Sensory neurons are often reported to adjust their coding accuracy to the stimulus statistics. The observed match is not always perfect and the maximal accuracy does not align with the most frequent stimuli. As an alternative to a physiological explanation we show that the match critically depends on the chosen stimulus measurement scale. More generally, we argue that if we measure the stimulus intensity on the scale which is proportional to the perception intensity, an improved adjustment in the coding accuracy is revealed. The unique feature of stimulus units based on the psychophysical scale is that the coding accuracy can be meaningfully compared for different stimuli intensities, unlike in the standard case of a metric scale.

Institute of Physiology Academy of Sciences of the Czech Republic Videnska 1083 14220 Prague 4 Czech Republic

See more in PubMed

Barlow H. B. Possible principles underlying the transformation of sensory messages. In Rosenblith W. (ed.) Sensory Communication, 217–234 (MIT Press, Cambridge, 1961).

Simoncelli E. P. & Olshausen B. A. Natural image statistics and neural representation. Annu. Rev. Neurosci. 24, 1193–1216 (2001). PubMed

Lewicki M. S. Efficient coding of natural sounds. Nat. Neurosci. 5, 356–363 (2002). PubMed

Kostal L., Lansky P. & Rospars J.-P. Efficient olfactory coding in the pheromone receptor neuron of a moth. PLoS Comput. Biol. 4, e1000053 (2008). PubMed PMC

Dean I., Harper N. S. & McAlpine D. Neural population coding of sound level adapts to stimulus statistics. Nat. Neurosci. 8, 1684–1689 (2005). PubMed

Wen B., Wang G. I., Dean I. & Delgutte B. Dynamic range adaptation to sound level statistics in the auditory nerve. J. Neurosci. 29, 13797–13808 (2009). PubMed PMC

Durant S., Clifford C. W. G., Crowder N. A., Price N. S. C. & Ibbotson M. R. Characterizing contrast adaptation in a population of cat primary visual cortical neurons using Fisher information. J. Opt. Soc. Am. A 24, 1529–1537 (2007). PubMed

Wark B., Lundstrom B. N. & Fairhall A. Sensory adaptation. Curr. Opin. Neurobiol. 17, 423–429 (2007). PubMed PMC

Watkins P. V. & Barbour D. L. Specialized neuronal adaptation for preserving input sensitivity. Nat. Neurosci. 11, 1259–1261 (2008). PubMed

Watkins P. V. & Barbour D. L. Level-tuned neurons in primary auditory cortex adapt differently to loud versus soft sounds. Cereb. Cortex 21, 178–190 (2011). PubMed PMC

Dahmen J. C., Keating P., Nodal F. R., Schulz A. L. & King A. J. Adaptation to stimulus statistics in the perception and neural representation of auditory space. Neuron 66, 937–948 (2010). PubMed PMC

Maier J. K. et al. Adaptive coding is constrained to midline locations in a spatial listening task. J. Neurophysiol. 108, 1856–1868 (2012). PubMed PMC

Garcia-Lazaro J. A., Ho S. S. M., Nair A. & Schnupp J. W. H. Shifting and scaling adaptation to dynamic stimuli in somatosensory cortex. Eur. J. Neurosci. 26, 2359–2368 (2007). PubMed

Berens P., Ecker A. S., Gerwinn S., Tolias A. S. & Bethge M. Reassessing optimal neural population codes with neurometric functions. Proc. Natl. Acad. Sci. USA 108, 4423–4428 (2011). PubMed PMC

Lehmann E. L. & Casella G. Theory of point estimation, Ch. 2, 115–117 (Springer Verlag, New York, 1998).

Seung H. S. & Sompolinsky H. Simple models for reading neuronal population codes. Proc. Natl. Acad. Sci. USA 90, 749–753 (1993). PubMed PMC

Dayan P. & Abbott L. F. The Effect of Correlated Variability on the Accuracy of a Population Code. Neural Comput. 11, 91–101 (1999). PubMed

Seriès P., Latham P. E. & Pouget A. Tuning curve sharpening for orientation selectivity: coding efficiency and the impact of correlations. Nat. Neurosci. 7, 1129–1135 (2004). PubMed

Zhang K., Ginzburg I., McNaughton B. L. & Sejnowski T. J. Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells. J. Neurophysiol. 79, 1017–1044 (1998). PubMed

Harper N. S. & McAlpine D. Optimal neural population coding of an auditory spatial cue. Nature 430, 682–686 (2004). PubMed

Sreenivasan S. & Fiete I. Grid cells generate an analog error-correcting code for singularly precise neural computation. Nat. Neurosci. 14, 1330–1337 (2011). PubMed

Raichel D. R. The Science and Applications of Acoustics (Springer, New York, 2006).

