMC is much less than that of producing a clean sample from noise. To verify the proposed concept, we show that Denoising Langevin Gibbs (DLG), an instance of DMCMC, successfully accelerates all six reverse-S/ODE integrators considered in this work on the tasks of CIFAR10 and CelebA-HQ-256 image generation. Notably, combined with integrators of Karras et al. (2022) and pre-trained score models of Song et al. (2021b), DLG achieves SOTA results. In the limited number of score function evaluation (NFE) settings on CIFAR10, we have 3.86 FID with approx 10 NFE and 2.63 FID with approx 20 NFE. On CelebA-HQ-256, we have 6.99 FID with approx 160 NFE, which beats the current best record of Kim et al. (2022) among score-based models, 7.16 FID with 4000 NFE. Code: https://github.com/1202kbs/DMCMC

Diffusion models have achieved remarkable success in generative modeling. However, this study confirms the existence of overfitting in diffusion model training, particularly in data-limited regimes. To address this challenge, we propose Score Augmentation (ScoreAug), a novel data augmentation framework specifically designed for diffusion models. Unlike conventional augmentation approaches that operate on clean data, ScoreAug applies transformations to noisy data, aligning with the inherent denoising mechanism of diffusion. Crucially, ScoreAug further requires the denoiser to predict the augmentation of the original target. This design establishes an equivariant learning objective, enabling the denoiser to learn scores across varied denoising spaces, thereby realizing what we term score augmentation. We also theoretically analyze the relationship between scores in different spaces under general transformations. In experiments, we extensively validate ScoreAug on multiple benchmarks including CIFAR-10, FFHQ, AFHQv2, and ImageNet, with results demonstrating significant performance improvements over baselines. Notably, ScoreAug effectively mitigates overfitting across diverse scenarios, such as varying data scales and model capacities, while exhibiting stable convergence properties. Another advantage of ScoreAug over standard data augmentation lies in its ability to circumvent data leakage issues under certain conditions. Furthermore, we show that ScoreAug can be synergistically combined with traditional data augmentation techniques to achieve additional performance gains.

Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate O(1/{T}^2) with T the number of steps, improving upon the O(1/T) rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate O(1/T), outperforming the rate O(1/T) for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates ell_2-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.

This paper approaches the problem of separating the notes from a quantized symbolic music piece (e.g., a MIDI file) into multiple voices and staves. This is a fundamental part of the larger task of music score engraving (or score typesetting), which aims to produce readable musical scores for human performers. We focus on piano music and support homophonic voices, i.e., voices that can contain chords, and cross-staff voices, which are notably difficult tasks that have often been overlooked in previous research. We propose an end-to-end system based on graph neural networks that clusters notes that belong to the same chord and connects them with edges if they are part of a voice. Our results show clear and consistent improvements over a previous approach on two datasets of different styles. To aid the qualitative analysis of our results, we support the export in symbolic music formats and provide a direct visualization of our outputs graph over the musical score. All code and pre-trained models are available at https://github.com/CPJKU/piano_svsep

We study the data selection problem, whose aim is to select a small representative subset of data that can be used to efficiently train a machine learning model. We present a new data selection approach based on k-means clustering and sensitivity sampling. Assuming access to an embedding representation of the data with respect to which the model loss is H\"older continuous, our approach provably allows selecting a set of ``typical'' k + 1/varepsilon^2 elements whose average loss corresponds to the average loss of the whole dataset, up to a multiplicative (1pmvarepsilon) factor and an additive varepsilon lambda Phi_k, where Phi_k represents the k-means cost for the input embeddings and lambda is the H\"older constant. We furthermore demonstrate the performance and scalability of our approach on fine-tuning foundation models and show that it outperforms state-of-the-art methods. We also show how it can be applied on linear regression, leading to a new sampling strategy that surprisingly matches the performances of leverage score sampling, while being conceptually simpler and more scalable.

We consider estimating the conditional distribution of a multivariate outcome given covariates when its coordinates may be continuous, binary, categorical, ordinal or rankings, and are conditionally dependent on one another. Different statistical methods have been developed for each outcome type, and most of them target a summary of the conditional distribution, such as the mean of each coordinate, rather than the joint distribution of the outcome vector. We develop generalized engression models, a unified nonparametric distributional regression framework for outcomes of any type. The proposed method builds upon engression, a scoring-rule-based deep generative model, and introduces a data-type-specific link function and a stochastic perturbation that smooths the loss, enabling gradient-based training even with discontinuous links. We establish universal representation results for continuous, discrete and mixed outcomes. In simulations and in two applications, 242 species in a community ecology benchmark and a 17-dimensional mixed-type health outcome, the method matches type-specific models on marginal scores, improves on them on the joint distribution, and matches or exceeds purpose-built state-of-the-art joint species distribution models. Software is available in Python.

