Activation-alignment measures such as Representational Similarity Analysis (RSA), Canonical Correlation Analysis (CCA), and Centered Kernel Alignment (CKA) are widely used to compare biological and artificial neural representations. Recent theoretical work interprets many of these methods as assessing agreement between optimal linear readouts over broad families of global tasks. However, agreement at the level of global readouts does not determine how a system uses local stimulus evidence. Specifically, representations may align in activation space yet differ in their sensitivity to small perturbations. To address this challenge, we introduce a complementary framework based on local decodable information, which focuses on a representation's ability, under noise, to discriminate small perturbations within a specified stimulus-coordinate subspace. Building on Fisher information and local representation geometry, we summarize each representation using the expected projected pullback/Fisher metric over that subspace. This formulation induces a second-moment family of local discrimination tasks, for which the resulting operator provides a minimal, complete dataset-level summary of expected discriminability. We compare these regularized signatures using a log-spectral distance on the manifold of symmetric positive definite (SPD) matrices, yielding the Spectral Riemannian Alignment Score (S-RAS) and a uniform multiplicative certificate over the corresponding family of lifted task values. Empirically, this framework enables the recovery of corresponding layers across independently trained artificial neural networks, supports transferable class-conditional probes, reveals controlled dissociations between standard and robust training, and uncovers stimulus-coordinate family effects across mouse visual cortex using the Allen Brain Observatory static gratings dataset.

Unsupervised domain adaptation excels in transferring knowledge from a labeled source domain to an unlabeled target domain, playing a critical role in time series applications. Existing time series domain adaptation methods either ignore frequency features or treat temporal and frequency features equally, which makes it challenging to fully exploit the advantages of both types of features.

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For efficient training, we seek to optimize an upper-bound of the objectiveresulting intwosimpleterms.

The ability for the brain to discriminate among visual stimuli is constrained by their retinal representations. Previous studies of visual discriminability have been limited to either low-dimensional artificial stimuli or pure theoretical considerations without a realistic encoding model. Here we propose a novel framework for understanding stimulus discriminability achieved by retinal representations of naturalistic stimuli with the method of information geometry. To model the joint probability distribution of neural responses conditioned on the stimulus, we created a stochastic encoding model of a population of salamander retinal ganglion cells based on a three-layer convolutional neural network model. This model not only accurately captured the mean response to natural scenes but also a variety of second-order statistics.

Unsupervised domain adaptation (UDA) is a pivotal form in machine learning to extend the in-domain model to the distinctive target domains where the data distributions differ. Most prior works focus on capturing the inter-domain transferability but largely overlook rich intra-domain structures, which empirically results in even worse discriminability. In this work, we introduce a novel graph SPectral Alignment (SPA) framework to tackle the tradeoff. The core of our method is briefly condensed as follows: (i)-by casting the DA problem to graph primitives, SPA composes a coarse graph alignment mechanism with a novel spectral regularizer towards aligning the domain graphs in eigenspaces; (ii)-we further develop a fine-grained message propagation module --- upon a novel neighbor-aware self-training mechanism --- in order for enhanced discriminability in the target domain. On standardized benchmarks, the extensive experiments of SPA demonstrate that its performance has surpassed the existing cutting-edge DA methods. Coupled with dense model analysis, we conclude that our approach indeed possesses superior efficacy, robustness, discriminability, and transferability. Code and data are available at: https://github.com/CrownX/SPA.