Kostal L. & Lansky P. Coding accuracy is not fully determined by the neuronal model. Neural Comput. 27, 1051–1057 (2015). PubMed

Gescheider G. A. Psychophysics: The fundamentals (Lawrence Erlbaum Associates, Mahwah, New Jersey, 1997).

Sun J. Z., Wang G. I., Goyal V. K. & Varshney L. R. A framework for Bayesian optimality of psychophysical laws. J. Math. Psychol. 56, 495–501 (2012).

Riesz R. R. Differential intensity sensitivity of the ear for pure tones. Phys. Rev. 31, 867–875 (1928).

Weber E. H. De pulsu, resorptione, auditu et tactu. Annotationes anatomicae et physiologicae (Koehler, Leipzig, 1834).

Dayan P. & Abbott L. F. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems (MIT Press, 2001).

Fechner G. T. Elemente der Psychophysik (Breitkopf und Härtel, Leipzig, 1860).

Masin S. C. The (Weber’s) law that never was. In Elliot M. A. et al. (eds) Proceedings of the twenty-fifth annual meeting of the International Society for Psychophysics, 441–446 (International Society for Psychophysics, Galway, Ireland, 2009).

Papoulis A. Probability, random variables, and stochastic processes, Ch. 5, 92–94 (McGraw-Hill, New York, 1991).

Kostal L. Stimulus reference frame and neural coding precision. J. Math. Psychol. in press (2016).

Jeffreys H. An invariant form for the prior probability in estimation problems. Proc. Roy. Soc. A 453–461 (1946). PubMed

Hecht S. The visual discrimination of intensity and the Weber-Fechner law. J. Gen. Physiol. 7, 235–267 (1924). PubMed PMC

Norwich K. H. & Wong W. Unification of psychophysical phenomena: The complete form of Fechner’s law. Percept. Psychophys. 59, 929–940 (1997). PubMed

Dzhafarov E. N. & Colonius H. The Fechnerian Idea. Am. J. Psychol. 124, 127–140 (2011). PubMed

Stevens S. S., Volkmann J. & Newman E. B. A scale for the measurement of the psychological magnitude pitch. J. Acoustic. Soc. Am. 8, 185–190 (1937).

Shannon C. E. Communication in the presence of noise. Proc. IRE 37, 10–21 (1949).

Rieke F., de Ruyter van Steveninck R., Warland D. & Bialek W. Spikes: Exploring the Neural Code (MIT Press, Cambridge, 1997).

Laughlin S. B. A simple coding procedure enhances a neuron’s information capacity. Z. Naturforsch. 36, 910–912 (1981). PubMed

de Ruyter van Steveninck R. R. & Laughlin S. B. The rate of information transfer at graded-potential synapses. Nature 379, 642–644 (1996).

Ikeda S. & Manton J. H. Capacity of a single spiking neuron channel. Neural Comput. 21, 1714–1748 (2009). PubMed

Suksompong P. & Berger T. Capacity analysis for integrate-and-fire neurons with descending action potential thresholds. IEEE Trans. Inf. Theory 56, 838–851 (2010).

Kostal L. & Kobayashi R. Optimal decoding and information transmission in Hodgkin-Huxley neurons under metabolic cost constraints. Biosystems 136, 3–10 (2015). PubMed

Bernardo J. M. Reference posterior distributions for Bayesian inference. J. Roy. Stat. Soc. B 41, 113–147 (1979).

Brunel N. & Nadal J.-P. Mutual information, Fisher information, and population coding. Neural Comput. 10, 1731–1757 (1998). PubMed

McDonnell M. D. & Stocks N. G. Maximally informative stimuli and tuning curves for sigmoidal rate-coding neurons and populations. Phys. Rev. Lett. 101, 058103 (2008). PubMed

Ganguli D. & Simoncelli E. P. Implicit encoding of prior probabilities in optimal neural populations. In Lafferty J., Williams C., Shawe-Taylor J., Zemel R. S. & Culotta A. (eds) Advances in Neural Information Processing Systems (NIPS), vol. 23, 658–666 (MIT Press, Cambridge, Massachusetts, 2010). PubMed PMC

Yarrow S., Challis E. & Seriès P. Fisher and Shannon information in finite neural populations. Neural Comput. 24, 1740–1780 (2012). PubMed

Kostal L., Lansky P. & McDonnell M. D. Metabolic cost of neuronal information in an empirical stimulus-response model. Biol. Cybern. 107, 355–365 (2013). PubMed

Wei X. & Stocker A. A. A Bayesian observer model constrained by efficient coding can explain ‘anti-bayesian’ percepts. Nat. Neurosci. 18, 1509–1517 (2015). PubMed