Real-time decoding of target variables from multiple simultaneously recorded neural time-series modalities, such as discrete spiking activity and continuous field potentials, is important across various neuroscience applications. However, a major challenge for doing so is that different neural modalities can have different timescales (i.e., sampling rates) and different probabilistic distributions, or can even be missing at some time-steps. Existing nonlinear models of multimodal neural activity do not address different timescales or missing samples across modalities. Further, some of these models do not allow for real-time decoding. Here, we develop a learning framework that can enable real-time recursive decoding while nonlinearly aggregating information across multiple modalities with different timescales and distributions and with missing samples. This framework consists of 1) a multiscale encoder that nonlinearly aggregates information after learning within-modality dynamics to handle different timescales and missing samples in real time, 2) a multiscale dynamical backbone that extracts multimodal temporal dynamics and enables real-time recursive decoding, and 3) modality-specific decoders to account for different probabilistic distributions across modalities. In both simulations and three distinct multiscale brain datasets, we show that our model can aggregate information across modalities with different timescales and distributions and missing samples to improve real-time target decoding. Further, our method outperforms various linear and nonlinear multimodal benchmarks in doing so.

Imitation learning seeks to estimate policies reflecting the values of demonstrated behaviors. Prevalent approaches learn to match or exceed the demonstrator's performance in expectation without knowing the demonstrator's reward function. Unfortunately, this does not induce pluralistic imitators that learn to support distinct demonstrations.

This paper addresses the problem of inverse covariance (also known as precision matrix) estimation in high-dimensional settings. Specifically, we focus on two classes of estimators: linear shrinkage estimators with a target proportional to the identity matrix, and estimators derived from data augmentation (DA). Here, DA refers to the common practice of enriching a dataset with artificial samples--typically generated via a generative model or through random transformations of the original data--prior to model fitting. For both classes of estimators, we derive estimators and provide concentration bounds for their quadratic error. This allows for both method comparison and hyperparameter tuning, such as selecting the optimal proportion of artificial samples. On the technical side, our analysis relies on tools from random matrix theory. We introduce a novel deterministic equivalent for generalized resolvent matrices, accommodating dependent samples with specific structure. We support our theoretical results with numerical experiments.

Bilevel optimization, in which one optimization problem is nested inside another, underlies many machine learning applications with a hierarchical structure--such as meta-learning and hyperparameter optimization. Such applications often involve sensitive training data, raising pressing concerns about individual privacy. Motivated by this, we study differentially private bilevel optimization. We first focus on settings where the outer-level objective is convex, and provide novel upper and lower bounds on the excess empirical risk for both pure and approximate differential privacy. These bounds are nearly tight and essentially match the optimal rates for standard single-level differentially private ERM, up to additional terms that capture the intrinsic complexity of the nested bilevel structure.

Recent probing studies reveal that large language models exhibit linear subspaces that separate true from false statements, yet the mechanism behind their emergence is unclear. We introduce a transparent, one-layer toy model that reproduces such truth subspaces end-to-end and exposes one concrete route by which they can arise. We study one simple setting in which truth encoding can emerge: a data distribution where factual statements co-occur with other factual statements (and vice-versa), encouraging the model to learn this distinction in order to lower the LM loss on future tokens. We corroborate this pattern with experiments in pretrained language models. Finally, in the toy setting we observe a two-phase learning dynamic: networks first memorize individual factual associations in a few steps, then--over a longer horizon--learn to linearly separate true from false, which in turn lowers language-modeling loss. Together, these results provide both a mechanistic demonstration and an empirical motivation for how and why linear truth representations can emerge in language models.

A major challenge in aligning large language models (LLMs) with human preferences is the issue of distribution shift. LLM alignment algorithms rely on static preference datasets, assuming that they accurately represent real-world user preferences. However, user preferences vary significantly across geographical regions, demographics, linguistic patterns, and evolving cultural trends. This preference distribution shift leads to catastrophic alignment failures in many real-world applications. We address this problem using the principled framework of distributionally robust optimization, and develop two novel distributionally robust direct preference optimization (DPO) algorithms, namely, Wasserstein DPO (WDPO) and Kullback-Leibler DPO (KLDPO). We characterize the sample complexity of learning the optimal policy parameters for WDPO and KLDPO. Moreover, we propose scalable gradient descent-style learning algorithms by developing suitable approximations for the challenging minimax loss functions of WDPO and KLDPO. Our empirical experiments using benchmark data sets and LLMs demonstrate the superior performance of WDPO and KLDPO in substantially improving the alignment when there is a preference distribution shift.

Existing post-hoc approaches can remove undesired concepts but often degrade useful signals. We introduce SPLINCE--Simultaneous Projection for LINear concept removal and Covariance prEservation--which eliminates sensitive concepts from representations while exactly preserving their covariance with a target label. SPLINCE achieves this via an oblique projection that "splices out" the unwanted direction yet protects important label correlations. Theoretically, it is the unique solution that removes linear concept predictability and maintains target covariance with minimal embedding distortion. Empirically, SPLINCE outperforms baselines on benchmarks such as Bias in Bios and Winobias, removing protected attributes while minimally damaging main-task information.

Explaining time series classification models is crucial, particularly in high-stakes applications such as healthcare and finance, where transparency and trust play a critical role. Although numerous time series classification methods have identified key subsequences, known as shapelets, as core features for achieving stateof-the-art performance and validating their pivotal role in classification outcomes, existing post-hoc time series explanation (PHTSE) methods primarily focus on timestep-level feature attribution. These explanation methods overlook the fundamental prior that classification outcomes are predominantly driven by key shapelets.

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.