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.

Determining how much of the sensory information carried by a neural code contributes to behavioral performance is key to understand sensory function and neural information flow. However, there are as yet no analytical tools to compute this information that lies at the intersection between sensory coding and behavioral readout.

Neural codes are inevitably shaped by various kinds of biological constraints, e.g.

Adapted with edits from [1].

We use adversarial robustness to probe Stringer et al's theory regarding the causal role of a 1/n covariance spectrum. We empirically investigate the benefits such a neural code confers in neural networks, and illuminate its role in multi-layer architectures.

We use adversarial robustness to probe Stringer et al's theory regarding the causal role of a 1/n covariance spectrum. We empirically investigate the benefits such a neural code confers in neural networks, and illuminate its role in multi-layer architectures.

Although it is widely believed that reinforcement learning is a suitable tool for describing behavioral learning, the mechanisms by which it can be implemented in networks of spiking neurons are not fully understood. Here, we show that different learning rules emerge from a policy gradient approach depending on which features of the spike trains are assumed to influence the reward signals, i.e., depending on which neural code is in effect. We use the framework of Williams (1992) to derive learning rules for arbitrary neural codes. For illustration, we present policy-gradient rules for three different example codes - a spike count code, a spike timing code and the most general "full spike train" code - and test them on simple model problems. In addition to classical synaptic learning, we derive learning rules for intrinsic parameters that control the excitability of the neuron. The spike count learning rule has structural similarities with established Bienenstock-Cooper-Munro rules. If the distribution of the relevant spike train features belongs to the natural exponential family, the learning rules have a characteristic shape that raises interesting prediction problems.

Although it is widely believed that reinforcement learning is a suitable tool for describing behavioral learning, the mechanisms by which it can be implemented in networks of spiking neurons are not fully understood. Here, we show that different learning rules emerge from a policy gradient approach depending on which features of the spike trains are assumed to influence the reward signals, i.e., depending on which neural code is in effect. We use the framework of Williams (1992) to derive learning rules for arbitrary neural codes. For illustration, we present policy-gradient rules for three different example codes - a spike count code, a spike timing code and the most general full spike train code - and test them on simple model problems. In addition to classical synaptic learning, we derive learning rules for intrinsic parameters that control the excitability of the neuron.