37 research outputs found
A Neuron as a Signal Processing Device
A neuron is a basic physiological and computational unit of the brain. While
much is known about the physiological properties of a neuron, its computational
role is poorly understood. Here we propose to view a neuron as a signal
processing device that represents the incoming streaming data matrix as a
sparse vector of synaptic weights scaled by an outgoing sparse activity vector.
Formally, a neuron minimizes a cost function comprising a cumulative squared
representation error and regularization terms. We derive an online algorithm
that minimizes such cost function by alternating between the minimization with
respect to activity and with respect to synaptic weights. The steps of this
algorithm reproduce well-known physiological properties of a neuron, such as
weighted summation and leaky integration of synaptic inputs, as well as an
Oja-like, but parameter-free, synaptic learning rule. Our theoretical framework
makes several predictions, some of which can be verified by the existing data,
others require further experiments. Such framework should allow modeling the
function of neuronal circuits without necessarily measuring all the microscopic
biophysical parameters, as well as facilitate the design of neuromorphic
electronics.Comment: 2013 Asilomar Conference on Signals, Systems and Computers, see
http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=681029
Non-Euclidean Independent Component Analysis and Oja's Learning
In the present contribution we tackle the problem of nonlinear independent component analysis by non-Euclidean Hebbian-like learning. Independent component analysis (ICA) and blind source separation originally were introduced as tools for the linear unmixing of the signals to detect the underlying sources. Hebbian methods became very popular and succesfully in this context. Many nonlinear ICA extensions are known. A promising strategy is the application of kernel mapping. Kernel mapping realizes an usually nonlinear but implicite data mapping of the data into a reproducing kernel Hilbert space. After that a linear demixing can be carried out there. However, explicit handling in this non-Euclidean kernel mapping space is impossible. We show in this paper an alternative using an isomorphic mapping space. In particular, we show that the idea of Hebbian-like learning of kernel ICA can be transferred to this non-Euclidean space realizing an non-Euclidean ICA
Nonlinear Hebbian learning as a unifying principle in receptive field formation
The development of sensory receptive fields has been modeled in the past by a
variety of models including normative models such as sparse coding or
independent component analysis and bottom-up models such as spike-timing
dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic
plasticity. Here we show that the above variety of approaches can all be
unified into a single common principle, namely Nonlinear Hebbian Learning. When
Nonlinear Hebbian Learning is applied to natural images, receptive field shapes
were strongly constrained by the input statistics and preprocessing, but
exhibited only modest variation across different choices of nonlinearities in
neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse
network activity are necessary for the development of localized receptive
fields. The analysis of alternative sensory modalities such as auditory models
or V2 development lead to the same conclusions. In all examples, receptive
fields can be predicted a priori by reformulating an abstract model as
nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural
statistics can account for many aspects of receptive field formation across
models and sensory modalities
View-tolerant face recognition and Hebbian learning imply mirror-symmetric neural tuning to head orientation
The primate brain contains a hierarchy of visual areas, dubbed the ventral
stream, which rapidly computes object representations that are both specific
for object identity and relatively robust against identity-preserving
transformations like depth-rotations. Current computational models of object
recognition, including recent deep learning networks, generate these properties
through a hierarchy of alternating selectivity-increasing filtering and
tolerance-increasing pooling operations, similar to simple-complex cells
operations. While simulations of these models recapitulate the ventral stream's
progression from early view-specific to late view-tolerant representations,
they fail to generate the most salient property of the intermediate
representation for faces found in the brain: mirror-symmetric tuning of the
neural population to head orientation. Here we prove that a class of
hierarchical architectures and a broad set of biologically plausible learning
rules can provide approximate invariance at the top level of the network. While
most of the learning rules do not yield mirror-symmetry in the mid-level
representations, we characterize a specific biologically-plausible Hebb-type
learning rule that is guaranteed to generate mirror-symmetric tuning to faces
tuning at intermediate levels of the architecture