Bayesian Efficient Coding

Bayesian efficient coding | bioRxiv Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Bayesian efficient coding View ORCID Profile Il Memming Park , View ORCID Profile Jonathan W. Pillow doi: https://doi.org/10.1101/178418 Il Memming Park 1 Champalimaud Research, Champalimaud Foundation , Lisbon, Portugal Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Il Memming Park For correspondence: memming.park{at}research.fchampalimaud.org pillow{at}princeton.edu Jonathan W. Pillow 2 Princeton Neuroscience Institute, Princeton University , Princeton, NJ, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Jonathan W. Pillow For correspondence: memming.park{at}research.fchampalimaud.org pillow{at}princeton.edu Abstract Full Text Info/History Metrics Preview PDF Abstract The efficient coding hypothesis, which proposes that neurons are optimized to maximize information about the environment, has provided a guiding theoretical framework for sensory and systems neuroscience. More recently, a theory known as the Bayesian Brain hypothesis has focused on the brain’s ability to integrate sensory and prior sources of information in order to perform Bayesian inference. Although pieces of a connection between these two hypotheses have appeared in prior work, a general formulation that treats the optimality criterion as an arbitrary functional of the posterior distribution – and thereby admits both information-theoretic and non-information-theoretic objectives within a single formalism – has remained largely implicit. Here we make this formulation explicit, developing a Bayesian theory of efficient coding that defines Bayesian efficient codes in terms of four basic ingredients: (1) a stimulus prior distribution; (2) an encoding model; (3) a capacity constraint, specifying a neural resource limit; and (4) a loss functional, quantifying the desirability or undesirability of various posterior distributions. Classic efficient codes arise as the special case in which the loss functional is the posterior entropy, leading to a code that maximizes mutual information, but alternate loss functionals give solutions that differ dramatically from information-maximizing codes. Within this framework we introduce covtropy , a novel family of posterior-functional losses parameterized by a single exponent, and use it to show that decorrelation of sensory inputs – optimal under classic efficient codes in low-noise settings – can be disadvantageous for objectives that penalize large errors. We then reanalyze Laughlin’s seminal data on contrast coding in the blowfly large monopolar cell, and find that the measured response nonlinearity is better explained by minimizing L p reconstruction error with p = 1 / 2 than by infomax, overturning a forty-year-old interpretation. Bayesian efficient coding thus enlarges the family of normatively optimal codes and provides a more general framework for understanding the design principles of sensory systems. Author summary Sensory neurons work under tight budgets. They represent a rich, noisy world with limited spikes, limited dynamic range, and limited energy. Two long-standing ideas address this problem. One, called efficient coding, asks why neurons encode signals in the ways they do: which signals to amplify, which to filter out. A second, the Bayesian brain hypothesis, asks how the brain turns those signals into a percept: how to combine sensory evidence with prior knowledge to form a best guess about the world. We develop a framework that asks both questions at once. An optimal sensory code in our framework is specified by four interlocking ingredients: a prior description of the world, a model of how neurons respond to it, a limit on the resources they can spend, and a rule for what counts as a good internal representation. Classical information-maximizing codes emerge as one special case, one corner of a much larger family of Bayesian efficient codes. Applying this framework to Laughlin’s 1981 blowfly experiment, long held up as the textbook example of information maximization, we find that the fly’s neurons are better explained by minimizing decoding error than by maximizing information. Competing Interest Statement I. M. Park is a co-founder of RyvivyR. J. W. Pillow declares no competing interests. RyvivyR had no role in the design, analysis, or writing of this manuscript, and this does not alter our adherence to PLOS Computational Biology policies on sharing data and materials. Footnotes This revision substantially updates the framing and related-work discussion relative to v4. - Emphasized covtropy as a novel single-parameter family of posterior-functional losses interpolating between infomax, MSE, and mini-max coding. - Cited Schaffner et al. (2023, Nature Human Behaviour), who independently provided a normative justification for the p = 1/2 exponent we identified empirically, grounded in fitness-maximizing two-alternative forced choice. - Spelled out methodological differences from Wang & Stocker (2016) in the H1 analysis. - Added a discussion paragraph documenting the uptake of the BEC framework since 2017, with representative citations across sensory coding, decision-making, and cognition. - Updated competing interests declaration. No equations, figures, or core results were changed. (table was beautified) Funder Information Declared Simons Foundation, https://ror.org/01cmst727 , SCGB AWD1004351 U.S. National Science Foundation , IIS-1150186 , IIS-1845836 National Institutes of Health, https://ror.org/01cwqze88 , EB-026946 , DA-056404 Thomas Hartman Center for Parkinson–s Research , 64249 Copyright The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission. Back to top Previous Next Posted April 12, 2026. Download PDF Email Thank you for your interest in spreading the word about bioRxiv. NOTE: Your email address is requested solely to identify you as the sender of this article. Your Email * Your Name * Send To * Enter multiple addresses on separate lines or separate them with commas. 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