A central question in sensory neuroscience is how much, but also what information neurons transmit about the world. While Shannon’s information theory provides a principled framework to quantify the amount of information neurons encode about all stimuli, it does not reveal which stimuli contribute most, or what stimulus features are encoded. As a concrete example, it is known that neurons in the early visual cortex are 'sensitive' to stimuli in a small region of space (their receptive field). However, it is not clear how such simple intuitions carry to more complex scenarios, e.g. with large, noisy & non-linear population of neurons and high-dimensional stimuli. Several previous measures of neural sensitivity have been proposed. For example, the Fisher information quantifies the sensitivity of neural responses to infinitesimal stimulus perturbations. However, as the Fisher is not a valid decomposition of the mutual information it cannot say how different stimuli contribute to the total encoded information. On the other hand, previous works have proposed stimulus dependent decompositions of mutual information, which define a function $ I(x) $ such that $ I(R; X) = \mathbb{E}[I(x)] $. However, this decomposition is inherently ill-posed: infinitely many functions $I(x)$ satisfy the constraint, with no principled way to select among them. Further, different decompositions behave in qualitatively different ways, making it hard to interpret what are they are telling us. Finally, most proposed decompositions are computationally intractable for the high-dimensional stimuli and non-linear encoding models relevant for neuroscience. To resolve these limitations, we propose a set of axioms that any stimulus specific and feature-specific information decomposition should satisfy in order to serve as a meaningful and interpretable measure of neural sensitivity. These axioms formalize intuitive desiderata: that the information assigned to each stimulus, and stimulus feature, should be non-negative, and additive with respect to repeated measurements. We also require the decomposition to respect a form of locality: changes in how a neuron responds to a stimulus $ x $ should not affect the information attributed to a distant stimulus $ x' $. Finally, the attribution must be insensitive to irrelevant features, which do not contribute to the total information. Together, these constraints ensure that the decomposition is both interpretable and theoretically grounded. We show that existing decompositions violate one or more of these axioms, limiting their interpretability and use as information theoretic measures of neural sensitivity. We then introduce a novel decomposition that satisfies all of our axioms. It generalizes Fisher information by capturing neural sensitivity to both infinitesimal and finite stimulus perturbations. Moreover, it supports further decomposition across individual stimulus features (e.g., image pixels), enabling fine-grained analysis of neural representations. Beyond satisfying our theoretical axioms, our decomposition is computationally tractable for large neural populations and high-dimensional naturalistic stimuli, through the use of diffusion models. We demonstrate the power of our method by quantifying the information encoded by a model of visual neurons about individual images and pixels. Our approach uncovers aspects of the neural code that are not picked up by standard methods, such as the Fisher information, and opens the door to similar analyses in higher-order sensory areas, and artificial neural networks.

The efficient coding hypothesis posits that early sensory neurons transmit maximal information about sensory stimuli, given internal constraints. A central prediction of this theory is that neurons should preferentially encode stimuli that are most surprising. Previous studies suggest this may be the case in early visual areas, where many neurons respond strongly to rare or surprising stimuli. For example, previous research showed that when presented with a rhythmic sequence of full-field flashes, many retinal ganglion cells (RGCs) respond strongly at the instance the flash sequence stops, and when another flash would be expected. This phenomenon is called the 'omitted stimulus response'. However, it is not known whether the responses of these cells varies in a graded way depending on the level of stimulus surprise. To investigate this, we presented retinal neurons with extended sequences of stochastic flashes. With this stimulus, the surprise associated with a particular flash/silence, could be quantified analytically, and varied in a graded manner depending on the previous sequences of flashes and silences. Interestingly, we found that RGC responses could be well explained by a simple normative model, which described how they optimally combined their prior expectations and recent stimulus history, so as to encode surprise. Further, much of the diversity in RGC responses could be explained by the model, due to the different prior expectations that different neurons had about the stimulus statistics. These results suggest that even as early as the retina many cells encode surprise, relative to their own, internally generated expectations.

Neuroprostheses show potential in restoring lost sensory function and enhancing human capabilities, but the sensations produced by current devices often seem unnatural or distorted. Exact placement of implants and differences in individual perception lead to significant variations in stimulus response, making personalized stimulus optimization a key challenge. Bayesian optimization could be used to optimize patient-specific stimulation parameters with limited noisy observations, but is not feasible for high-dimensional stimuli. Alternatively, deep learning models can optimize stimulus encoding strategies, but typically assume perfect knowledge of patient-specific variations. Here we propose a novel, practically feasible approach that overcomes both of these fundamental limitations. First, a deep encoder network is trained to produce optimal stimuli for any individual patient by inverting a forward model mapping electrical stimuli to visual percepts. Second, a preferential Bayesian optimization strategy utilizes this encoder to learn the optimal patient-specific parameters for a new patient, using a minimal number of pairwise comparisons between candidate stimuli. We demonstrate the viability of this approach on a novel, state-of-the-art visual prosthesis model. Our approach quickly learns a personalized stimulus encoder and leads to dramatic improvements in the quality of restored vision, outperforming existing encoding strategies. Further, this approach is robust to noisy patient feedback and misspecifications in the underlying forward model. Overall, our results suggest that combining the strengths of deep learning and Bayesian optimization could significantly improve the perceptual experience of patients fitted with visual prostheses and may prove a viable solution for a range of neuroprosthetic technologies

In order to respond reliably to specific features of their environment, sensory neurons need to integrate multiple incoming noisy signals. Crucially, they also need to compete for the interpretation of those signals with other neurons representing similar features. The form that this competition should take depends critically on the noise corrupting these signals. In this study we show that for the type of noise commonly observed in sensory systems, whose variance scales with the mean signal, sensory neurons should selectively divide their input signals by their predictions, suppressing ambiguous cues while amplifying others. Any change in the stimulus context alters which inputs are suppressed, leading to a deep dynamic reshaping of neural receptive fields going far beyond simple surround suppression. Paradoxically, these highly variable receptive fields go alongside and are in fact required for an invariant representation of external sensory features. In addition to offering a normative account of context-dependent changes in sensory responses, perceptual inference in the presence of signal-dependent noise accounts for ubiquitous features of sensory neurons such as divisive normalization, gain control and contrast dependent temporal dynamics.

In many applications, it is desirable to extract only the relevant aspects of data. A principled way to do this is the information bottleneck (IB) method, where one seeks a code that maximises information about a relevance variable, Y, while constraining the information encoded about the original data, X. Unfortunately however, the IB method is computationally demanding when data are high-dimensional and/or non-gaussian. Here we propose an approximate variational scheme for maximising a lower bound on the IB objective, analogous to variational EM. Using this method, we derive an IB algorithm to recover features that are both relevant and sparse. Finally, we demonstrate how kernelised versions of the algorithm can be used to address a broad range of problems with non-linear relation between X and Y.

Attention causes diverse changes to visual neuron responses, including alterations in receptive field structure, and firing rates. A common theoretical approach to investigate why sensory neurons behave as they do is based on the efficient coding hypothesis: that sensory processing is optimized toward the statistics of the received input. We extend this approach to account for the influence of task demands, hypothesizing that the brain learns a probabilistic model of both the sensory input and reward received for performing different actions. Attention-dependent changes to neural responses reflect optimization of this internal model to deal with changes in the sensory environment (stimulus statistics) and behavioral demands (reward statistics). We use this framework to construct a simple model of visual processing that is able to replicate a number of attention-dependent changes to the responses of neurons in the midlevel visual cortices. The model is consistent with and provides a normative explanation for recent divisive normalization models of attention (Reynolds & Heeger, 2009).