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Optimal Properties of Analog Perceptrons with Excitatory Weights
The cerebellum is a brain structure which has been traditionally devoted to supervised learning. According to this theory, plasticity at the Parallel Fiber (PF) to Purkinje Cell (PC) synapses is guided by the Climbing fibers (CF), which encode an ‘error signal’. Purkinje cells have thus been modeled as perceptrons, learning input/output binary associations. At maximal capacity, a perceptron with excitatory weights expresses a large fraction of zero-weight synapses, in agreement with experimental findings. However, numerous experiments indicate that the firing rate of Purkinje cells varies in an analog, not binary, manner. In this paper, we study the perceptron with analog inputs and outputs. We show that the optimal input has a sparse binary distribution, in good agreement with the burst firing of the Granule cells. In addition, we show that the weight distribution consists of a large fraction of silent synapses, as in previously studied binary perceptron models, and as seen experimentally
Optimal Learning with Excitatory and Inhibitory synapses
Characterizing the relation between weight structure and input/output
statistics is fundamental for understanding the computational capabilities of
neural circuits. In this work, I study the problem of storing associations
between analog signals in the presence of correlations, using methods from
statistical mechanics. I characterize the typical learning performance in terms
of the power spectrum of random input and output processes. I show that optimal
synaptic weight configurations reach a capacity of 0.5 for any fraction of
excitatory to inhibitory weights and have a peculiar synaptic distribution with
a finite fraction of silent synapses. I further provide a link between typical
learning performance and principal components analysis in single cases. These
results may shed light on the synaptic profile of brain circuits, such as
cerebellar structures, that are thought to engage in processing time-dependent
signals and performing on-line prediction.Comment: 16 pages, 5 figure
Liquid State Machine with Dendritically Enhanced Readout for Low-power, Neuromorphic VLSI Implementations
In this paper, we describe a new neuro-inspired, hardware-friendly readout
stage for the liquid state machine (LSM), a popular model for reservoir
computing. Compared to the parallel perceptron architecture trained by the
p-delta algorithm, which is the state of the art in terms of performance of
readout stages, our readout architecture and learning algorithm can attain
better performance with significantly less synaptic resources making it
attractive for VLSI implementation. Inspired by the nonlinear properties of
dendrites in biological neurons, our readout stage incorporates neurons having
multiple dendrites with a lumped nonlinearity. The number of synaptic
connections on each branch is significantly lower than the total number of
connections from the liquid neurons and the learning algorithm tries to find
the best 'combination' of input connections on each branch to reduce the error.
Hence, the learning involves network rewiring (NRW) of the readout network
similar to structural plasticity observed in its biological counterparts. We
show that compared to a single perceptron using analog weights, this
architecture for the readout can attain, even by using the same number of
binary valued synapses, up to 3.3 times less error for a two-class spike train
classification problem and 2.4 times less error for an input rate approximation
task. Even with 60 times larger synapses, a group of 60 parallel perceptrons
cannot attain the performance of the proposed dendritically enhanced readout.
An additional advantage of this method for hardware implementations is that the
'choice' of connectivity can be easily implemented exploiting address event
representation (AER) protocols commonly used in current neuromorphic systems
where the connection matrix is stored in memory. Also, due to the use of binary
synapses, our proposed method is more robust against statistical variations.Comment: 14 pages, 19 figures, Journa
A three-threshold learning rule approaches the maximal capacity of recurrent neural networks
Understanding the theoretical foundations of how memories are encoded and
retrieved in neural populations is a central challenge in neuroscience. A
popular theoretical scenario for modeling memory function is the attractor
neural network scenario, whose prototype is the Hopfield model. The model has a
poor storage capacity, compared with the capacity achieved with perceptron
learning algorithms. Here, by transforming the perceptron learning rule, we
present an online learning rule for a recurrent neural network that achieves
near-maximal storage capacity without an explicit supervisory error signal,
relying only upon locally accessible information. The fully-connected network
consists of excitatory binary neurons with plastic recurrent connections and
non-plastic inhibitory feedback stabilizing the network dynamics; the memory
patterns are presented online as strong afferent currents, producing a bimodal
distribution for the neuron synaptic inputs. Synapses corresponding to active
inputs are modified as a function of the value of the local fields with respect
to three thresholds. Above the highest threshold, and below the lowest
threshold, no plasticity occurs. In between these two thresholds,
potentiation/depression occurs when the local field is above/below an
intermediate threshold. We simulated and analyzed a network of binary neurons
implementing this rule and measured its storage capacity for different sizes of
the basins of attraction. The storage capacity obtained through numerical
simulations is shown to be close to the value predicted by analytical
calculations. We also measured the dependence of capacity on the strength of
external inputs. Finally, we quantified the statistics of the resulting
synaptic connectivity matrix, and found that both the fraction of zero weight
synapses and the degree of symmetry of the weight matrix increase with the
number of stored patterns.Comment: 24 pages, 10 figures, to be published in PLOS Computational Biolog
Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective
On metrics of density and power efficiency, neuromorphic technologies have
the potential to surpass mainstream computing technologies in tasks where
real-time functionality, adaptability, and autonomy are essential. While
algorithmic advances in neuromorphic computing are proceeding successfully, the
potential of memristors to improve neuromorphic computing have not yet born
fruit, primarily because they are often used as a drop-in replacement to
conventional memory. However, interdisciplinary approaches anchored in machine
learning theory suggest that multifactor plasticity rules matching neural and
synaptic dynamics to the device capabilities can take better advantage of
memristor dynamics and its stochasticity. Furthermore, such plasticity rules
generally show much higher performance than that of classical Spike Time
Dependent Plasticity (STDP) rules. This chapter reviews the recent development
in learning with spiking neural network models and their possible
implementation with memristor-based hardware
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