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Approximating nonlinear functions with latent boundaries in low-rank excitatory-inhibitory spiking networks
Neurons and Cognition · Submitted 18 Jul 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings.
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The abstract, sentence by sentence
Deep feedforward and recurrent rate-based neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Deep feedforward and recurrent rate-based neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. | background 0.85 | 0.05 | 0.03 | asserted 1.00 |
| s1 | Here we argue that these details are crucial in order to understand how real neural circuits operate. | gap 0.52 | 0.13 | 0.08 | asserted 0.95 |
| s2 | Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. | contribution 0.99 | 0.83 | 0.08 | asserted 0.90 |
| s3 | By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. | method 0.91 | 0.90 | 0.07 | asserted 1.00 |
| s4 | We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. | result 0.94 | 0.93 | 0.09 | asserted 1.00 |
| s5 | Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. | method 0.40 | 0.87 | 0.13 | asserted 1.00 |
| s6 | The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. | result 0.72 | 0.90 | 0.58 | asserted 0.98 |
| s7 | We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. | result 0.70 | 0.92 | 0.07 | asserted 1.00 |
| s8 | Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. | limitation 0.78 | 0.59 | 0.04 | hedged possibility 0.58 |
| s9 | Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation. | interpretation 0.65 | 0.58 | 0.38 | hedged possibility 0.95 |
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The paper
Original abstract
Deep feedforward and recurrent rate-based neural networks have become successful functional models of the brain, but they neglect obvious biological details such as spikes and Dale's law. Here we argue that these details are crucial in order to understand how real neural circuits operate. Towards this aim, we put forth a new framework for spike-based computation in low-rank excitatory-inhibitory spiking networks. By considering populations with rank-1 connectivity, we cast each neuron's spiking threshold as a boundary in a low-dimensional input-output space. We then show how the combined thresholds of a population of inhibitory neurons form a stable boundary in this space, and those of a population of excitatory neurons form an unstable boundary. Combining the two boundaries results in a rank-2 excitatory-inhibitory (EI) network with inhibition-stabilized dynamics at the intersection of the two boundaries. The computation of the resulting networks can be understood as the difference of two convex functions and is thereby capable of approximating arbitrary non-linear input-output mappings. We demonstrate several properties of these networks, including noise suppression and amplification, irregular activity and synaptic balance, as well as how they relate to rate network dynamics in the limit that the boundary becomes soft. Finally, while our work focuses on small networks (5-50 neurons), we discuss potential avenues for scaling up to much larger networks. Overall, our work proposes a new perspective on spiking networks that may serve as a starting point for a mechanistic understanding of biological spike-based computation.
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How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
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Recently, this low-rank framework has been applied to analyze the low-rank excitatory-inhibitory spiking networks, with a focus either on mean-field analysis of random networks [ref] , decomposition of synaptic input into factor based (partially trained and low-rank) and non-factor based (random) components [ref] , or on the capability of approximating arbitrary non-linear input-output mappings using small size networks [ref] .
Spiking mode-based neural networks · Introduction · 0.94
What it cites · 1 sentence without a confident label
Compares with 1 paper
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Many previous models, in contrast, typically start with Dale's law as a biological constraint, then attempt to achieve performance on par with an unconstrained network, and finally reflect on the potential benefits of such a constraint for, e.g., stability or robustness [ref] .
The computational and learning benefits of Daleian neural networks · Discussion · 0.80
Cites as background 2 papers
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More generally, the spike-coding framework has been extended in various ways for other computational aims (e.g., [ref] ), as well as to incorporate additional biologically-plausible details or activity regimes (e.g., [ref] ), and it will be interesting to see how our perspective here may be integrated with these other studies.
Closed-form control with spike coding networks · Discussion · 0.95
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Functional models of static input-output mappings are perhaps best represented by feedforward rate networks [ref] .
Spiking Deep Networks with LIF Neurons · Discussion · 0.93
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