Common population codes produce extremely nonlinear neural manifolds.

Populations of neurons represent sensory, motor, and cognitive variables via patterns of activity distributed across the population. The size of the population used to encode a variable is typically much greater than the dimension of the variable itself, and thus, the corresponding neural population activity occupies lower-dimensional subsets of the full set of possible activity states. Given population activity data with such lower-dimensional structure, a fundamental question asks how close the low-dimensional data lie to a linear subspace. The linearity or nonlinearity of the low-dimensional structure reflects important computational features of the encoding, such as robustness and generalizability. Moreover, identifying such linear structure underlies common data analysis methods such as Principal Component Analysis (PCA). Here, we show that for data drawn from many common population codes the resulting point clouds and manifolds are exceedingly nonlinear, with the dimension of the best-fitting linear subspace growing at least exponentially with the true dimension of the data. Consequently, linear methods like PCA fail dramatically at identifying the true underlying structure, even in the limit of arbitrarily many data points and no noise.

Robust parallel decision-making in neural circuits with nonlinear inhibition.

An elemental computation in the brain is to identify the best in a set of options and report its value. It is required for inference, decision-making, optimization, action selection, consensus, and foraging. Neural computing is considered powerful because of its parallelism; however, it is unclear whether neurons can perform this max-finding operation in a way that improves upon the prohibitively slow optimal serial max-finding computation (which takes [Formula: see text] time for N noisy candidate options) by a factor of N, the benchmark for parallel computation. Biologically plausible architectures for this task are winner-take-all (WTA) networks, where individual neurons inhibit each other so only those with the largest input remain active. We show that conventional WTA networks fail the parallelism benchmark and, worse, in the presence of noise, altogether fail to produce a winner when N is large. We introduce the nWTA network, in which neurons are equipped with a second nonlinearity that prevents weakly active neurons from contributing inhibition. Without parameter fine-tuning or rescaling as N varies, the nWTA network achieves the parallelism benchmark. The network reproduces experimentally observed phenomena like Hick's law without needing an additional readout stage or adaptive N-dependent thresholds. Our work bridges scales by linking cellular nonlinearities to circuit-level decision-making, establishes that distributed computation saturating the parallelism benchmark is possible in networks of noisy, finite-memory neurons, and shows that Hick's law may be a symptom of near-optimal parallel decision-making with noisy input.

The intrinsic attractor manifold and population dynamics of a canonical cognitive circuit across waking and sleep.

Neural circuits construct distributed representations of key variables-external stimuli or internal constructs of quantities relevant for survival, such as an estimate of one's location in the world-as vectors of population activity. Although population activity vectors may have thousands of entries (dimensions), we consider that they trace out a low-dimensional manifold whose dimension and topology match the represented variable. This manifold perspective enables blind discovery and decoding of the represented variable using only neural population activity (without knowledge of the input, output, behavior or topography). We characterize and directly visualize manifold structure in the mammalian head direction circuit, revealing that the states form a topologically nontrivial one-dimensional ring. The ring exhibits isometry and is invariant across waking and rapid eye movement sleep. This result directly demonstrates that there are continuous attractor dynamics and enables powerful inference about mechanism. Finally, external rather than internal noise limits memory fidelity, and the manifold approach reveals new dynamical trajectories during sleep.

Random Recurrent Networks Near Criticality Capture the Broadband Power Distribution of Human ECoG Dynamics.

Brain electric field potentials are dominated by an arrhythmic broadband signal, but the underlying mechanism is poorly understood. Here we propose that broadband power spectra characterize recurrent neural networks of nodes (neurons or clusters of neurons), endowed with an effective balance between excitation and inhibition tuned to keep the network on the edge of dynamical instability. These networks show a fast mode reflecting local dynamics and a slow mode emerging from distributed recurrent connections. Together, the 2 modes produce power spectra similar to those observed in human intracranial EEG (i.e., electrocorticography, ECoG) recordings. Moreover, such networks convert spatial input correlations across nodes into temporal autocorrelation of network activity. Consequently, increased independence between nodes reduces low-frequency power, which may explain changes observed during behavioral tasks. Lastly, varying network coupling causes activity changes that resemble those observed in human ECoG across different arousal states. The model links macroscopic features of empirical ECoG power to a parsimonious underlying network structure, and suggests mechanisms for changes observed across behavioral and arousal states. This work provides a computational framework to generate and test hypotheses about cellular and network mechanisms underlying whole brain electrical dynamics, their variations across states, and potential alterations in brain diseases.

Computational principles of memory.

The ability to store and later use information is essential for a variety of adaptive behaviors, including integration, learning, generalization, prediction and inference. In this Review, we survey theoretical principles that can allow the brain to construct persistent states for memory. We identify requirements that a memory system must satisfy and analyze existing models and hypothesized biological substrates in light of these requirements. We also highlight open questions, theoretical puzzles and problems shared with computer science and information theory.

A Large-Scale Circuit Mechanism for Hierarchical Dynamical Processing in the Primate Cortex.

We developed a large-scale dynamical model of the macaque neocortex, which is based on recently acquired directed- and weighted-connectivity data from tract-tracing experiments, and which incorporates heterogeneity across areas. A hierarchy of timescales naturally emerges from this system: sensory areas show brief, transient responses to input (appropriate for sensory processing), whereas association areas integrate inputs over time and exhibit persistent activity (suitable for decision-making and working memory). The model displays multiple temporal hierarchies, as evidenced by contrasting responses to visual versus somatosensory stimulation. Moreover, slower prefrontal and temporal areas have a disproportionate impact on global brain dynamics. These findings establish a circuit mechanism for "temporal receptive windows" that are progressively enlarged along the cortical hierarchy, suggest an extension of time integration in decision making from local to large circuits, and should prompt a re-evaluation of the analysis of functional connectivity (measured by fMRI or electroencephalography/magnetoencephalography) by taking into account inter-areal heterogeneity.

A diversity of localized timescales in network activity.

Neurons show diverse timescales, so that different parts of a network respond with disparate temporal dynamics. Such diversity is observed both when comparing timescales across brain areas and among cells within local populations; the underlying circuit mechanism remains unknown. We examine conditions under which spatially local connectivity can produce such diverse temporal behavior. In a linear network, timescales are segregated if the eigenvectors of the connectivity matrix are localized to different parts of the network. We develop a framework to predict the shapes of localized eigenvectors. Notably, local connectivity alone is insufficient for separate timescales. However, localization of timescales can be realized by heterogeneity in the connectivity profile, and we demonstrate two classes of network architecture that allow such localization. Our results suggest a framework to relate structural heterogeneity to functional diversity and, beyond neural dynamics, are generally applicable to the relationship between structure and dynamics in biological networks. DOI: http://dx.doi.org/10.7554/eLife.01239.001.