Neural codes are inevitably shaped by various kinds of biological constraints, \emph{e.g.} noise and metabolic cost. Here we formulate a coding framework which explicitly deals with noise and the metabolic costs associated with the neural representation of information, and analytically derive the optimal neural code for monotonic response functions and arbitrary stimulus distributions. For a single neuron, the theory predicts a family of optimal response functions depending on the metabolic budget and noise characteristics. Interestingly, the well-known histogram equalization solution can be viewed as a special case when metabolic resources are unlimited. For a pair of neurons, our theory suggests that under more severe metabolic constraints, ON-OFF coding is an increasingly more efficient coding scheme compared to ON-ON or OFF-OFF. The advantage could be as large as one-fold, substantially larger than the previous estimation. Some of these predictions could be generalized to the case of large neural populations. In particular, these analytical results may provide a theoretical basis for the predominant segregation into ONand OFF-cells in early visual processing areas. Overall, we provide a unified framework for optimal neural codes with monotonic tuning curves in the brain, and makes predictions that can be directly tested with physiology experiments.

Recent work in theoretical neuroscience has shown that information-theoretic efficient neural codes, which allocate neural resources to maximize the mutual information between stimuli and neural responses, give rise to a lawful relationship between perceptual bias and discriminability that is observed across a wide variety of psychophysical tasks in human observers (Wei & Stocker 2017). Here we generalize these results to show that the same law arises under a much larger family of optimal neural codes, introducing a unifying framework that we call power-law efficient coding. Specifically, we show that the same lawful relationship between bias and discriminability arises whenever Fisher information is allocated proportional to any power of the prior distribution. This family includes neural codes that are optimal for minimizing Lp error for any p, indicating that the lawful relationship observed in human psychophysical data does not require information-theoretically optimal neural codes. Furthermore, we derive the exact constant of proportionality governing the relationship between bias and discriminability for different power laws (which includes information-theoretically optimal codes, where the power is 2, and so-called discrimax codes, where power is 1/2), and different choices of optimal decoder. As a bonus, our framework provides new insights into anti-Bayesian perceptual biases, in which percepts are biased away from the center of mass of the prior. We derive an explicit formula that clarifies precisely which combinations of neural encoder and decoder can give rise to such biases.

Neural codes are inevitably shaped by various kinds of biological constraints, \emph{e.g.} noise and metabolic cost. Here we formulate a coding framework which explicitly deals with noise and the metabolic costs associated with the neural representation of information, and analytically derive the optimal neural code for monotonic response functions and arbitrary stimulus distributions. For a single neuron, the theory predicts a family of optimal response functions depending on the metabolic budget and noise characteristics. Interestingly, the well-known histogram equalization solution can be viewed as a special case when metabolic resources are unlimited. For a pair of neurons, our theory suggests that under more severe metabolic constraints, ON-OFF coding is an increasingly more efficient coding scheme compared to ON-ON or OFF-OFF. The advantage could be as large as one-fold, substantially larger than the previous estimation. Some of these predictions could be generalized to the case of large neural populations. In particular, these analytical results may provide a theoretical basis for the predominant segregation into ONand OFF-cells in early visual processing areas. Overall, we provide a unified framework for optimal neural codes with monotonic tuning curves in the brain, and makes predictions that can be directly tested with physiology experiments.

