A new analysis says the insects’ visual responses fit a model that limits reconstruction errors better than one that maximizes information.
The researchers connect two major ideas in neuroscience: efficient coding, which traditionally treats neurons as maximizing information about the environment, and Bayesian inference, in which the brain combines sensory evidence with prior expectations. Their framework defines an optimal neural code using a stimulus prior, an encoding model, a neural capacity limit and a loss function describing which errors matter most.
The framework predicts that different goals can produce very different neural codes. In particular, reducing correlations between sensory inputs—a familiar result of information-maximizing models—can be disadvantageous when large decoding errors are costly. Applying the framework to data from blowfly large monopolar cells, the researchers found that the measured contrast response was better explained by a model minimizing average square-root error than by a model maximizing mutual information.
What the blowfly data suggest
The study formalizes Bayesian efficient coding as a family of models rather than a single information-maximizing rule. Classic efficient coding appears as one special case, using posterior uncertainty—or entropy—as the loss to minimize. Other loss functions produce different predictions.
The researchers introduced a family of loss functions called covtropy and used the framework to study both populations of neurons with linear receptive fields and single neurons with nonlinear responses. Their calculations showed that decorrelating sensory inputs can be harmful for objectives that penalize large errors, and that even in high-signal-to-noise conditions, an optimal code may increase correlations between neurons.
For the blowfly analysis, the team extracted data points from figures in Laughlin’s original study and fitted models to them. They reported that the observed response nonlinearity was more consistent with minimizing an average square-root reconstruction error, corresponding to p = 1/2, than with maximizing mutual information.
Why the coding goal matters
The findings broaden the question of what sensory neurons might be optimized to do. Instead of assuming that neural systems always maximize information, researchers can consider the kinds of mistakes that matter for a particular task and environment.
This changes the interpretation of a well-known blowfly contrast-coding result: the measured response may fit an error-reduction objective better than the traditional information-maximization explanation. The framework also provides a way to compare different proposed goals for sensory coding, rather than treating information as the only measure of efficiency.
Evidence and caveats
The work is a theoretical analysis illustrated with numerical solutions and a reanalysis of data extracted from figures in an earlier blowfly study. The model calculations rely on simplifying assumptions, including shared diagonalizable structure for several matrices in the population-coding analysis.
The researchers stress that the framework does not determine which loss function the nervous system actually uses. Its priors, encoding models, constraints and loss functions were chosen mainly for mathematical tractability rather than established biological realism. Different combinations of these ingredients can explain the same encoding pattern, and the framework is therefore under-constrained by current neural and behavioral observations. The examples are also simplified and do not address all issues, including continuous time, computational limits and hidden variables.
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PLoS Computational Biology · 2026 · DOI: 10.1371/journal.pcbi.1014894
Authors: Il Memming Park, Jonathan W. Pillow
Institutions: Stony Brook University, Princeton University, Champalimaud Foundation
