Palimpsest memories: a new high-capacity forgetful learning rule for Hopfield networks

Palimpsest or forgetful learning rules for attractor neural networks do not suffer from catastrophic forgetting. Instead they selectively forget older memories in order to store new patterns. Standard palimpsest learning algorithms have a capacity of up to 0:05n, where n is the size of the network. Here a new learning rule is introduced. This rule is local and incremental. It is shown that it has palimpsest properties, and it has a palimpsest capacity of about 0:25n, much higher than the capacity of standard palimpsest schemes. It is shown that the algorithm acts as an iterated function sequence on the space of matrices, and this is used to illustrate the performance of the learning rule. 1 1 Introduction Attractor networks such as Hopfield [1] networks are used as autoassociative content addressable memories. The aim of such networks is to retrieve a previously learnt pattern from an example which is similar to, or a noisy version of, one of the previously presented patterns. To do ..

How can realistic networks process time-varying signals?

The brain is easily able to process and categorise complex time-varying signals. For example, the two sentences "it is cold in London this time of year" and "it is hot in London this time of year" have different meanings, even though the words "hot" and "cold" appear about 3000 ms before the ends of the two sentences. A network that can perform this kind of processing must, therefore, have a long memory. In other words, the current state of the network must depend on events that happened many seconds ago. This is particularly difficult because neurons are dominated by relatively short time constants---10s to 100s of ms. Recently Jaeger and Haas 2004 (see also Jaeger 2001 ) and Maass et al. 2002, 2004 proposed that randomly connected networks could exhibit the long memories necessary for complex temporal processing. This is an attractive idea, both for its simplicity and because little fine tuning is required. However, a necessary condition for it to work is that the underlying network dynamics must be non-chaotic that is, it must exhibit negative Lyapunov exponents White et al., 2004, Bertschinger and Natschlager, 2004 . Real networks, though, tend to be chaotic Banerjee, 2001a,b , an observation that we have corroborated based on an extension of the analysis used by Bertschinger and Natschlager. Real networks also tend to be very noisy---they exhibit synaptic failures 10-90% of the time in the central nervous system Walmsley et al., 1987, Volgushev et al., 2004 . The question we ask here, then, is: given the chaotic dynamics and high noise intrinsic to biologically realistic networks, can randomly connected networks exhibit memories that are significantly longer than the time constants of their constituent neurons

Constructing and Analyzing Neural Network Dynamics for Information Objectives and Working Memory

Creation of quantitative models of neural functions and discovery of underlying principles of how neural circuits learn and compute are long-standing challenges in the field of neuroscience. In this work, we blend ideas from computational neuroscience, information and control theories with machine learning to shed light on how certain key functions are encoded through the dynamics of neural circuits. In this regard, we pursue the ‘top-down’ modeling approach of engineering neuroscience to relate brain functions to basic generative dynamical mechanisms. Our approach encapsulates two distinct paradigms in which ‘function’ is understood. In the first part of this research, we explore the synthesis of neural dynamics for task-independent, well-defined objective function: the information processing capacity of neural circuits/networks. We contribute our efforts to devise a strategy to optimize the dynamics of the network at hand using information maximization as an objective function. In this vein, our principle contributions are in terms of mathematical formulation of the optimization problem and proposing a simplification method to reduce the computational burden associated with mutual information optimization. Then, we illustrate the novelty of our ideas for well-understood dynamical systems. Our methodology results in dynamics that generically perform as encoder of afferent inputs distribution and facilitate information propagation. However, determining a well-defined mathematical objective function may not be straightforward in all cases, e.g. complex cognitive functions. To address this issue, in the second part of this research we consider top-down synthesis on the basis of a surrogate task. In particular, we optimize ‘artificial’ recurrent networks in order to perform a computational task that embodies the function we are interested in studying, i.e. working memory. We contribute our efforts to propose a realistic training paradigm for recurrent neural networks and elucidate how dynamics of the optimized artificial networks can support computations implemented in memory functions. We will discuss the theoretical and technical steps involved in our interpretations, as well as remaining open questions and future directions

Cognitive architecture with evolutionary dynamics solves insight problem

In this paper, we show that a neurally implemented a cognitive architecture with evolutionary dynamics can solve the four-tree problem. Our model, called Darwinian Neurodynamics, assumes that the unconscious mechanism of problem solving during insight tasks is a Darwinian process. It is based on the evolution of patterns that represent candidate solutions to a problem, and are stored and reproduced by a population of attractor networks. In our first experiment, we used human data as a benchmark and showed that the model behaves comparably to humans: it shows an improvement in performance if it is pretrained and primed appropriately, just like human participants in Kershaw et al. (2013)'s experiment. In the second experiment, we further investigated the effects of pretraining and priming in a two-by-two design and found a beginner's luck type of effect: solution rate was highest in the condition that was primed, but not pretrained with patterns relevant for the task. In the third experiment, we showed that deficits in computational capacity and learning abilities decreased the performance of the model, as expected. We conclude that Darwinian Neurodynamics is a promising model of human problem solving that deserves further investigation

