ArticlePhysical review research
Geometric framework to predict structure from function in neural networks.
Article in Physical review research. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 14 papers.
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Who cites it
14 citing papers in PubMed.
- Attractor-Based Models for Sequences and Pattern Generation in Neural Circuits.Neural computation · 2026Article
- A complex network perspective on brain disease.Biological reviews of the Cambridge Philosophical Society · 2026Review
- Stability through plasticity: Finding robust memories through representational drift.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Biological detail and graph structure in network neuroscience.Frontiers in network physiology · 2025Review
- Maintaining and updating accurate internal representations of continuous variables with a handful of neurons.Nature neuroscience · 2024Article
- Article
- Vertebrate behavioral thermoregulation: knowledge and future directions.Neurophotonics · 2024Review
- A vast space of compact strategies for effective decisions.Science advances · 2024Article
- Stable fixed points of combinatorial threshold-linear networks.Advances in applied mathematics · 2024Article
- The mechanics of correlated variability in segregated cortical excitatory subnetworks.bioRxiv : the preprint server for biology · 2023Article
- Article
- Sequential Attractors in Combinatorial Threshold-Linear Networks.SIAM journal on applied dynamical systems · 2022Article
- Article
- Theoretical principles for illuminating sensorimotor processing with brain-wide neuronal recordings.Current opinion in neurobiology · 2020Review
Corrections and comments
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Authors and funding
2 authors.
Funding
Abstract
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but quantitative links between neural network structure and function are complex and subtle. For example, many networks can give rise to similar functional responses, and the same network can function differently depending on context. Whether certain patterns of synaptic connectivity are required to generate specific network-level computations is largely unknown. Here we introduce a geometric framework for identifying synaptic connections required by steady-state responses in recurrent networks of threshold-linear neurons. Assuming that the number of specified response patterns does not exceed the number of input synapses, we analytically calculate the solution space of all feedforward and recurrent connectivity matrices that can generate the specified responses from the network inputs. A generalization accounting for noise further reveals that the solution space geometry can undergo topological transitions as the allowed error increases, which could provide insight into both neuroscience and machine learning. We ultimately use this geometric characterization to derive certainty conditions guaranteeing a nonzero synapse between neurons. Our theoretical framework could thus be applied to neural activity data to make rigorous anatomical predictions that follow generally from the model architecture.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.