The organization of behavior: A neuropsychological theory

This ebook is the first authorized digital version of Kernighan and Ritchie's 1988 classic, The C Programming Language (2nd Ed.). One of the best-selling programming books published in the last fifty years, "K&R" has been called everything from the "bible" to "a landmark in computer science" and it has influenced generations of programmers. Available now for all leading ebook platforms, this concise and beautifully written text is a "must-have" reference for every serious programmers digital library.

As modestly described by the authors in the Preface to the First Edition, this "is not an introductory programming manual; it assumes some familiarity with basic programming concepts like variables, assignment statements, loops, and functions. Nonetheless, a novice programmer should be able to read along and pick up the language, although access to a more knowledgeable colleague will help."

The C programming language

Continual lifelong learning with neural networks: A review.

http://www.buzsakilab.com/content/PDFs/Buzsaki2010Neuron.pdf

Neural Syntax: Cell Assemblies, Synapsembles, and Readers

Pattern recognition systems usually have a relatively small number of patterns to be recognized. As a rule the number of handwritten symbols, number of phonemes or number of human faces are of the order of some dozens. But sometimes the pattern recognition task demands much more classes. For example, a continuous speech recognition system can be created on the base of syllables; a handwriting recognition system will be more efficient if the recognized units are not different letters, but triplets of letters. In these cases it is necessary to have various thousands of classes. In this paper we will consider the situation of the recognition problem that demands many thousands of classes to be recognized. For such problems we propose the use of the neural networks with ensembles. We give a short description of this type of neural network and calculate its storage capacity.

Neural network with ensembles

The hippocampal formation plays a crucial role in organizing cortical long-term memory. It is believed that the hippocampus is capable of fast (one-shot) learning of new episodic information followed by extensive time periods where corresponding neocortical representations are trained and "compressed" [1]. Here, compression usually refers to processes such as chunking spatially and temporally distributed activity patterns. We take the complementary approach and optimize the synaptic network by structural plasticity, e.g., replacing unused synapses, thereby making full use of the potential connectivity [2].

We apply the frameworks of structural plasticity and hippocampus-induced learning to the training of neocortical associative networks [3]. Associative networks such as the Hopfield or Willshaw model are at the heart of many cortex theories and have been analyzed for a long time with respect to information storage capacity and plausible retrieval strategies [3,4]. For example, it is well known that a completely connected network can store about 0.7 bits per synapse. However, for incompletely connected networks the capacity per synapse can be massively reduced or even vanish, depending on the retrieval algorithm [4].

In this work we analyze how structural processes and synaptic consolidation [5] during hippocampal training can improve the performance of neocortical associative networks by emulating full (or increased) synaptic connectivity. In our model the hippocampus can store a set of activity patterns by one-shot learning. Then the hippocampus trains the neocortex by repeatedly replaying the patterns in a sequence. The synapses of the neocortical network are consolidated depending on Hebbian learning. In each time step a fraction of the unconsolidated synapses are removed and replaced by the same number of new synapses at random locations thereby maintaining total connectivity. We show that this procedure can massively increase the synaptic capacity of a cortical macrocolumn (factor 10–20 or even up to factor 200 for pattern capacity). In a second step we analyze the model with respect to the time (or number of repetitions) necessary to increase effective connectivity from base level to a desired level. The analysis shows that acceptable training time requires a certain fraction of unconsolidated synapses to keep the network plastic.

/pdf/a-model-for-structural-plasticity-in-neocortical-associative-1k2xa2t1ic.pdf

A model for structural plasticity in neocortical associative networks trained by the hippocampus

Gamma oscillations are a prominent feature in experimental as well as theoretical descriptions of brain activity. One of the network models which has the capability to generate such oscillations is what we call a local cell assembly (CA), i.e. a group of neighboring neurons which are strongly interconnected in an excitatory manner. Postulated by experimenters and extensively used in theoretical studies, these local networks seem to be a good candidate for investigating the impact of biological constraints given by models of spike-timing-dependent plasticity (STDP) on local gamma oscillating structures in the mammalian brain. Therefore we fi*tted a two-compartment neuron model with AMPA- and NMDA-receptor mediated synaptic currents to desired properties of a local CA, meaning pattern completion and after-activity. We simulated 100 recurrently connected neurons with fi*xed axonal transmission delays. In addition, every neuron receives Poissonian spikes from 1000 input cells *firing at low background rate. During simulation the network is stimulated every second by increasing the input rate 10-fold for 35 msec. As a quality measure for keeping or even enhancing the properties of the network, we counted the relative amount of synapses with increased synaptic strengths with reference to the initial values. Three phenomenological STDP models (Song et al., Nature Neuroscience, 3, 2000; Pfi*ster and Gerstner, The J. of Neuroscience, 26, 2006; Clopath et al., Nature Neuroscience, 13, 2010) were implemented. Model-specifi*c parameters were varied in ranges determined by experimental measurements. We conclude that more recent STDP models which take into account frequency-dependent terms lead to a higher probability of strengthening synapses in a local CA (larger LTP region). This corresponds to experimental observations that long-term potentiation (LTP) outweighs long-term depression (LTD) in high-frequency pairing protocols. Furthermore, our simulations show that short axonal transmission delays clearly enlarge the LTP region of STDP parameter space.