Recent work in theoretical neuroscience has shown that information-theoretic efficient neural codes, which allocate neural resources to maximize the mutual information between stimuli and neural responses, give rise to a lawful relationship between perceptual bias and discriminability that is observed across a wide variety of psychophysical tasks in human observers (Wei & Stocker 2017). Here we generalize these results to show that the same law arises under a much larger family of optimal neural codes, introducing a unifying framework that we call power-law efficient coding. Specifically, we show that the same lawful relationship between bias and discriminability arises whenever Fisher information is allocated proportional to any power of the prior distribution. This family includes neural codes that are optimal for minimizing Lp error for any p, indicating that the lawful relationship observed in human psychophysical data does not require information-theoretically optimal neural codes. Furthermore, we derive the exact constant of proportionality governing the relationship between bias and discriminability for different power laws (which includes information-theoretically optimal codes, where the power is 2, and so-called discrimax codes, where power is 1/2), and different choices of optimal decoder. As a bonus, our framework provides new insights into anti-Bayesian perceptual biases, in which percepts are biased away from the center of mass of the prior. We derive an explicit formula that clarifies precisely which combinations of neural encoder and decoder can give rise to such biases.

Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision making and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations. While in standard control settings the sensors are assumed fixed, biological systems often gain from the extra flexibility of optimizing the sensors themselves. However, this sensory adaptation is geared towards control rather than perception, as is often assumed. In this work we show that sensory adaptation for control differs from sensory adaptation for perception, even for simple control setups. This implies, consistently with recent experimental results, that when studying sensory adaptation, it is essential to account for the task being performed.

Recent work in theoretical neuroscience has shown that information-theoretic "efficient" neural codes, which allocate neural resources to maximize the mutual information between stimuli and neural responses, give rise to a lawful relationship between perceptual bias and discriminability that is observed across a wide variety of psychophysical tasks in human observers (Wei & Stocker 2017). Here we generalize these results to show that the same law arises under a much larger family of optimal neural codes, introducing a unifying framework that we call power-law efficient coding. Specifically, we show that the same lawful relationship between bias and discriminability arises whenever Fisher information is allocated proportional to any power of the prior distribution. This family includes neural codes that are optimal for minimizing Lp error for any p, indicating that the lawful relationship observed in human psychophysical data does not require information-theoretically optimal neural codes. Furthermore, we derive the exact constant of proportionality governing the relationship between bias and discriminability for different power laws (which includes information-theoretically optimal codes, where the power is 2, and so-called discrimax codes, where power is 1/2), and different choices of optimal decoder. As a bonus, our framework provides new insights into "anti-Bayesian" perceptual biases, in which percepts are biased away from the center of mass of the prior.

Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision making and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations. While in standard control settings the sensors are assumed fixed, biological systems often gain from the extra flexibility of optimizing the sensors themselves. However, this sensory adaptation is geared towards control rather than perception, as is often assumed. In this work we show that sensory adaptation for control differs from sensory adaptation for perception, even for simple control setups. This implies, consistently with recent experimental results, that when studying sensory adaptation, it is essential to account for the task being performed.

Recent work in theoretical neuroscience has shown that information-theoretic "efficient" neural codes, which allocate neural resources to maximize the mutual information between stimuli and neural responses, give rise to a lawful relationship between perceptual bias and discriminability that is observed across a wide variety of psychophysical tasks in human observers (Wei & Stocker 2017). Here we generalize these results to show that the same law arises under a much larger family of optimal neural codes, introducing a unifying framework that we call power-law efficient coding. Specifically, we show that the same lawful relationship between bias and discriminability arises whenever Fisher information is allocated proportional to any power of the prior distribution. This family includes neural codes that are optimal for minimizing Lp error for any p, indicating that the lawful relationship observed in human psychophysical data does not require information-theoretically optimal neural codes. Furthermore, we derive the exact constant of proportionality governing the relationship between bias and discriminability for different power laws (which includes information-theoretically optimal codes, where the power is 2, and so-called discrimax codes, where power is 1/2), and different choices of optimal decoder.

Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision making and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations. While in standard control settings the sensors are assumed fixed, biological systems often gain from the extra flexibility of optimizing the sensors themselves. However, this sensory adaptation is geared towards control rather than perception, as is often assumed. In this work we show that sensory adaptation for control differs from sensory adaptation for perception, even for simple control setups. This implies, consistently with recent experimental results, that when studying sensory adaptation, it is essential to account for the task being performed.