In both artificial and biological systems, the centered kernel alignment (CKA) has become a widely used tool for quantifying neural representation similarity. While current CKA estimators typically correct for the effects of finite stimuli sampling, the effects of sampling a subset of neurons are overlooked, introducing notable bias in standard experimental scenarios. Here, we provide a theoretical analysis showing how this bias is affected by the representation geometry. We then introduce a novel estimator that corrects for both input and feature sampling. We use our method for evaluating both brain-to-brain and model-to-brain alignments and show that it delivers reliable comparisons even with very sparsely sampled neurons. We perform within-animal and across-animal comparisons on electrophysiological data from visual cortical areas V1, V4, and IT data, and use these as benchmarks to evaluate model-to-brain alignment. We also apply our method to reveal how object representations become progressively disentangled across layers in both biological and artificial systems. These findings underscore the importance of correcting feature-sampling biases in CKA and demonstrate that our bias-corrected estimator provides a more faithful measure of representation alignment. The improved estimates increase our understanding of how neural activity is structured across both biological and artificial systems.

Analyzing the structure of sampled features from an input data distribution is challenging when constrained by limited measurements in both the number of inputs and features. Traditional approaches often rely on the eigenvalue spectrum of the sample covariance matrix derived from finite measurement matrices; however, these spectra are sensitive to the size of the measurement matrix, leading to biased insights. In this paper, we introduce a novel algorithm that provides unbiased estimates of the spectral moments of the kernel integral operator in the limit of infinite inputs and features from finitely sampled measurement matrices. Our method, based on dynamic programming, is efficient and capable of estimating the moments of the operator spectrum. We demonstrate the accuracy of our estimator on radial basis function (RBF) kernels, highlighting its consistency with the theoretical spectra. Furthermore, we showcase the practical utility and robustness of our method in understanding the geometry of learned representations in neural networks.

We present a general class of machine learning algorithms called parametric matrix models. Parametric matrix models are based on matrix equations, and the design is motivated by the efficiency of reduced basis methods for approximating solutions of parametric equations. The dependent variables can be defined implicitly or explicitly, and the equations may use algebraic, differential, or integral relations. Parametric matrix models can be trained with empirical data only, and no high-fidelity model calculations are needed. While originally designed for scientific computing, parametric matrix models are universal function approximators that can be applied to general machine learning problems. After introducing the underlying theory, we apply parametric matrix models to a series of different challenges that show their performance for a wide range of problems. For all the challenges tested here, parametric matrix models produce accurate results within a computational framework that allows for parameter extrapolation and interpretability.

Continuous trajectories are inherently infinite-dimensional objects that can vary in complex ways in both time and space. However, in many practical situations, they contain intrinsic sources of variability that can be wellapproximated by projection onto a low-dimensional manifold. For instance, when a human demonstrates trajectories for a robot, it is useful for the robot to learn to model the most expressive latent factors controlling the spatial paths of the demonstration trajectories. For certain types of demonstrations, such as in gesture control or quasistatic manipulation, it is highly advantageous to explicitly separate the exact timing of the trajectory from the spatial latent factors. As an illustrative example, consider trying to average two samples from a handwriting dataset generated by humans drawing the letter "A" in the air (Chen et al., 2012). If we scale two trajectories linearly in time so that both their timestamps go from 0 to 1, and then average the two trajectories at each timestep, the resulting average does not maintain the style of the "A"s. This is because the average is taken between parts of the two trajectories that do not naturally correspond to each other. An example of this averaging, with lines showing examples of points that are averaged, is shown in Figure 1a. A common approach like Dynamic Time Warping (DTW) (Sakoe & Chiba, 1978) can lead to unintuitive results.

We investigate how sparse neural activity affects the generalization performance of a deep Bayesian neural network at the large width limit. To this end, we derive a neural network Gaussian Process (NNGP) kernel with rectified linear unit (ReLU) activation and a predetermined fraction of active neurons. Using the NNGP kernel, we observe that the sparser networks outperform the non-sparse networks at shallow depths on a variety of datasets.

