59 research outputs found
Bayesian optimization for sparse neural networks with trainable activation functions
In the literature on deep neural networks, there is considerable interest in
developing activation functions that can enhance neural network performance. In
recent years, there has been renewed scientific interest in proposing
activation functions that can be trained throughout the learning process, as
they appear to improve network performance, especially by reducing overfitting.
In this paper, we propose a trainable activation function whose parameters need
to be estimated. A fully Bayesian model is developed to automatically estimate
from the learning data both the model weights and activation function
parameters. An MCMC-based optimization scheme is developed to build the
inference. The proposed method aims to solve the aforementioned problems and
improve convergence time by using an efficient sampling scheme that guarantees
convergence to the global maximum. The proposed scheme is tested on three
datasets with three different CNNs. Promising results demonstrate the
usefulness of our proposed approach in improving model accuracy due to the
proposed activation function and Bayesian estimation of the parameters
Integration of continuous-time dynamics in a spiking neural network simulator
Contemporary modeling approaches to the dynamics of neural networks consider
two main classes of models: biologically grounded spiking neurons and
functionally inspired rate-based units. The unified simulation framework
presented here supports the combination of the two for multi-scale modeling
approaches, the quantitative validation of mean-field approaches by spiking
network simulations, and an increase in reliability by usage of the same
simulation code and the same network model specifications for both model
classes. While most efficient spiking simulations rely on the communication of
discrete events, rate models require time-continuous interactions between
neurons. Exploiting the conceptual similarity to the inclusion of gap junctions
in spiking network simulations, we arrive at a reference implementation of
instantaneous and delayed interactions between rate-based models in a spiking
network simulator. The separation of rate dynamics from the general connection
and communication infrastructure ensures flexibility of the framework. We
further demonstrate the broad applicability of the framework by considering
various examples from the literature ranging from random networks to neural
field models. The study provides the prerequisite for interactions between
rate-based and spiking models in a joint simulation
Dynamical principles in neuroscience
Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA
On fixed points, their geometry and application to satellite web coupling problem in S−metric spaces
We introduce an M−class function in an S−metric space which is a viable, productive, and powerful technique for finding the existence of a fixed point and fixed circle. Our conclusions unify, improve, extend, and generalize numerous results to a widespread class of discontinuous maps. Next, we introduce notions of a fixed ellipse (elliptic disc) in an S−metric space to investigate the geometry of the collection of fixed points and prove fixed ellipse (elliptic disc) theorems. In the sequel, we validate these conclusions with illustrative examples. We explore some conditions which eliminate the possibility of the identity map in the existence of an ellipse (elliptic disc). Some remarks, propositions, and examples to exhibit the feasibility of the results are presented. The paper is concluded with a discussion of activation functions that are discontinuous in nature and, consequently, utilized in a neural network for increasing the storage capacity. Towards the end, we solve the satellite web coupling problem and propose two open problems
The importance of different timings of excitatory and inhibitory pathways in neural field models
In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity
Experimental Manipulation of Action Perception Based on Modeling Computations in Visual Cortex
Action perception, planning and execution is a broad area of study, crucial for future
development of clinical therapies treating social cognitive disorders, as well as for
building human-computer interaction systems and for giving foundation to an
emerging field of developmental robotics. We took interest in basic mechanisms of
action perception, and as a model area chose dynamic perception of body motion.
The focus of this thesis has been on understanding how perception of actions can be
manipulated, how to distill this understanding experimentally, and how to
summarize via numerical simulation the neural mechanisms helping explain
observed dynamic phenomena.
Experimentally we have, first, shown how a careful manipulation of a static object
depth cue can in principle modulate perception of actions. We chose the luminance
gradient as a model cue, and linked action perception to a perceptual prior previously
studied in object recognition – the lighting from above-prior. Second, we have
explored the dynamic relationship between representations of actions that are
naturally observed in spatiotemporal proximity. We have shown an adaptation
aftereffect that may speak of brain mechanisms encoding social interactions.
To qualitatively capture neural mechanisms behind ours and previous findings, we
have additionally appealed to the perceptual bistability phenomenon. Bistable
perception refers to the ability to spontaneously switch between two perceptual
alternatives arising from an observation of a single stimulus. Addition of depth cues
to biological motion stimulus resolves depth-ambiguity. To account for neural
dynamics as well as for modulation of action percept by light source position, we used
a combined architecture with a convolutional neural network computing shading and
form features in biological motion stimuli, and a 2-dimensional neural field coding for
walking direction and body configuration in the gait cycle. This single unified model
matches experimentally observed switching statistics, dependence of recognized
walking direction on the light source position, and makes a prediction for the
adaptation aftereffect in perception of biological motion
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