Understanding the inductive bias and generalization properties of large overparametrized machine learning models requires to characterize the dynamics of the training algorithm. We study the learning dynamics of large two-layer neural networks via dynamical mean field theory, a well established technique of nonequilibrium statistical physics. We show that, for large network width m, and large number of samples per input dimension n/d, the training dynamics exhibits a separation of timescales which implies: (i) The emergence of a slow time scale associated with the growth in Gaussian/Rademacher complexity of the network; (ii) Inductive bias towards small complexity if the initialization has small enough complexity; (iii) A dynamical decoupling between feature learning and overfitting regimes; (iv)A non-monotone behavior of the test error, associated'feature unlearning' regime at large times.

The Poisson Generalized Linear Model (GLM) is a foundational tool for analyzing neural spike train data. However, standard implementations rely on discretizing spike times into binned count data, limiting temporal resolution and scalability. Here, we develop Monte Carlo (MC) methods and polynomial approximations (PA) to the continuous-time analog of these models, and show them to be advantageous over their discrete-time counterparts. Further, we propose using a set of exponentially scaled Laguerre polynomials as an orthogonal temporal basis, which improves filter identification and yields closed-form integral solutions under the polynomial approximation. Applied to both synthetic and real spike-time data from rodent hippocampus, our methods demonstrate superior accuracy and scalability compared to traditional binned GLMs, enabling functional connectivity inference in large-scale neural recordings that are temporally precise on the order of synaptic dynamical timescales and in agreement with known anatomical properties of hippocampal subregions. We provide open-source implementations of both MC and PA estimators, optimized for GPU acceleration, to facilitate adoption in the neuroscience community1.

Learning effective multi-modal 3D representations of objects is essential for numerous applications, such as augmented reality and robotics. Existing methods often rely on task-specific embeddings that are tailored either for semantic understanding or geometric reconstruction. As a result, these embeddings typically cannot be decoded into explicit geometry and simultaneously reused across tasks. In this paper, we propose Object-X, a versatile multi-modal object representation framework capable of encoding rich object embeddings (e.g., images, point cloud, text) and decoding them back into detailed geometric and visual reconstructions. Object-X operates by geometrically grounding the captured modalities in a 3D voxel grid and learning an unstructured embedding fusing the information from the voxels with the object attributes. The learned embedding enables 3D Gaussian Splatting-based object reconstruction, while also supporting a range of downstream tasks, including scene alignment, single-image 3D object reconstruction, and localization. Evaluations on two challenging real-world datasets demonstrate that Object-X achieves high-fidelity novel-view synthesis comparable to standard 3DGaussian Splatting, while significantly improving geometric accuracy. Moreover, Object-X achieves competitive performance with specialized methods in scene alignment and localization. Critically, our object-centric descriptors require 3-4 orders of magnitude less storage compared to traditional imageor point cloud-based approaches, establishing Object-X as a scalable and highly practical solution for multi-modal 3D scene representation.

The problem of optimally covering a given compact subset of RN with a preassigned number n of Euclidean metric balls has a long-standing history and it is well-recognized to be computationally hard. This article establishes a numerically viable algorithm for obtaining optimal covers of compact sets via two key contributions. The first is a foundational result establishing Lipschitz continuity of the marginal function of a certain parametric non-convex maximization problem in the optimal covering problem, and it provides the substrate for numerical gradient algorithms to be employed in this context. The second is an adaptation of a stochastically smoothed numerical gradient-based (zeroth-order) algorithm for a non-convex minimization problem, that, equipped with randomized restarts, spurs global convergence to an optimal cover. Several numerical experiments with complicated nonconvex compact sets demonstrate the excellent performance of our techniques.

Vision-Language Models (VLMs) exhibit impressive performance, yet the integration of powerful vision encoders has significantly broadened their attack surface, rendering them increasingly susceptible to jailbreak attacks.

