The sign rule and beyond: Boundary effects, flexibility, and noise correlations in neural population codes

Over repeat presentations of the same stimulus, sensory neurons show variable responses. This "noise" is typically correlated between pairs of cells, and a question with rich history in neuroscience is how these noise correlations impact the population's ability to encode the stimulus. Here, we consider a very general setting for population coding, investigating how information varies as a function of noise correlations, with all other aspects of the problem - neural tuning curves, etc. - held fixed. This work yields unifying insights into the role of noise correlations. These are summarized in the form of theorems, and illustrated with numerical examples involving neurons with diverse tuning curves. Our main contributions are as follows. (1) We generalize previous results to prove a sign rule (SR) - if noise correlations between pairs of neurons have opposite signs vs. their signal correlations, then coding performance will improve compared to the independent case. This holds for three different metrics of coding performance, and for arbitrary tuning curves and levels of heterogeneity. This generality is true for our other results as well. (2) As also pointed out in the literature, the SR does not provide a necessary condition for good coding. We show that a diverse set of correlation structures can improve coding. Many of these violate the SR, as do experimentally observed correlations. There is structure to this diversity: we prove that the optimal correlation structures must lie on boundaries of the possible set of noise correlations. (3) We provide a novel set of necessary and sufficient conditions, under which the coding performance (in the presence of noise) will be as good as it would be if there were no noise present at all.Comment: 41 pages, 5 figure

Searching for modified growth patterns with tomographic surveys

In alternative theories of gravity, designed to produce cosmic acceleration at the current epoch, the growth of large scale structure can be modified. We study the potential of upcoming and future tomographic surveys such as DES and LSST, with the aid of CMB and supernovae data, to detect departures from the growth of cosmic structure expected within General Relativity. We employ parametric forms to quantify the potential time- and scale-dependent variation of the effective gravitational constant, and the differences between the two Newtonian potentials. We then apply the Fisher matrix technique to forecast the errors on the modified growth parameters from galaxy clustering, weak lensing, CMB, and their cross-correlations across multiple photometric redshift bins. We find that even with conservative assumptions about the data, DES will produce non-trivial constraints on modified growth, and that LSST will do significantly better.Comment: Matches the version accepted to PRD. New plots, typos fixed, references added. The MGCAMB code is available at http://www.sfu.ca/~gza5/MGCAMB.htm

A sparse coding model with synaptically local plasticity and spiking neurons can account for the diverse shapes of V1 simple cell receptive fields

Sparse coding algorithms trained on natural images can accurately predict the features that excite visual cortical neurons, but it is not known whether such codes can be learned using biologically realistic plasticity rules. We have developed a biophysically motivated spiking network, relying solely on synaptically local information, that can predict the full diversity of V1 simple cell receptive field shapes when trained on natural images. This represents the first demonstration that sparse coding principles, operating within the constraints imposed by cortical architecture, can successfully reproduce these receptive fields. We further prove, mathematically, that sparseness and decorrelation are the key ingredients that allow for synaptically local plasticity rules to optimize a cooperative, linear generative image model formed by the neural representation. Finally, we discuss several interesting emergent properties of our network, with the intent of bridging the gap between theoretical and experimental studies of visual cortex.Comment: 33 pages, 6 figures. To appear in PLoS Computational Biology. Some of these data were presented by author JZ at the 2011 CoSyNe meeting in Salt Lake Cit

Identifying Shared Decodable Concepts in the Human Brain Using Image-Language Foundation Models

We introduce a method that takes advantage of high-quality pretrained multimodal representations to explore fine-grained semantic networks in the human brain. Previous studies have documented evidence of functional localization in the brain, with different anatomical regions preferentially activating for different types of sensory input. Many such localized structures are known, including the fusiform face area and parahippocampal place area. This raises the question of whether additional brain regions (or conjunctions of brain regions) are also specialized for other important semantic concepts. To identify such brain regions, we developed a data-driven approach to uncover visual concepts that are decodable from a massive functional magnetic resonance imaging (fMRI) dataset. Our analysis is broadly split into three sections. First, a fully connected neural network is trained to map brain responses to the outputs of an image-language foundation model, CLIP (Radford et al., 2021). Subsequently, a contrastive-learning dimensionality reduction method reveals the brain-decodable components of CLIP space. In the final section of our analysis, we localize shared decodable concepts in the brain using a voxel-masking optimization method to produce a shared decodable concept (SDC) space. The accuracy of our procedure is validated by comparing it to previous localization experiments that identify regions for faces, bodies, and places. In addition to these concepts, whose corresponding brain regions were already known, we localize novel concept representations which are shared across participants to other areas of the human brain. We also demonstrate how this method can be used to inspect fine-grained semantic networks for individual participants. We envisage that this extensible method can also be adapted to explore other questions at the intersection of AI and neuroscience.Comment: Under revie