The nature of neural codes is central to neuroscience. Do neurons encode information through relatively slow changes in the firing rates of individual spikes (rate code) or by the precise timing of every spike (temporal code)? Here we compare the loss of information due to correlations for these two possible neural codes. The essence of Shannon's definition of information is to combine information with uncertainty: the higher the uncertainty of a given event, the more information is conveyed by that event. Correlations can reduce uncertainty or the amount of information, but by how much? In this paper we address this question by a direct comparison of the information per symbol conveyed by the words coming from a binary Markov source (temporal code) with the information per symbol coming from the corresponding Bernoulli source (uncorrelated, rate code). In a previous paper we found that a crucial role in the relation between information transmission rates (ITRs) and firing rates is played by a parameter s, which is the sum of transition probabilities from the no-spike state to the spike state and vice versa. We found that in this case too a crucial role is played by the same parameter s. We calculated the maximal and minimal bounds of the quotient of ITRs for these sources. Next, making use of the entropy grouping axiom, we determined the loss of information in a Markov source compared with the information in the corresponding Bernoulli source for a given word length. Our results show that in the case of correlated signals the loss of information is relatively small, and thus temporal codes, which are more energetically efficient, can replace rate codes effectively. These results were confirmed by experiments.

Icahn School of Medicine at Mount Sinai One Gustave Levy Place New York NY 10029 USA Department of Philosophy and History of Science Faculty of Science Charles University Albertov 6 128 43 Praha 2 Czech Republic The National Institute of Mental Health Topolová 748 250 67 Klecany Czech Republic

Institute of Fundamental Technological Research Polish Academy of Sciences ul Pawinskiego 5B 02 106 Warsaw Poland

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$a Pregowska, Agnieszka $u Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5B, 02-106 Warsaw, Poland.

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$a How Far can Neural Correlations Reduce Uncertainty? Comparison of Information Transmission Rates for Markov and Bernoulli Processes / $c A. Pregowska, E. Kaplan, J. Szczepanski,

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$a The nature of neural codes is central to neuroscience. Do neurons encode information through relatively slow changes in the firing rates of individual spikes (rate code) or by the precise timing of every spike (temporal code)? Here we compare the loss of information due to correlations for these two possible neural codes. The essence of Shannon's definition of information is to combine information with uncertainty: the higher the uncertainty of a given event, the more information is conveyed by that event. Correlations can reduce uncertainty or the amount of information, but by how much? In this paper we address this question by a direct comparison of the information per symbol conveyed by the words coming from a binary Markov source (temporal code) with the information per symbol coming from the corresponding Bernoulli source (uncorrelated, rate code). In a previous paper we found that a crucial role in the relation between information transmission rates (ITRs) and firing rates is played by a parameter s, which is the sum of transition probabilities from the no-spike state to the spike state and vice versa. We found that in this case too a crucial role is played by the same parameter s. We calculated the maximal and minimal bounds of the quotient of ITRs for these sources. Next, making use of the entropy grouping axiom, we determined the loss of information in a Markov source compared with the information in the corresponding Bernoulli source for a given word length. Our results show that in the case of correlated signals the loss of information is relatively small, and thus temporal codes, which are more energetically efficient, can replace rate codes effectively. These results were confirmed by experiments.

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$a Kaplan, Ehud $u Icahn School of Medicine at Mount Sinai, One Gustave Levy Place, New York, NY 10029, USA. Department of Philosophy and History of Science, Faculty of Science, Charles University, Albertov 6, 128 43 Praha 2, Czech Republic. The National Institute of Mental Health, Topolová 748, 250 67 Klecany, Czech Republic.

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$a Szczepanski, Janusz $u Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5B, 02-106 Warsaw, Poland.

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$w MED00002342 $t International journal of neural systems $x 1793-6462 $g Roč. 29, č. 8 (2019), s. 1950003

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