In the domain of symbolic music research, the progress of developing scalable systems has been notably hindered by the scarcity of available training data and the demand for models tailored to specific tasks. To address these issues, we propose MelodyT5, a novel unified framework that leverages an encoder-decoder architecture tailored for symbolic music processing in ABC notation. This framework challenges the conventional task-specific approach, considering various symbolic music tasks as score-to-score transformations. Consequently, it integrates seven melody-centric tasks, from generation to harmonization and segmentation, within a single model. Pre-trained on MelodyHub, a newly curated collection featuring over 261K unique melodies encoded in ABC notation and encompassing more than one million task instances, MelodyT5 demonstrates superior performance in symbolic music processing via multi-task transfer learning. Our findings highlight the efficacy of multi-task transfer learning in symbolic music processing, particularly for data-scarce tasks, challenging the prevailing task-specific paradigms and offering a comprehensive dataset and framework for future explorations in this domain.

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

Developing text-driven symbolic music generation models remains challenging due to the scarcity of aligned text-music datasets and the unreliability of automated captioning pipelines. While most efforts have focused on MIDI, sheet music representations are largely underexplored in text-driven generation. We present Text2Score, a two-stage framework comprising a planning stage and an execution stage for generating sheet music from natural language prompts. By deriving supervision signals directly from symbolic XML data, we propose an alternative training paradigm that bypasses noisy or scarce text-music pairs. In the planning stage, an LLM orchestrator translates a natural language prompt into a structured measure-wise plan defining musical attributes such as instruments, key, time signatures, harmony, etc. This plan is then consumed by a generative model in the execution stage to produce interleaved ABC notation conditioned on the plan's structural constraints. To assess output quality, we introduce an evaluation framework covering playability, readability, instrument utilization, structural complexity, and prompt adherence, validated by expert musicians. Text2Score consistently outperforms both a pure LLM-based agentic framework and three end-to-end baselines across objective and subjective dimensions. We open-source the dataset, code, evaluation set and LLM prompts used in this work; a demo is available on our project page (https://keshavbhandari.github.io/portfolio/text2score).

We introduce TuneJury, an open, instance-level pairwise reward model for text-to-music that predicts a music preference score from a text prompt and an audio clip. The released checkpoint is trained on publicly available human-preference labels covering arena-style (A vs. B) votes, metric-alignment preference pairs, crowdsourced pairwise comparisons, and expert aesthetic ratings. The predicted score margin between two clips is well calibrated on our held-out test split, supporting data filtering via a simple score threshold. TuneJury generalizes to both held-out test pairs and out-of-distribution benchmarks, remaining competitive with prior baselines on the latter. For generators released after training, we introduce anchor calibration, a post-hoc, per-system Bradley-Terry calibration that recovers agreement at substantially better data efficiency than from-scratch retraining. The same frozen reward drives consistent reward-axis gains across three downstream applications: inference-time best-of-N selection, DITTO-style latent optimization, and expert-iteration post-training. TuneJury is available at https://github.com/yonghyunk1m/TuneJury.

We develop new conformal inference methods for obtaining validity guarantees on the output of large language models (LLMs). Prior work in conformal language modeling identifies a subset of the text that satisfies a high-probability guarantee of correctness. These methods work by filtering claims from the LLM's original response if a scoring function evaluated on the claim fails to exceed a threshold calibrated via split conformal prediction. Existing methods in this area suffer from two deficiencies. First, the guarantee stated is not conditionally valid. The trustworthiness of the filtering step may vary based on the topic of the response. Second, because the scoring function is imperfect, the filtering step can remove many valuable and accurate claims. We address both of these challenges via two new conformal methods. First, we generalize the conditional conformal procedure of Gibbs et al. (2023) in order to adaptively issue weaker guarantees when they are required to preserve the utility of the output. Second, we show how to systematically improve the quality of the scoring function via a novel algorithm for differentiating through the conditional conformal procedure. We demonstrate the efficacy of our approach on biography and medical question-answering datasets.

