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Efficient and adaptive sensory codes

Nature Neuroscience volume 24, pages 998–1009 (2021)Cite this article

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Abstract

The ability to adapt to changes in stimulus statistics is a hallmark of sensory systems. Here, we developed a theoretical framework that can account for the dynamics of adaptation from an information processing perspective. We use this framework to optimize and analyze adaptive sensory codes, and we show that codes optimized for stationary environments can suffer from prolonged periods of poor performance when the environment changes. To mitigate the adversarial effects of these environmental changes, sensory systems must navigate tradeoffs between the ability to accurately encode incoming stimuli and the ability to rapidly detect and adapt to changes in the distribution of these stimuli. We derive families of codes that balance these objectives, and we demonstrate their close match to experimentally observed neural dynamics during mean and variance adaptation. Our results provide a unifying perspective on adaptation across a range of sensory systems, environments, and sensory tasks.

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Fig. 1: Adaptation can improve performance on sensory tasks.
Fig. 2: Adaptive sensory codes exhibit different patterns of error.
Fig. 3: Biased codes improve global performance.
Fig. 4: Biased codes improve performance across a range of stimulus conditions.
Fig. 5: Biased codes capture diverse profiles and timescales of adaptive dynamics.
Fig. 6: Feed-forward network can increase information transmission by biasing away from local stimulus statistics.

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Data availability

Data sharing is not applicable as no datasets were generated or analyzed in the current study.

Code availability

Code was written in MATLAB and is available at https://github.com/HermundstadLab/EfficientAdaptiveCodes.

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Acknowledgements

We thank D. Kastner and T. Münch for generously providing figures from their work. We also thank V. Jayaraman, M. Noorman, T. Ma, and K. Krishnamurthy for useful discussions and feedback on the manuscript. W.F.M. was funded by the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skłodowska-Curie Grant Agreement No. 754411. A.M.H. was supported by the Howard Hughes Medical Institute.

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Author notes

  1. These authors contributed equally: Wiktor F. Młynarski, Ann M. Hermundstad.

Authors and Affiliations

  1. Institute of Science and Technology Austria, Klosterneuburg, Austria

    Wiktor F. Młynarski

  2. Janelia Research Campus, Howard Hughes Medical Institute, Ashburn, VA, USA

    Ann M. Hermundstad

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  1. Wiktor F. Młynarski
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Contributions

W.F.M. and A.M.H. conceived the study, developed the theoretical framework, conducted the mathematical analysis, performed the simulations, interpreted the results, and wrote the paper.

Corresponding authors

Correspondence to Wiktor F. Młynarski or Ann M. Hermundstad.

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Peer review information Nature Neuroscience thanks the anonymous reviewers for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Smoothing does not alter results.

a-c, Same results as shown in Fig. 3d-f, here without smoothing. Optimal values of αNL (stars) were chosen prior to smoothing.

Extended Data Fig. 2 Optimal dynamics are robust to parameter variations.

a, b, Optimal nonlinearies (left; shown in Fig. 4d,e) closely resemble those derived by linearly-interpolating parameters between the naively-adaptive code and the fully-biased code (right). Shown here as a function of the system’s posterior belief P(high) = \({P}_{t}^{H}\), for variance adaptation (a) and mean adaptation (b). c, d, The dependence of the offset (upper row) and slope (lower row) of the optimal nonlinearities on the bias αI can be approximated by a line that interpolates between the naively-adaptive code (αI = 0) and the fully-based code (αI = 1). Shown here for variance adaptation (c) and mean adaptation (d), for several different values of the posterior belief P(high).

Extended Data Fig. 3 Abrupt changes in encoding parameters arise from bifurcations in error landscapes.

a,b, Encoding nonlinearies (left panels; shown in Fig. 4d,e) show abrupt changes for small variations in the system’s posterior belief P(high) = \({P}_{t}^{H}\). These changes arise from variations in the underlying error landscapes (right panels) in which a single minimum bifurcates into two minima or vice-versa (a, upper row; global minima marked by red x’s), or when one of multiple local minima becomes the global minimum (a, lower row; b, both rows). In the case of variance adaptation, the error landscape is symmetric to positive versus negative variations in the offset of the encoding nonlinearity (x0), and thus bifurcations in the error landscape lead to two symmetric solutions (a, upper row). In such scenarios, we chose the solution corresponding to the lower value of x0 (marked by circles), because it produces lower spike counts on average.

Extended Data Fig. 4 Balance of errors is robust to changes in volatility.

a, As volatility increases, the posterior is faster to update and the error faster to decay (shown for the naively-adaptive code in response to an increase in variance). b-d, Biased codes produce qualitatively consistent patterns of performance regardless of volatility (upper panels), but the relative impact of biasing the code increases as volatility increases (lower panels). Higher volatility leads to relatively longer periods of mismatch (b, upper), higher mismatched errors and lower matched errors (c, upper), and higher global errors (d, upper). The percent change in each of these errors (measured relative to the naively-adaptive code and scaled by the difference in error between the static and oracle codes) increases as volatility increases (lower row), and the global error is thus minimized for larger values of bias (c-d; circled markers in upper panels).

Extended Data Fig. 5 Entropy coding transforms response levels and reduces average firing rates.

a-c, Entropy coding reassigns response levels to spike counts based on the predicted probability that a response level will be used. a, The encoding nonlinearity partitions stimuli drawn from the actual stimulus distribution (black) or predicted stimulus distribution (red) into discrete response levels. This partitioning determines the predicted (b, left) and actual (c, left) probability with which response levels will be used. b, Entropy coding reassigns spike counts in order of decreasing predicted probability (left); response levels that have higher predicted probability (darker red) will be assigned fewer spikes (middle). This leads to a recoded histogram that is weighted toward lower spike counts (right). The reassignment could be approximated by a quadratic nonlinearity, or by a thresholding exponential nonlinearity. c, The recoding scheme, which is based on predicted probability (b), determines how stimuli sampled from the actual stimulus distribution will be transformed into spike counts. d, Before recoding (left), firings rates do not change in response to a change between low (L) and high (H) stimulus variance, regardless of the value of αI. After recoding (right), all codes show a transient response to both increases and decreases in variance, and time-averaged firing rates are lower (inset). e, Before recoding (left), firing rates increase following a change from low (L) to high (H) stimulus mean, and decrease following a change from high to low mean. After recoding (right), all codes show a symmetric response to increases and decreases in mean, and time-averaged firing rates are lower (inset).

Extended Data Fig. 6 Volatility shapes posterior dynamics.

a,c, As volatility increases (that is, as the switching period decreases), the posterior is faster to respond to both increases (upper) and decreases (lower) in stimulus variance (a) and mean (c). We estimated this timescale by linearly interpolating the posterior before computing the time at which it crosses 0.5. b, When stimulus variance is changing in time, the naively-adaptive code (αI = 0, upper left) is faster to respond to decreases in variance (solid lines) than to increases (dashed lines). In contrast, biased codes (upper middle, right) are faster to respond to increases in variance. This is largely driven by a more rapid response to increases in variance with increasing bias (lower left), but is also weakly affected by a slower response to decreases in variance (lower right). d, The posterior is equally fast to respond to increases and decreases in the stimulus mean (upper row), with a timescale that decreases as bias increases (lower row).

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Młynarski, W.F., Hermundstad, A.M. Efficient and adaptive sensory codes. Nat Neurosci 24, 998–1009 (2021). https://doi.org/10.1038/s41593-021-00846-0

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