Intracortical Brain-Computer Interfaces (iBCI) decode behavior from neural population activity to restore motor functions and communication abilities in individuals with motor impairments. A central challenge for long-term iBCI deployment is the nonstationarity of neural recordings, where the composition and tuning profiles of the recorded populations are unstable across recording sessions. Existing approaches attempt to address this issue by explicit alignment techniques; however, they rely on fixed neural identities and require test-time labels or parameter updates, limiting their generalization across sessions and imposing additional computational burden during deployment. In this work, we address the problem of cross-session nonstationarity in long-term iBCI systems and introduce SPINT a Spatial Permutation-Invariant Neural Transformer framework for behavioral decoding that operates directly on unordered sets of neural units. Central to our approach is a novel context-dependent positional embedding scheme that dynamically infers unit-specific identities, enabling flexible generalization across recording sessions. SPINT supports inference on variable-size populations and allows fewshot, gradient-free adaptation using a small amount of unlabeled data from the test session. We evaluate SPINT on three multi-session datasets from the FALCON Benchmark, covering continuous motor decoding tasks in human and non-human primates. SPINT demonstrates robust cross-session generalization, outperforming existing zero-shot and few-shot unsupervised baselines while eliminating the need for test-time alignment and fine-tuning. Our work contributes an initial step toward a robust and scalable neural decoding framework for long-term iBCI applications.

Pre-training datasets are typically collected from web content and lack inherent domain divisions. For instance, widely used datasets like Common Crawl do not include explicit domain labels, while manually curating labeled datasets such as The Pile is labor-intensive. Consequently, identifying an optimal pre-training data mixture remains a challenging problem, despite its significant benefits for pre-training performance. To address these challenges, we propose CLusteringbased Iterative Data Mixture Bootstrapping (Nemotron-CLIMB), an automated framework that discovers, evaluates, and refines data mixtures in a pre-training setting. Specifically, Nemotron-CLIMB embeds and clusters large-scale datasets in a semantic space and then iteratively searches for optimal mixtures using a smaller proxy model and a predictor. This strategy enables effective domain adaptation without relying solely on curated data. When continuously trained on 400B tokens with this mixture, our 1B model exceeds the state-of-the-art Llama-3.2-1B by 2.0%. Moreover, we observe that optimizing for a specific domain (e.g., Social Sciences) yields a 5% improvement over random sampling.

Dimensionality reduction via linear sketching is a powerful and widely used technique, but it is known to be vulnerable to adversarial inputs. We study the black-box adversarial setting, where a fixed, hidden sketching matrix A Rk n maps highdimensional vectors v Rn to lower-dimensional sketches Av Rk, and an adversary can query the system to obtain approximate ℓ2-norm estimates that are computed from the sketch. We present a universal, nonadaptive attack that, using O(k2)queries, either causes a failure in norm estimation or constructs an adversarial input on which the optimal estimator for the query distribution (used by the attack) fails. The attack is completely agnostic to the sketching matrix and to the estimator--it applies to any linear sketch and any query responder, including those that are randomized, adaptive, or tailored to the query distribution. Our lower bound construction tightly matches the known upper bounds of Ω(k2), achieved by specialized estimators for Johnson-Lindenstrauss transforms and AMS sketches. Beyond sketching, our results uncover structural parallels to adversarial attacks in image classification, highlighting fundamental vulnerabilities of compressed representations.

Multimodal Large Language Models (MLLMs) are increasingly deployed in finetuning-as-a-service (FTaaS) settings, where user-submitted datasets adapt generalpurpose models to downstream tasks. This flexibility, however, introduces serious security risks, as malicious fine-tuning can implant backdoors into MLLMs with minimal effort. In this paper, we observe that backdoor triggers systematically disrupt cross-modal processing by causing abnormal attention concentration on non-semantic regions--a phenomenon we term attention collapse. Based on this insight, we propose Believe Your Eyes (BYE), a data filtering framework that leverages attention entropy patterns as self-supervised signals to identify and filter backdoor samples. BYE operates via a three-stage pipeline: (1) extracting attention maps using the fine-tuned model, (2) computing entropy scores and profiling sensitive layers via bimodal separation, and (3) performing unsupervised clustering to remove suspicious samples. Unlike prior defenses, BYE requires no clean supervision, auxiliary labels, or model modifications. Extensive experiments across various datasets, models, and diverse trigger types validate BYE's effectiveness: it achieves near-zero attack success rates while maintaining clean-task performance, offering a robust and generalizable solution against backdoor threats in MLLMs.

Generating diverse, all-atom conformational ensembles of dynamic proteins such as G-protein-coupled receptors (GPCRs) is critical for understanding their function, yet most generative models simplify atomic detail or ignore conformational diversity altogether.