Event-based sensors have recently drawn increasing interest in robotic perception due to their lower latency, higher dynamic range, and lower bandwidth requirements compared to standard CMOS-based imagers. These properties make them ideal tools for real-time perception tasks in highly dynamic environments. In this work, we demonstrate an application where event cameras excel: accurately estimating the impact location of fast-moving objects. We introduce a lightweight event representation called Binary Event History Image (BEHI) to encode event data at low latency, as well as a learning-based approach that allows real-time inference of a confidence-enabled control signal to the robot. To validate our approach, we present an experimental catching system in which we catch fast-flying ping-pong balls. We show that the system is capable of achieving a success rate of 81% in catching balls targeted at different locations, with a velocity of up to 13 m/s even on compute-constrained embedded platforms such as the Nvidia Jetson NX.

Large-scale AI systems that combine search and learning have reached super-human levels of performance in game-playing, but have also been shown to fail in surprising ways. The brittleness of such models limits their efficacy and trustworthiness in real-world deployments. In this work, we systematically study one such algorithm, AlphaZero, and identify two phenomena related to the nature of exploration. First, we find evidence of policy-value misalignment -- for many states, AlphaZero's policy and value predictions contradict each other, revealing a tension between accurate move-selection and value estimation in AlphaZero's objective. Further, we find inconsistency within AlphaZero's value function, which causes it to generalize poorly, despite its policy playing an optimal strategy. From these insights we derive VISA-VIS: a novel method that improves policy-value alignment and value robustness in AlphaZero. Experimentally, we show that our method reduces policy-value misalignment by up to 76%, reduces value generalization error by up to 50%, and reduces average value error by up to 55%.

Being able to grasp objects is a fundamental component of most robotic manipulation systems. In this paper, we present a new approach to simultaneously reconstruct a mesh and a dense grasp quality map of an object from a depth image. At the core of our approach is a novel camera-centric object representation called the "object shell" which is composed of an observed "entry image" and a predicted "exit image". We present an image-to-image residual ConvNet architecture in which the object shell and a grasp-quality map are predicted as separate output channels. The main advantage of the shell representation and the corresponding neural network architecture, ShellGrasp-Net, is that the input-output pixel correspondences in the shell representation are explicitly represented in the architecture. We show that this coupling yields superior generalization capabilities for object reconstruction and accurate grasp quality estimation implicitly considering the object geometry. Our approach yields an efficient dense grasp quality map and an object geometry estimate in a single forward pass. Both of these outputs can be used in a wide range of robotic manipulation applications. With rigorous experimental validation, both in simulation and on a real setup, we show that our shell-based method can be used to generate precise grasps and the associated grasp quality with over 90% accuracy. Diverse grasps computed on shell reconstructions allow the robot to select and execute grasps in cluttered scenes with more than 93% success rate.

We propose a curriculum-driven learning strategy for solving difficult multi-agent coordination tasks. Our method is inspired by a study of animal communication, which shows that two straightforward design features (mutual reward and decentralization) support a vast spectrum of communication protocols in nature. We highlight the importance of similarly interpreting emergent communication as a spectrum. We introduce a toroidal, continuous-space pursuit-evasion environment and show that naive decentralized learning does not perform well. We then propose a novel curriculum-driven strategy for multi-agent learning. Experiments with pursuit-evasion show that our approach enables decentralized pursuers to learn to coordinate and capture a superior evader, significantly outperforming sophisticated analytical policies. We argue through additional quantitative analysis -- including influence-based measures such as Instantaneous Coordination -- that emergent implicit communication plays a large role in enabling superior levels of coordination.

We study fairness through the lens of cooperative multi-agent learning. Our work is motivated by empirical evidence that naive maximization of team reward yields unfair outcomes for individual team members. To address fairness in multi-agent contexts, we introduce team fairness, a group-based fairness measure for multi-agent learning. We then incorporate team fairness into policy optimization -- introducing Fairness through Equivariance (Fair-E), a novel learning strategy that achieves provably fair reward distributions. We then introduce Fairness through Equivariance Regularization (Fair-ER) as a soft-constraint version of Fair-E and show that Fair-ER reaches higher levels of utility than Fair-E and fairer outcomes than policies with no equivariance. Finally, we investigate the fairness-utility trade-off in multi-agent settings.