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.

The adaptation of neural codes to the statistics of their environment is well captured by efficient coding approaches.

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.

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.

Recent advancements in brain-computer interfaces (BCIs) have enabled the decoding of lexical tones from intracranial recordings, offering the potential to restore the communication abilities of speech-impaired tonal language speakers. However, data heterogeneity induced by both physiological and instrumental factors poses a significant challenge for unified invasive brain tone decoding. Traditional subject-specific models, which operate under a heterogeneous decoding paradigm, fail to capture generalized neural representations and cannot effectively leverage data across subjects. To address these limitations, we introduce Homogeneity-Heterogeneity Disentangled Learning for neural Representations (H2DiLR), a novel framework that disentangles and learns both the homogeneity and heterogeneity from intracranial recordings across multiple subjects. To evaluate H2DiLR, we collected stereoelectroencephalography (sEEG) data from multiple participants reading Mandarin materials comprising 407 syllables, representing nearly all Mandarin characters. Extensive experiments demonstrate that H2DiLR, as a unified decoding paradigm, significantly outperforms the conventional heterogeneous decoding approach. Furthermore, we empirically confirm that H2DiLR effectively captures both homogeneity and heterogeneity during neural representation learning. The human language system, with its intricate and expansive syntactic structure, enables rich and complex communication. Decoding spoken language from within human brains has emerged as a significant topic of interest in neuroscience (Anumanchipalli et al., 2019; Willett et al., 2023; Feng et al., 2023; Lu et al., 2023; Liu et al., 2023). The decoding of vocal tone from brain measurements (Lu et al., 2023; Liu et al., 2023) is of particular research interest, due to the prominence of tonal languages, which make up over 60% of the world's languages (Yip, 2002) and are spoken by approximately one-third of the global population (Dryer & Haspelmath, 2013). In these languages, tone plays a critical role in distinguishing lexical meaning at the syllable level. Mandarin, for instance, is a widely spoken tonal language that has an extensive inventory of over 50,000 characters, with each associated with a syllable composed of an initial, a final, and a tone (Duanmu, 2007).