Reduced rank regression for neural communication: a tutorial for neuroscientists

Bichan Wu; Jonathan Pillow

Home/Archive/arXiv

arXiv · 2512.12467

Reduced rank regression for neural communication: a tutorial for neuroscientists

Bichan Wu·Jonathan Pillow

View original source ↗Read source document ↗Export metadata ↓

Abstract

Reduced rank regression (RRR) is a statistical method for finding a low-dimensional linear mapping between a set of high-dimensional inputs and outputs. In recent years, RRR has found numerous applications in neuroscience, in particular for identifying "communication subspaces" governing the interactions between brain regions. This tutorial article seeks to provide an introduction to RRR and its mathematical foundations, with a particular emphasis on neural communication. We discuss RRR's relationship to alternate dimensionality reduction techniques such as singular value decomposition (SVD), principal components analysis (PCA), principal components regression (PCR), and canonical correlation analysis (CCA). We also derive important extensions to RRR, including ridge regularization and non-spherical noise. Finally, we introduce new metrics for quantifying communication strength as well as the alignment between communication axes and the principal modes of neural activity. By the end of this article, readers should have a clear understanding of RRR and the practical considerations involved in applying it to their own data.

Explore related subjects

q-bio.NC

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Bichan Wu, Jonathan Pillow. 2025-12-13. Reduced rank regression for neural communication: a tutorial for neuroscientists. https://arxiv.org/abs/2512.12467

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Improving the adaptive and continuous learning capabilities of artificial neural networks: Lessons from multi-neuromodulatory dynamics

Continuous adaptive learning, the ability to adapt to the environment and keep improving performance, is a hallmark of natural intelligence. Biological organisms excel in acquiring, transferring, and retaining knowledge while adapting to volatile environments, making them a source of inspiration for artificial neural networks (ANNs). This study explores how neuromodulation, a building block of learning in biological systems, can help address catastrophic forgetting and enhance the robustness of ANNs in continual learning. Driven by neuromodulators including dopamine (DA), acetylcholine (ACh), serotonin (5-HT) and noradrenaline (NA), neuromodulatory processes in the brain operate at multiple scales, facilitating dynamic responses to environmental changes through mechanisms ranging from local synaptic plasticity to global network-wide adaptability. Importantly, the relationship between neuromodulators and their interplay in modulating sensory and cognitive processes is more complex than previously expected, demonstrating a "many-to-many" neuromodulator-to-task mapping. To inspire neuromodulation-aware learning rules, we highlight (i) how multi-neuromodulatory interactions enrich single-neuromodulator-driven learning, (ii) the impact of neuromodulators across multiple spatio-temporal scales, and correspondingly, (iii) strategies for approximating and integrating neuromodulated learning processes in ANNs, and (iv) an architectural-general formulation of multi-neuromodulatory dynamics. We also present a conceptual study to showcase how neuromodulation-inspired mechanisms, such as DA-driven reward processing and NA-based cognitive flexibility, can enhance ANN performance in a Go/No-Go task. Though multi-scale neuromodulation, we aim to bridge the gap between biological and artificial learning, paving the way for ANNs with greater flexibility, robustness, and adaptability.

q-bio.NC↗

arXiv2026

Axonal delay dispersion decides whether a neuron detects an event or a sequence, and predicts cortical column diameter

Cortical neurons fire sparsely -- often fewer than one spike per sensory window -- making rate coding insufficient and temporal coding a necessity. That conduction delays convert firing order into synchrony is long established. What governs which class of temporal feature a neuron detects -- one volley of coincident input, or two in a particular order -- has not been examined. We propose a delay-signature framework in which the axonal conduction delays converging on a dendritic branch constitute a physical key: only input sequences whose spike-time differences the delays compensate arrive synchronously, and coincidence detection, via calcium plateau thresholds, converts that synchrony into an all-or-none output. In simulations of an integrator-neuron model we report three results. First, a single physical scalar -- the dispersion of the delay set -- moves a population from event detection to order-selective sequence detection. The transition is emergent under random delays and connectivity: at narrow dispersion sequence detectors do not exist, and the dispersion at which they overtake event detectors tracks the inter-event interval with a slope statistically indistinguishable from one. This maps a computational distinction onto the anatomical one between myelinated and unmyelinated projections, making myelination a switch on what a neuron computes, not only a regulator of speed. Second, the same dispersion sets the code's limits: it bounds the longest codable interval and fixes an absolute timing tolerance of about a millisecond, with slowing better tolerated than speeding. Third, that millisecond window and horizontal conduction velocity together predict cortical column diameter, and the two areas with direct measurements fall where the relation puts them. One anatomically measurable parameter thus sets what a neuron detects and the limits of what it can represent.

q-bio.NC↗

arXiv2026

A Roadmap for MEG Foundation Models

Foundation models are beginning to reshape brain-signal analysis by moving the field beyond task-specific decoding pipelines toward reusable models pretrained on broad neural datasets. Magnetoencephalography (MEG) is a compelling but still underdeveloped target for this shift: it captures human cortical dynamics at millisecond resolution while offering stronger spatial interpretability than EEG, making it especially valuable for source-resolved studies of perception, language, cognition, and clinical brain function. Yet MEG foundation models remain at an early stage, with only a small number of MEG-specific and MEG-inclusive multi-modal models, modest pretraining corpora, and emerging but still limited benchmarks. This perspective lays down the basic concepts needed to understand MEG foundation models and provides a didactic overview of the field's key design choices, including tokenization, sensor- versus source-space representations, sensor-geometry encoding, backbone architectures, self-supervised objectives, and pretraining data. We then offer a roadmap for future development, organized around native MEG pretraining, adaptation of EEG foundation models, transfer from generic time-series models, and multi-modal integration with EEG, fMRI, MRI, behaviour, and stimulus features. We highlight the need for coordinated infrastructure, including diverse and reusable MEG datasets, rigorous evaluation across subjects, sites, tasks, and clinical settings, and responsible data-sharing practices that address consent, privacy, access, and governance.

q-bio.NC↗