Statistical Mechanics of On-Line Learning Under Concept Drift

We introduce a modeling framework for the investigation of on-line machine learning processes in non-stationary environments. We exemplify the approach in terms of two specific model situations: In the first, we consider the learning of a classification scheme from clustered data by means of prototype-based Learning Vector Quantization (LVQ). In the second, we study the training of layered neural networks with sigmoidal activations for the purpose of regression. In both cases, the target, i.e., the classification or regression scheme, is considered to change continuously while the system is trained from a stream of labeled data. We extend and apply methods borrowed from statistical physics which have been used frequently for the exact description of training dynamics in stationary environments. Extensions of the approach allow for the computation of typical learning curves in the presence of concept drift in a variety of model situations. First results are presented and discussed for stochastic drift processes in classification and regression problems. They indicate that LVQ is capable of tracking a classification scheme under drift to a non-trivial extent. Furthermore, we show that concept drift can cause the persistence of sub-optimal plateau states in gradient based training of layered neural networks for regression

Statistical physics of neural systems

The ability of processing and storing information is considered a characteristic trait of intelligent systems. In biological neural networks, learning is strongly believed to take place at the synaptic level, in terms of modulation of synaptic efficacy. It can be thus interpreted as the expression of a collective phenomena, emerging when neurons connect each other in constituting a complex network of interactions. In this work, we represent learning as an optimization problem, actually implementing a local search, in the synaptic space, of specific configurations, known as solutions and making a neural network able to accomplish a series of different tasks. For instance, we would like the network to adapt the strength of its synaptic connections, in order to be capable of classifying a series of objects, by assigning to each object its corresponding class-label. Supported by a series of experiments, it has been suggested that synapses may exploit a very few number of synaptic states for encoding information. It is known that this feature makes learning in neural networks a challenging task. Extending the large deviation analysis performed in the extreme case of binary synaptic couplings, in this work, we prove the existence of regions of the phase space, where solutions are organized in extremely dense clusters. This picture turns out to be invariant to the tuning of all the parameters of the model. Solutions within the clusters are more robust to noise, thus enhancing the learning performances. This has inspired the design of new learning algorithms, as well as it has clarified the effectiveness of the previously proposed ones. We further provide quantitative evidence that the gain achievable when considering a greater number of available synaptic states for encoding information, is consistent only up to a very few number of bits. This is in line with the above mentioned experimental results. Besides the challenging aspect of low precision synaptic connections, it is also known that the neuronal environment is extremely noisy. Whether stochasticity can enhance or worsen the learning performances is currently matter of debate. In this work, we consider a neural network model where the synaptic connections are random variables, sampled according to a parametrized probability distribution. We prove that, this source of stochasticity naturally drives towards regions of the phase space at high densities of solutions. These regions are directly accessible by means of gradient descent strategies, over the parameters of the synaptic couplings distribution. We further set up a statistical physics analysis, through which we show that solutions in the dense regions are characterized by robustness and good generalization performances. Stochastic neural networks are also capable of building abstract representations of input stimuli and then generating new input samples, according to the inferred statistics of the input signal. In this regard, we propose a new learning rule, called Delayed Correlation Matching (DCM), that relying on the matching between time-delayed activity correlations, makes a neural network able to store patterns of neuronal activity. When considering hidden neuronal states, the DCM learning rule is also able to train Restricted Boltzmann Machines as generative models. In this work, we further require the DCM learning rule to fulfil some biological constraints, such as locality, sparseness of the neural coding and the Dale’s principle. While retaining all these biological requirements, the DCM learning rule has shown to be effective for different network topologies, and in both on-line learning regimes and presence of correlated patterns. We further show that it is also able to prevent the creation of spurious attractor states

The interdependence of nature and nurture in the establishment and maintenance of mind: an eco-dynamic paradigm

This dissertation makes the case that the human mind is established and maintained by the interdependence or enmeshment of multiple complex, dynamic systems; biological, social, and technological. These are not merely peripheral but rather, jointly are constitutive of mind. I develop this thesis in what I call the “eco-dynamic paradigm,” which modifies and supplements enactivism. This dissertation has two main theses: first, mind is established and maintained by features that draw on the resources of the brain, body and the contextual environment in which one is embedded. The second thesis is that Dynamic Systems Theory is an important resource in modelling, explaining and analysing the complex, dynamic relationships within and between scales of brain, body and contextual environment. I use the language and concepts of Dynamic Systems Theory qualitatively to describe the dynamics of brain, body, environmental relationships. Methodologically, this dissertation is both interdisciplinary and cross-cultural. I refer to Indo-Tibetan Buddhism as an excellent example of a culture whose goal is to transform the mind to clarity by utilising a symbiotic package of meditation and visualisation practices, teachings, rituals and philosophies. These elements together provide an interconnected web which are used to support and assist the cognitive transformation of the practitioner. The conceptual and practical elements of Indo-Tibetan Buddhism, the relations between them and even the process of cognitive transformation can also be analysed by Dynamic Systems Theory. Death and dying provide a fulcrum in which the resources of the eco-dynamic paradigm are best utilised. Indo-Tibetan Buddhist practices, concepts and philosophy related to the nature of the mind come into contrast with those of Western medical science sharply in death and dying. The challenge posed to medical science is to study and explain what might appear to be anomalous cases of alleged cognition or mental activity without brain function in near death experience. A specific programme of research is suggested in which the nature of the mind is explored neurophenomenologically.