Torus Graphs for Large Scale Neural Phase Analysis

Oscillatory neural signals such as electroencephalography (EEG) and local field potentials (LFPs) show phase relationships that coordinate communication across brain regions. Modern recordings capture hundreds of channels across many frequency bins, yet standard phase analyses are restricted to only a few variables. The Torus Graph (TG) model, an exponential-family distribution over phases whose univariate and pairwise potentials generalize von Mises distributions, infers principled structure among oscillations but models only static, undirected dependencies and is limited to $\sim \! 100$ variables because its score matching inference scales as $\mathcal{O}(d^{6})$. We introduce a stochastic score matching procedure that reduces the per-iteration cost to $\mathcal{O}(d^{2})$, enabling inference on datasets with thousands of variables. This scalable foundation supports analyses of 1,860 frequency-phase features from multi-electrode LFPs and enables two extensions previously inaccessible to TGs or classical circular statistics: (i) a TG Hidden Markov Model capturing state-dependent phase-coupling changes (e.g., spindle-related states during sleep) and (ii) an autoregressive TG inferring directional interactions via transfer-entropy estimation. Applied to LFP recordings, these models reveal state-dependent phase-interaction patterns between wakefulness and NREM sleep. Together, they enable systematic, large-scale mapping of dynamic and directional phase relationships across brain and cognitive states.

HiPPO Zoo: Explicit Memory Mechanisms for Interpretable State Space Models

Representing the past in a compressed, efficient, and informative manner is a central problem for systems trained on sequential data. The HiPPO framework, originally proposed by Gu & Dao et al., provides a principled approach to sequential compression by projecting signals onto orthogonal polynomial (OP) bases via structured linear ordinary differential equations. Subsequent works have embedded these dynamics in state space models (SSMs), where HiPPO structure serves as an initialization. Nonlinear successors of these SSM methods such as Mamba are state-of-the-art for many tasks with long-range dependencies, but the mechanisms by which they represent and prioritize history remain largely implicit. In this work, we revisit the HiPPO framework with the goal of making these mechanisms explicit. We show how polynomial representations of history can be extended to support capabilities of modern SSMs such as adaptive allocation of memory and associative memory while retaining direct interpretability in the OP basis. We introduce a unified framework comprising five such extensions, which we collectively refer to as a "HiPPO zoo." Each extension exposes a specific modeling capability through an explicit, interpretable modification of the HiPPO framework. The resulting models adapt their memory online and train in streaming settings with efficient updates. We illustrate the behaviors and modeling advantages of these extensions through a range of synthetic sequence modeling tasks, demonstrating that capabilities typically associated with modern SSMs can be realized through explicit, interpretable polynomial memory structures.

Pose Splatter: A 3D Gaussian Splatting Model for Quantifying Animal Pose and Appearance

Accurate and scalable quantification of animal pose and appearance is crucial for studying behavior. Current 3D pose estimation techniques, such as keypoint- and mesh-based techniques, often face challenges including limited representational detail, labor-intensive annotation requirements, and expensive per-frame optimization. These limitations hinder the study of subtle movements and can make large-scale analyses impractical. We propose Pose Splatter, a novel framework leveraging shape carving and 3D Gaussian splatting to model the complete pose and appearance of laboratory animals without prior knowledge of animal geometry, per-frame optimization, or manual annotations. We also propose a novel rotation-invariant visual embedding technique for encoding pose and appearance, designed to be a plug-in replacement for 3D keypoint data in downstream behavioral analyses. Experiments on datasets of mice, rats, and zebra finches show Pose Splatter learns accurate 3D animal geometries. Notably, Pose Splatter represents subtle variations in pose, provides better low-dimensional pose embeddings over state-of-the-art as evaluated by humans, and generalizes to unseen data. By eliminating annotation and per-frame optimization bottlenecks, Pose Splatter enables analysis of large-scale, longitudinal behavior needed to map genotype, neural activity, and micro-behavior at unprecedented resolution.