3,481 research outputs found
Coverage, Continuity and Visual Cortical Architecture
The primary visual cortex of many mammals contains a continuous
representation of visual space, with a roughly repetitive aperiodic map of
orientation preferences superimposed. It was recently found that orientation
preference maps (OPMs) obey statistical laws which are apparently invariant
among species widely separated in eutherian evolution. Here, we examine whether
one of the most prominent models for the optimization of cortical maps, the
elastic net (EN) model, can reproduce this common design. The EN model
generates representations which optimally trade of stimulus space coverage and
map continuity. While this model has been used in numerous studies, no
analytical results about the precise layout of the predicted OPMs have been
obtained so far. We present a mathematical approach to analytically calculate
the cortical representations predicted by the EN model for the joint mapping of
stimulus position and orientation. We find that in all previously studied
regimes, predicted OPM layouts are perfectly periodic. An unbiased search
through the EN parameter space identifies a novel regime of aperiodic OPMs with
pinwheel densities lower than found in experiments. In an extreme limit,
aperiodic OPMs quantitatively resembling experimental observations emerge.
Stabilization of these layouts results from strong nonlocal interactions rather
than from a coverage-continuity-compromise. Our results demonstrate that
optimization models for stimulus representations dominated by nonlocal
suppressive interactions are in principle capable of correctly predicting the
common OPM design. They question that visual cortical feature representations
can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure
Perspective: network-guided pattern formation of neural dynamics
The understanding of neural activity patterns is fundamentally linked to an
understanding of how the brain's network architecture shapes dynamical
processes. Established approaches rely mostly on deviations of a given network
from certain classes of random graphs. Hypotheses about the supposed role of
prominent topological features (for instance, the roles of modularity, network
motifs, or hierarchical network organization) are derived from these
deviations. An alternative strategy could be to study deviations of network
architectures from regular graphs (rings, lattices) and consider the
implications of such deviations for self-organized dynamic patterns on the
network. Following this strategy, we draw on the theory of spatiotemporal
pattern formation and propose a novel perspective for analyzing dynamics on
networks, by evaluating how the self-organized dynamics are confined by network
architecture to a small set of permissible collective states. In particular, we
discuss the role of prominent topological features of brain connectivity, such
as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the
notion of network-guided pattern formation with numerical simulations and
outline how it can facilitate the understanding of neural dynamics
Limits and dynamics of randomly connected neuronal networks
Networks of the brain are composed of a very large number of neurons
connected through a random graph and interacting after random delays that both
depend on the anatomical distance between cells. In order to comprehend the
role of these random architectures on the dynamics of such networks, we analyze
the mesoscopic and macroscopic limits of networks with random correlated
connectivity weights and delays. We address both averaged and quenched limits,
and show propagation of chaos and convergence to a complex integral
McKean-Vlasov equations with distributed delays. We then instantiate a
completely solvable model illustrating the role of such random architectures in
the emerging macroscopic activity. We particularly focus on the role of
connectivity levels in the emergence of periodic solutions
Deterministic networks for probabilistic computing
Neural-network models of high-level brain functions such as memory recall and
reasoning often rely on the presence of stochasticity. The majority of these
models assumes that each neuron in the functional network is equipped with its
own private source of randomness, often in the form of uncorrelated external
noise. However, both in vivo and in silico, the number of noise sources is
limited due to space and bandwidth constraints. Hence, neurons in large
networks usually need to share noise sources. Here, we show that the resulting
shared-noise correlations can significantly impair the performance of
stochastic network models. We demonstrate that this problem can be overcome by
using deterministic recurrent neural networks as sources of uncorrelated noise,
exploiting the decorrelating effect of inhibitory feedback. Consequently, even
a single recurrent network of a few hundred neurons can serve as a natural
noise source for large ensembles of functional networks, each comprising
thousands of units. We successfully apply the proposed framework to a diverse
set of binary-unit networks with different dimensionalities and entropies, as
well as to a network reproducing handwritten digits with distinct predefined
frequencies. Finally, we show that the same design transfers to functional
networks of spiking neurons.Comment: 22 pages, 11 figure
Affective neuroscience, emotional regulation, and international relations
International relations (IR) has witnessed an emerging interest in neuroscience, particularly for its relevance to a now widespread scholarship on emotions. Contributing to this scholarship, this article draws on the subfields of affective neuroscience and neuropsychology, which remain largely unexplored in IR. Firstly, the article draws on affective neuroscience in illuminating affect's defining role in consciousness and omnipresence in social behavior, challenging the continuing elision of emotions in mainstream approaches. Secondly, it applies theories of depth neuropsychology, which suggest a neural predisposition originating in the brain's higher cortical regions to attenuate emotional arousal and limit affective consciousness. This predisposition works to preserve individuals' self-coherence, countering implicit assumptions about rationality and motivation within IR theory. Thirdly, it outlines three key implications for IR theory. It argues that affective neuroscience and neuropsychology offer a route towards deep theorizing of ontologies and motivations. It also leads to a reassessment of the social regulation of emotions, particularly as observed in institutions, including the state. It also suggests a productive engagement with constructivist and poststructuralist approaches by addressing the agency of the body in social relations. The article concludes by sketching the potential for a therapeutically-attuned approach to IR
From receptive profiles to a metric model of V1
In this work we show how to construct connectivity kernels induced by the
receptive profiles of simple cells of the primary visual cortex (V1). These
kernels are directly defined by the shape of such profiles: this provides a
metric model for the functional architecture of V1, whose global geometry is
determined by the reciprocal interactions between local elements. Our
construction adapts to any bank of filters chosen to represent a set of
receptive profiles, since it does not require any structure on the
parameterization of the family. The connectivity kernel that we define carries
a geometrical structure consistent with the well-known properties of long-range
horizontal connections in V1, and it is compatible with the perceptual rules
synthesized by the concept of association field. These characteristics are
still present when the kernel is constructed from a bank of filters arising
from an unsupervised learning algorithm.Comment: 25 pages, 18 figures. Added acknowledgement
Stochasticity from function -- why the Bayesian brain may need no noise
An increasing body of evidence suggests that the trial-to-trial variability
of spiking activity in the brain is not mere noise, but rather the reflection
of a sampling-based encoding scheme for probabilistic computing. Since the
precise statistical properties of neural activity are important in this
context, many models assume an ad-hoc source of well-behaved, explicit noise,
either on the input or on the output side of single neuron dynamics, most often
assuming an independent Poisson process in either case. However, these
assumptions are somewhat problematic: neighboring neurons tend to share
receptive fields, rendering both their input and their output correlated; at
the same time, neurons are known to behave largely deterministically, as a
function of their membrane potential and conductance. We suggest that spiking
neural networks may, in fact, have no need for noise to perform sampling-based
Bayesian inference. We study analytically the effect of auto- and
cross-correlations in functionally Bayesian spiking networks and demonstrate
how their effect translates to synaptic interaction strengths, rendering them
controllable through synaptic plasticity. This allows even small ensembles of
interconnected deterministic spiking networks to simultaneously and
co-dependently shape their output activity through learning, enabling them to
perform complex Bayesian computation without any need for noise, which we
demonstrate in silico, both in classical simulation and in neuromorphic
emulation. These results close a gap between the abstract models and the
biology of functionally Bayesian spiking networks, effectively reducing the
architectural constraints imposed on physical neural substrates required to
perform probabilistic computing, be they biological or artificial
- âŠ