A simulation study on different STDP models concerning localized gamma oscillations

The question whether neural activity follows a rate code or a temporal code is still an unsolved issue in neuroscience. Recent theoretical works have suggested that realistic models of spike-timing-dependent-plasticity (STDP) in recurrent networks could resolve this issue because they observed a seemingly unique relation between the neural code and the resulting pattern of synaptic connections [1]. In particular, these works argue that temporal coding would be inconsistent with bidirectional synaptic connectivity as observed in visual cortex [2] and expected for Hebbian cell assemblies (“what fires together wires together”). This conclusion is based on two assumptions, first, that simple STDP based on spike doublets would be generally unable to produce bidirectional synaptic connectivity (see references in [1]) and, second, that realistic voltage-based STDP would be able to produce bidirectional synaptic connectivity only for rate coding where signals are coded by cell ensembles jointly elevating firing rates on a time scale of hundreds of milliseconds [1].

We have disproved both assumptions. In particular, here we show that already simple STDP models can easily grow bidirectional connections for a temporal code based on spike synchronization unless synchronization is extremely precise (see [3] for disproving the second assumption). To this end we present simulation results for various STDP models [4] including all-to-all (AA) doublet STDP, nearest-neighbor (NN) doublet STDP, and various triplet STDP model variants with parameters fitted to experimental data and including realistic propagation delays. It turns out that all model variants can grow functional cell assemblies as reflected by strong bidirectional connectivity and tested within an associative memory framework [5]. This requires coarsely synchronized inputs such that spikes of the neurons within a cell assembly get synchronized on a time scale of 5 to 50 milliseconds, whereas more precise synchronization leads to depression of synaptic weights and, thus, destruction of the cell assembly. For NN doublet STDP and triplet STDP synaptic potentiation is boosted by increasing the rate of synchronized inputs, whereas high rates destroy cell assemblies for AA doublet STDP.

Thus, both rate coding and temporal coding based on coarse synaptic synchronization can account for the bidirectional connectivity observed, for example, in visual cortex [2]. However, we argue that the temporal code will be much more energy efficient for learning because it allows to grow and preserve cell assemblies at low mean firing rates at the level of spontaneous activity, whereas a rate code (based on uncorrelated Poissonian firing) can grow cell assemblies only by maintaining high firing rates over longer time intervals. Moreover, additional simulation experiments demonstrate how STDP can quickly grow multiple independent cell assemblies reflecting the spike timing relations of simultaneously active input neurons. We speculate that such a multiplexing mechanism may play a role both for working memory and long-range communication where “copies” or “indices” [6] of cell assemblies could easily be transmitted between cortical areas.

/pdf/stdp-hebbian-cell-assemblies-and-temporal-coding-by-spike-4f2rqal2ci.pdf

STDP, Hebbian cell assemblies, and temporal coding by spike synchronization

This invention is in the field of machine learning and neural associative memory. In particular the invention discloses a neural associative memory structure for storing and maintaining associations between memory address patterns and memory content patterns using a neural network, as well as methods for storing and retrieving such associations. Bayesian learning is applied to achieve non-linear learning.

Method and structure for a neural associative memory based on optimal Bayesian learning

Recent studies on phenomenological models of spike-timing-dependent plasticity (STDP) extend the idea of a pure spike-based paradigm to the level of dendritic voltage [1] In such models, the decision to induce early long-term potentiation (eLTP) or long-term depression (eLTD) not solely depends on the time difference between pre- and post-synaptic spikes but also on the precise dynamics of the post-synaptic potential From simulations of small neural networks and different stimulation schemes corresponding to different neural codes, these studies have concluded that the pattern of synaptic connectivity would directly follow from the neural code and vice versa For example, they have suggested that strong uni-directional connectivity would emerge through temporal coding, whereas bidirectional connectivity would be indicative for a rate code Relying on results from earlier studies on first generation STDP models [2-4], synchronous temporal codes forming bidirectional connectivity patterns were considered unlikely in [1] However, recent findings revise a general exclusion of this relationship [5] even for first generation STDP models In particular, our work shows that realistic STDP models as proposed in [1] can actually not predict the neural code (temporal vs rate coding) by looking at the pattern of synaptic connectivity within a specific brain area With the same kind of simulations as in [1], but additionally considering stimulation conditions for synchronous temporal coding, we show that bidirectional connections are still possible Furthermore we discuss the influence of synchronization precision and oscillatory activity

https://link.springer.com/content/pdf/10.1186%2F1471-2202-12-S1-P247.pdf

Andreas Knoblauch

Papers

A model for structural plasticity in neocortical associative networks trained by the hippocampus

A simulation study on different STDP models concerning localized gamma oscillations

STDP, Hebbian cell assemblies, and temporal coding by spike synchronization

Method and structure for a neural associative memory based on optimal Bayesian learning

Different neural codes result in bidirectional connectivity formed by the same model of spike-timing-dependent plasticity