We propose a simple multiple outlier identification method for parametric location-scale and shape-scale models when the number of possible outliers is not specified. The method is based on a result giving asymptotic properties of extreme z-scores. Robust estimators of model parameters are used defining z-scores. An extensive simulation study was done for comparing of the proposed method with existing methods. For the normal family, the method is compared with the well known Davies-Gather, Rosner's, Hawking's and Bolshev's multiple outlier identification methods. The choice of an upper limit for the number of possible outliers in case of Rosner's test application is discussed. For other families, the proposed method is compared with a method generalizing Gather-Davies method. In most situations, the new method has the highest outlier identification power in terms of masking and swamping values. We also created R package outliersTests for proposed test.

We examine a simple stochastic strategy for adapting well-known single-point acquisition functions to allow batch active learning. Unlike acquiring the top-K points from the pool set, score- or rank-based sampling takes into account that acquisition scores change as new data are acquired. This simple strategy for adapting standard single-sample acquisition strategies can even perform just as well as compute-intensive state-of-the-art batch acquisition functions, like BatchBALD or BADGE, while using orders of magnitude less compute. In addition to providing a practical option for machine learning practitioners, the surprising success of the proposed method in a wide range of experimental settings raises a difficult question for the field: when are these expensive batch acquisition methods pulling their weight?

Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM scoring systems are built by solving an integer program that directly encodes measures of accuracy (the 0-1 loss) and sparsity (the ell_0-seminorm) while restricting coefficients to coprime integers. SLIM can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce highly tailored models without parameter tuning. We provide bounds on the testing and training accuracy of SLIM scoring systems, and present a new data reduction technique that can improve scalability by eliminating a portion of the training data beforehand. Our paper includes results from a collaboration with the Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create a highly tailored scoring system for sleep apnea screening

Strictly proper scoring rules identify the true conditional class distribution at population level, but their curvature can alter optimization and finite-sample behavior. We study three multiclass objectives: a class-aware quadratic Bregman score (CAPM), a strongly convex generator with constrained log-cosh ridges (HPG), and an HPG objective with an annealed probability-margin penalty (APMS). CAPM is treated as a structured instance of established quadratic scoring-rule theory. We derive conditional-regret, curvature, range, and logit-gradient bounds for CAPM and HPG, and prove exact penalty-range and conditional-target displacement bounds for APMS. Controlled five-seed experiments use Digits, Wisconsin breast cancer, and synthetic confusion and long-tail problems under clean labels, symmetric and pair-flip corruption, class imbalance, calibration evaluation, input corruption, and first-order adversarial perturbations. The candidates are close to cross-entropy on clean data and show descriptive gains in some noisy-label cells, but the five-seed comparisons are interpreted descriptively rather than as significance evidence. The selected noisy-label baselines perform better on Digits with 40% symmetric label noise, and explicit prior-adjustment methods perform better in the 30:1 synthetic long-tail experiment. Ablations do not show a consistent benefit from the candidate-specific graph, ridge, or margin components. The mathematical analysis establishes the stated properties, and the experiments delimit the empirical evidence; together they do not support a claim of general superiority.

We propose a transformer-based rhythm quantization model that incorporates beat and downbeat information to quantize MIDI performances into metrically-aligned, human-readable scores. We propose a beat-based preprocessing method that transfers score and performance data into a unified token representation. We optimize our model architecture and data representation and train on piano and guitar performances. Our model exceeds state-of-the-art performance based on the MUSTER metric.

We propose the PeerRank method for peer assessment. This constructs a grade for an agent based on the grades proposed by the agents evaluating the agent. Since the grade of an agent is a measure of their ability to grade correctly, the PeerRank method weights grades by the grades of the grading agent. The PeerRank method also provides an incentive for agents to grade correctly. As the grades of an agent depend on the grades of the grading agents, and as these grades themselves depend on the grades of other agents, we define the PeerRank method by a fixed point equation similar to the PageRank method for ranking web-pages. We identify some formal properties of the PeerRank method (for example, it satisfies axioms of unanimity, no dummy, no discrimination and symmetry), discuss some examples, compare with related work and evaluate the performance on some synthetic data. Our results show considerable promise, reducing the error in grade predictions by a factor of 2 or more in many cases over the natural baseline of averaging peer grades.

