Computation in recurrent networks of neurons has been hypothesized to occur at the level of low-dimensional latent dynamics, both in artificial systems and in the brain. This hypothesis seems at odds with evidence from large-scale neuronal recordings in mice showing that neuronal population activity is high-dimensional. To demonstrate that low-dimensional latent dynamics and high-dimensional activity can be two sides of the same coin, we present an analytically solvable recurrent neural network (RNN) model whose dynamics can be exactly reduced to a low-dimensional dynamical system, but generates an activity manifold that has a high linear embedding dimension. This raises the question: Do low-dimensional latents explain the high-dimensional activity observed in mouse visual cortex? Spectral theory tells us that the covariance eigenspectrum alone does not allow us to recover the dimensionality of the latents, which can be low or high, when neurons are nonlinear. To address this indeterminacy, we develop Neural Cross-Encoder (NCE), an interpretable, nonlinear latent variable modeling method for neuronal recordings, and find that high-dimensional neuronal responses to drifting gratings and spontaneous activity in visual cortex can be reduced to low-dimensional latents, while the responses to natural images cannot. We conclude that the high-dimensional activity measured in certain conditions, such as in the absence of a stimulus, is explained by low-dimensional latents that are nonlinearly processed by individual neurons.

Understanding the nature of representation in neural networks is a goal shared by neuroscience and machine learning. It is therefore exciting that both fields converge not only on shared questions but also on similar approaches. A pressing question in these areas is understanding how the structure of the representation used by neural networks affects both their generalization, and robustness to perturbations. In this work, we investigate the latter by juxtaposing experimental results regarding the covariance spectrum of neural representations in the mouse V1 (Stringer et al) with artificial neural networks. 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. Our results show that imposing the experimentally observed structure on artificial neural networks makes them more robust to adversarial attacks. Moreover, our findings complement the existing theory relating wide neural networks to kernel methods, by showing the role of intermediate representations.

In recent years, two-photon calcium imaging has become a standard tool to probe the function of neural circuits and to study computations in neuronal populations. However, the acquired signal is only an indirect measurement of neural activity due to the comparatively slow dynamics of fluorescent calcium indicators. Different algorithms for estimating spike rates from noisy calcium measurements have been proposed in the past, but it is an open question how far performance can be improved. Here, we report the results of the spikefinder challenge, launched to catalyze the development of new spike rate inference algorithms through crowd-sourcing. We present ten of the submitted algorithms which show improved performance compared to previously evaluated methods. Interestingly, the top-performing algorithms are based on a wide range of principles from deep neural networks to generative models, yet provide highly correlated estimates of the neural activity. The competition shows that benchmark challenges can drive algorithmic developments in neuroscience.

New silicon technology is enabling large-scale electrophysiological recordings in vivo from hundreds to thousands of channels. Interpreting these recordings requires scalable and accurate automated methods for spike sorting, which should minimize the time required for manual curation of the results. Here we introduce KiloSort, a new integrated spike sorting framework that uses template matching both during spike detection and during spike clustering. KiloSort models the electrical voltage as a sum of template waveforms triggered on the spike times, which allows overlapping spikes to be identified and resolved. Unlike previous algorithms that compress the data with PCA, KiloSort operates on the raw data which allows it to construct a more accurate model of the waveforms. Processing times are faster than in previous algorithms thanks to batch-based optimization on GPUs. We compare KiloSort to an established algorithm and show favorable performance, at much reduced processing times. A novel post-clustering merging step based on the continuity of the templates further reduced substantially the number of manual operations required on this data, for the neurons with near-zero error rates, paving the way for fully automated spike sorting of multichannel electrode recordings.

Cluster analysis faces two problems in high dimensions: the "curse of dimensionality" that can lead to overfitting and poor generalization performance and the sheer time taken for conventional algorithms to process large amounts of high-dimensional data. We describe a solution to these problems, designed for the application of spike sorting for next-generation, high-channel-count neural probes. In this problem, only a small subset of features provides information about the cluster membership of any one data vector, but this informative feature subset is not the same for all data points, rendering classical feature selection ineffective. We introduce a "masked EM" algorithm that allows accurate and time-efficient clustering of up to millions of points in thousands of dimensions. We demonstrate its applicability to synthetic data and to real-world high-channel-count spike sorting data.

The phenomenology and cellular mechanisms of cortical synaptic plasticity are becoming known in increasing detail, but the computational principles by which cortical plasticity enables the development of sensory representations are unclear. Here we describe a framework for cortical synaptic plasticity termed the "Convallis rule", mathematically derived from a principle of unsupervised learning via constrained optimization. Implementation of the rule caused a recurrent cortex-like network of simulated spiking neurons to develop rate representations of real-world speech stimuli, enabling classification by a downstream linear decoder. Applied to spike patterns used in in vitro plasticity experiments, the rule reproduced multiple results including and beyond STDP. However STDP alone produced poorer learning performance. The mathematical form of the rule is consistent with a dual coincidence detector mechanism that has been suggested by experiments in several synaptic classes of juvenile neocortex. Based on this confluence of normative, phenomenological, and mechanistic evidence, we suggest that the rule may approximate a fundamental computational principle of the neocortex.

The ultimate product of an electrophysiology experiment is often a decision on which biological hypothesis or model best explains the observed data. We outline a paradigm designed for comparison of different models, which we refer to as spike train prediction. A key ingredient of this paradigm is a prediction quality valuation that estimates how close a predicted conditional intensity function is to an actual observed spike train. Although a valuation based on log likelihood (L) is most natural, it has various complications in this context. We propose that a quadratic valuation (Q) can be used as an alternative to L. Q shares some important theoretical properties with L, including consistency, and the two valuations perform similarly on simulated and experimental data. Moreover, Q is more robust than L, and optimization with Q can dramatically improve computational efficiency. We illustrate the utility of Q for comparing models of peer prediction, where it can be computed directly from cross-correlograms. Although Q does not have a straightforward probabilistic interpretation, Q is essentially given by Euclidean distance.