ArticlePLoS computational biology2020
On the choice of metric in gradient-based theories of brain function.
Article in PLoS computational biology, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers, 1 of them a synthesis that pooled it.
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Who cites it
12 citing papers in PubMed, 1 synthesis or guideline pooled it.
- Mathematical expansion and clinical application of chronic kidney disease stage as vector field.PloS one · 2024Pooled it
- Spike-based alignment learning solves the weight transport problem.Nature communications · 2026Article
- Remembering the "when": Hebbian memory models for the time of past events.PLoS computational biology · 2026Article
- Deep-learning-assisted simulation of a cortical circuit: integrating anatomy, physiology and function.bioRxiv : the preprint server for biology · 2026Article
- Interactions between long- and short-term synaptic plasticity transform temporal neural representations into spatial.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Inferring learning rules during de novo task learning.bioRxiv : the preprint server for biology · 2025Article
- Confidence and second-order errors in cortical circuits.PNAS nexus · 2024Article
- High-performance deep spiking neural networks with 0.3 spikes per neuron.Nature communications · 2024Article
- Fast adaptation to rule switching using neuronal surprise.PLoS computational biology · 2024Article
- Natural-gradient learning for spiking neurons.eLife · 2022Article
- Learning as filtering: Implications for spike-based plasticity.PLoS computational biology · 2022Article
- Bayesian mechanics of perceptual inference and motor control in the brain.Biological cybernetics · 2021Article
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Authors and funding
4 authors.
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Abstract
This is a PLOS Computational Biology Education paper. The idea that the brain functions so as to minimize certain costs pervades theoretical neuroscience. Because a cost function by itself does not predict how the brain finds its minima, additional assumptions about the optimization method need to be made to predict the dynamics of physiological quantities. In this context, steepest descent (also called gradient descent) is often suggested as an algorithmic principle of optimization potentially implemented by the brain. In practice, researchers often consider the vector of partial derivatives as the gradient. However, the definition of the gradient and the notion of a steepest direction depend on the choice of a metric. Because the choice of the metric involves a large number of degrees of freedom, the predictive power of models that are based on gradient descent must be called into question, unless there are strong constraints on the choice of the metric. Here, we provide a didactic review of the mathematics of gradient descent, illustrate common pitfalls of using gradient descent as a principle of brain function with examples from the literature, and propose ways forward to constrain the metric.
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