Large Language Model agents excel at solving complex tasks through iterative reasoning and tool use, but typically depend on ultra-large, costly backbones. Existing distillation approaches train smaller students to imitate full teacher trajectories, yet reasoning and knowledge gaps between the teacher and student often lead to compounding errors. We propose SCoRe, a student-centered framework in which the student generates trajectories and the teacher intervenes only at the first critical error, producing training data matched to the student's ability and exposing specific weaknesses. The student is first fine-tuned on corrected trajectories. Subsequently, short-horizon reinforcement learning starts from the verified prefix before the first critical error, with target rewards assigned at that step. This design encourages autonomous problem-solving beyond imitation and improves training stability. Particularly, on 12 challenging benchmarks, a 7B-parameter student distilled with SCoRe matches the agentic performance of a 72B-parameter teacher.

We investigate the mechanism design problem faced by a principal who hires multiple agents to gather and report costly information. Then, the principal exploits the information to make an informed decision. We model this problem as a game, where the principal announces a mechanism consisting in action recommendations and a payment function, a.k.a. scoring rule. Then, each agent chooses an effort level and receives partial information about an underlying state of nature based on the effort. Finally, the agents report the information (possibly non-truthfully), the principal takes a decision based on this information, and the agents are paid according to the scoring rule. While previous work focuses on single-agent problems, we consider multi-agents settings. This poses the challenge of coordinating the agents' efforts and aggregating correlated information. Indeed, we show that optimal mechanisms must correlate agents' efforts, which introduces externalities among the agents, and hence complex incentive compatibility constraints and equilibrium selection problems. First, we design a polynomial-time algorithm to find an optimal incentive compatible mechanism. Then, we study an online problem, where the principal repeatedly interacts with a group of unknown agents. We design a no-regret algorithm that provides mathcal{O}(T^{2/3}) regret with respect to an optimal mechanism, matching the state-of-the-art bound for single-agent settings.

The neural semi-Markov Conditional Random Field (semi-CRF) framework has demonstrated promise for event-based piano transcription. In this framework, all events (notes or pedals) are represented as closed time intervals tied to specific event types. The neural semi-CRF approach requires an interval scoring matrix that assigns a score for every candidate interval. However, designing an efficient and expressive architecture for scoring intervals is not trivial. This paper introduces a simple method for scoring intervals using scaled inner product operations that resemble how attention scoring is done in transformers. We show theoretically that, due to the special structure from encoding the non-overlapping intervals, under a mild condition, the inner product operations are expressive enough to represent an ideal scoring matrix that can yield the correct transcription result. We then demonstrate that an encoder-only structured non-hierarchical transformer backbone, operating only on a low-time-resolution feature map, is capable of transcribing piano notes and pedals with high accuracy and time precision. The experiment shows that our approach achieves the new state-of-the-art performance across all subtasks in terms of the F1 measure on the Maestro dataset.

We present a novel approach to symbolic regression using vision-capable large language models (LLMs) and the ideas behind Google DeepMind's Funsearch. The LLM is given a plot of a univariate function and tasked with proposing an ansatz for that function. The free parameters of the ansatz are fitted using standard numerical optimisers, and a collection of such ansätze make up the population of a genetic algorithm. Unlike other symbolic regression techniques, our method does not require the specification of a set of functions to be used in regression, but with appropriate prompt engineering, we can arbitrarily condition the generative step. By using Kolmogorov Arnold Networks (KANs), we demonstrate that ``univariate is all you need'' for symbolic regression, and extend this method to multivariate functions by learning the univariate function on each edge of a trained KAN. The combined expression is then simplified by further processing with a language model.

Reinforcement learning from human feedback (RLHF) is one of the key techniques that helps large language models (LLMs) to follow instructions and provide helpful and harmless responses. While direct policy optimization methods exist, state-of-the-art LLMs adopt RL-based methods (usually PPO) in RLHF to train the policy to generate good responses guided by a reward model learned from preference data. The main challenge of these methods is the inaccuracy of the intermediate reward model, especially in code generation tasks that require long and complex reasoning to score a response. We find that the reliability of the reward model varies across responses assigned with different rewards. This motivates us to filter the samples whose rewards may be unreliable to improve signal-to-noise ratio during policy learning, resulting in Policy Filtration for Proximal Policy Optimization (PF-PPO). To choose a proper policy filtration strategy for a given reward model, the coefficient of determination (R^2) between rewards and actual scores on filtered samples serves as a good metrics and helps us find several promising strategies. We provide extensive experiments to validate the effectiveness of PF-PPO in code generation tasks, and find that some variants of PF-PPO are highly effective and achieve new state-of-the-art performance across 7-billion-parameter models on HumanEval, MBPP, and a new and more challenging LeetCode Contest benchmark.