We propose a spectral-based, unsupervised representation learning framework to derive low-dimensional embeddings for clinical concepts and patients in rare disease cohorts from electronic health records, where data are high-dimensional but sample sizes are limited. To overcome this challenge, we incorporate a knowledge matrix extracted from a broader population that shares a partially overlapping subspace with the rare-disease cohort. Our method departs from existing approaches by relaxing restrictive one-to-one signal-alignment assumptions between the latent data matrix and knowledge matrix, allowing more flexible and realistic forms of structured sharing. We introduce a novel two-step spectral embedding procedure: first, we identify and remove irrelevant components from the knowledge matrix; then, we apply a projection-based method to separately recover shared and heterogeneous components. Simulations and an analysis of a real-world multiple sclerosis cohort show that the proposed method outperforms competing approaches, particularly in challenging scenarios where shared signals are weak and only partially aligned, as is common in rare-disease data.

We study a dynamic assortment problem on a two-sided service platform with incomplete information and heterogeneous customers in a discrete-time setting. In each period, a customer arrives seeking service, and the platform chooses an assortment of sellers to display. The customer then proposes a transaction to at most one seller in the assortment according to a multinomial logit choice model. After a fixed number of periods, sellers review the proposals they have received and each chooses at most one customer according to another multinomial logit choice model, after which the cycle repeats. A key challenge is that the platform does not know the choice-model parameters of either customers or sellers in advance. To our knowledge, this is the first study of a dynamic assortment problem in which both sides' choice parameters are unknown. We develop a data-driven algorithm that learns these parameters while optimizing the platform's objective over time. We evaluate performance using regret, which measures revenue loss relative to a clairvoyant benchmark that knows all parameters and customer arrivals in advance. We show that the algorithm's worst-case regret grows polylogarithmically over time, and we derive a matching lower bound, establishing its rate optimality.

Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate matrices, particularly between uniform and absorbing rate matrices. While empirical results suggest that absorbing rate matrices often yield better generation quality compared to uniform rate matrices, existing theoretical works have largely focused on the uniform rate matrices case. Notably, convergence guarantees and error analyses for absorbing diffusion models are still missing. In this work, we provide the first finite-time error bounds and convergence rate analysis for discrete diffusion models using absorbing rate matrices.

The neural activity in the visual processing is influenced by both external stimuli and internal brain states. Ideally, a neural predictive model should account for both of them. Currently, there are no dynamic encoding models that explicitly model a latent state and the entire neuronal response distribution. We address this gap by proposing a probabilistic model that predicts the joint distribution of the neuronal responses from video stimuli and stimulus-independent latent factors. After training and testing our model on mouse V1 neuronal responses, we find that it outperforms video-only models in terms of log-likelihood and achieves improvements in likelihood and correlation when conditioned on responses from other neurons. Furthermore, we find that the learned latent factors strongly correlate with mouse behavior and that they exhibit patterns related to the neurons' position on the visual cortex, although the model was trained without behavior and cortical coordinates. Our findings demonstrate that unsupervised learning of latent factors from population responses can reveal biologically meaningful structure that bridges sensory processing and behavior, without requiring explicit behavioral annotations during training. The code is attached to the submission.

Protein design is a fundamental challenge in biotechnology, aiming to design novel sequences with specific functions within the vast space of possible proteins. Recent advances in deep generative models have enabled function-based protein design from textual descriptions, yet struggle with structural plausibility. Inspired by classical protein design methods that leverage natural protein structures, we explore whether incorporating fragments from natural proteins can enhance foldability in generative models. Our empirical results show that even random incorporation of fragments improves foldability. Building on this insight, we introduce ProDVa, a novel protein design approach that integrates a text encoder for functional descriptions, a protein language model for designing proteins, and a fragment encoder to dynamically retrieve protein fragments based on textual functional descriptions. Experimental results demonstrate that our approach effectively designs protein sequences that are both functionally aligned and structurally plausible. Compared to state-of-the-art models, ProDVa achieves comparable function alignment using less than 0.04% of the training data, while designing significantly more well-folded proteins, with the proportion of proteins having pLDDT above 70 increasing by 7.38% and those with PAE below 10 increasing by 9.62%.

Best-of-N selection is a key technique for improving the reasoning performance of Large Language Models (LLMs) through increased test-time computation. Current state-of-the-art methods often employ computationally intensive reward models for response evaluation and selection. Reward-free alternatives, like self-consistency and universal self-consistency, are limited in their ability to handle open-ended generation tasks or scale effectively. To address these limitations, we propose self-certainty, a novel and efficient metric that leverages the inherent probability distribution of LLM outputs to estimate response quality without requiring external reward models. We hypothesize that higher distributional self-certainty, aggregated across multiple samples, correlates with improved response accuracy, as it reflects greater confidence in the generated output. Through extensive experiments on various reasoning tasks, we demonstrate that self-certainty (1) scales effectively with increasing sample size $N$, akin to reward models but without the computational overhead; (2) complements chain-of-thought, improving reasoning performance beyond greedy decoding; and (3) generalizes to open-ended tasks where traditional self-consistency methods fall short. Our findings establish self-certainty as a practical and efficient way for improving LLM reasoning capabilities.

Aircraft manufacturing is the jewel in the crown of industry, in which generating high-fidelity airfoil geometries with controllable and editable representations remains a fundamental challenge. Existing deep learning methods, which typically rely on predefined parametric representations (e.g., Bézier curves) or discrete point sets, face an inherent trade-off between expressive power and resolution adaptability. To tackle this challenge, we introduce FuncGenFoil, a novel function-space generative model that directly reconstructs airfoil geometries as function curves. Our method inherits the advantages of arbitrary-resolution sampling and smoothness from parametric functions, as well as the strong expressiveness of discrete point-based representations. Empirical evaluations demonstrate that FuncGenFoil improves upon state-of-the-art methods in airfoil generation, achieving a relative 74.4% reduction in label error and a 23.2% increase in diversity on the AF-200K dataset. Our results highlight the advantages of function-space modeling for aerodynamic shape optimization, offering a powerful and flexible framework for high-fidelity airfoil design.

Numerous well-established studies have demonstrated the superhuman capabilities of modern Vision-Language Models (VLMs) across a wide range of tasks. However, growing is the doubt about the continuing availability of reliable high-quality labeling (supervision) from human annotators, leading to stagnation of the model's performance. To address this challenge, ``superalignment'' employs the so-called weak-to-strong generalization paradigm, where the supervision from a weak model can provide generalizable knowledge for a strong model. While effective in aligning knowledge for clean samples between the strong and weak models, the standard weak-to-strong approach typically fails to capture adversarial robustness, exposing strong VLMs to adversarial attacks. This inability to transfer adversarial robustness is because adversarial samples are normally missing in the superalignment stage. To this end, we are the first to propose the weak-to-strong (adversarial) robustness generalization method to elicit zero-shot robustness in large-scale models by an unsupervised scheme, mitigating the unreliable information source for alignment from two perspectives: alignment re-weighting and source guidance refinement. We analyze settings under which robustness generalization is possible.

Combining math concepts with sports can help boost your fractions game. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Students also saw improvement in other math areas after participating in the workshop. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .

Portions of the rock date back billions of years to when the moon was molten rock. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. NWA 12593 was discovered in Mali in 2017. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .