Invariant template matching in systems with spatiotemporal coding: A matter of instability

Instability and Uncertainty Are Critical for Psychotherapy: How the Therapeutic Alliance Opens Us Up

Tschacher and Haken have recently applied a systems-based approach to modeling psychotherapy process in terms of potentially beneficial tendencies toward deterministic as well as chaotic forms of change in the client's behavioral, cognitive and affective experience during the course of therapy. A chaotic change process refers to a greater exploration of the states that a client can be in, and it may have a potential positive role to play in their development. A distinction is made between on the one hand, specific instances of instability which are due to techniques employed by the therapist, and on the other, a more general instability which is due to the therapeutic relationship, and a key, necessary result of a successful therapeutic alliance. Drawing on Friston's systems-based model of free energy minimization and predictive coding, it is proposed here that the increase in the instability of a client's functioning due to therapy can be conceptualized as a reduction in the precisions (certainty) with which the client's prior beliefs about themselves and their world, are held. It is shown how a good therapeutic alliance (characterized by successful interpersonal synchrony of the sort described by Friston and Frith) results in the emergence of a new hierarchical level in the client's generative model of themselves and their relationship with the world. The emergence of this new level of functioning permits the reduction of the precisions of the client's priors, which allows the client to 'open up': to experience thoughts, emotions and experiences they did not have before. It is proposed that this process is a necessary precursor to change due to psychotherapy. A good consilience can be found between this approach to understanding the role of the therapeutic alliance, and the role of epistemic trust in psychotherapy as described by Fonagy and Allison. It is suggested that beneficial forms of instability in clients are an underappreciated influence on psychotherapy process, and thoughts about the implications, as well as situations in which instability may not be beneficial (or potentially harmful) for therapy, are considered.

Learning process for identifying different types of communication via repetitive stimulation: feasibility study in a cultured neuronal network

It is well known that various types of information can be learned and memorized via repetitive training. In brain information science, it is very important to determine how neuronal networks comprising neurons with fluctuating characteristics reliably learn and memorize information. The aim of this study is to investigate the learning process in cultured neuronal networks and to address the question described above. Previously, we reported that the spikes resulting from stimulation at a specific neuron propagate as a cluster of excitation waves called spike wave propagation in cultured neuronal networks. We also reported that these waves have an individual spatiotemporal pattern that varies according to the type of neuron that is stimulated. Therefore, different spike wave propagations can be identified via pattern analysis of spike trains at particular neurons. Here, we assessed repetitive stimulation using intervals of 0.5 and 1.5 ms. Subsequently, we analyzed the relationship between the repetition of the stimulation and the identification of the different spike wave propagations. We showed that the various spike wave propagations were identified more precisely after stimulation was repeated several times using an interval of 1.5 ms. These results suggest the existence of a learning process in neuronal networks that occurs via repetitive training using a suitable interval.

Asynchronous Multiplex Communication Channels in 2-D Neural Network With Fluctuating Characteristics

Neurons behave like transistors, but have fluctuating characteristics. In this paper, we show that several asynchronous multiplex communication channels can be established in a 2-D mesh neural network with randomly generated weights between eight neighbors. Neurons were simulated by integrate-and-fire neuron models without leakage and with fluctuating refractory period and output delay. If one of the transmitting neuron groups is stimulated, the signal is propagated in the form of spike waves. The corresponding receiving neuron group is able to identify the signal after having learned to form an asynchronous multiplex communication channel. The channel is composed of many intermediate/interstitial neurons working as relays. Each neuron can work as an I/O and as a relay element, i.e., as a multiuse unit. Grouping and synchronic firing is often seen in natural neuronal networks and seems to be effective for stable/robust communication in conjunction with spatial multiplex communication. This communication pattern corresponds to our wet lab experiments on cultured neuronal networks and is similar to sound identification by the ear and mobile adaptive communication systems.

Effect of correlating adjacent neurons for identifying communications: Feasibility experiment in a cultured neuronal network

Neuronal networks have fluctuating characteristics, unlike the stable characteristics seen in computers. The underlying mechanisms that drive reliable communication among neuronal networks and their ability to perform intelligible tasks remain unknown. Recently, in an attempt to resolve this issue, we showed that stimulated neurons communicate via spikes that propagate temporally, in the form of spike trains. We named this phenomenon “spike wave propagation”. In these previous studies, using neural networks cultured from rat hippocampal neurons, we found that multiple neurons, e.g., 3 neurons, correlate to identify various spike wave propagations in a cultured neuronal network. Specifically, the number of classifiable neurons in the neuronal network increased through correlation of spike trains between current and adjacent neurons. Although we previously obtained similar findings through stimulation, here we report these observations on a physiological level. Considering that individual spike wave propagation corresponds to individual communication, a correlation between some adjacent neurons to improve the quality of communication classification in a neuronal network, similar to a diversity antenna, which is used to improve the quality of communication in artificial data communication systems, is suggested.

Breeding novel solutions in the brain: a model of Darwinian neurodynamics

Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain.

Methods: We combine known components of the brain – recurrent neural networks (acting as attractors), the action selection loop and implicit working memory – to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory.

Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors.

Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.

Breeding novel solutions in the brain: a model of Darwinian neurodynamics

Background: The fact that surplus connections and neurons are pruned during development is well established. We complement this selectionist picture by a proof-of-principle model of evolutionary search in the brain, that accounts for new variations in theory space. We present a model for Darwinian evolutionary search for candidate solutions in the brain. Methods: We combine known components of the brain - recurrent neural networks (acting as attractors), the action selection loop and implicit working memory - to provide the appropriate Darwinian architecture. We employ a population of attractor networks with palimpsest memory. The action selection loop is employed with winners-share-all dynamics to select for candidate solutions that are transiently stored in implicit working memory. Results: We document two processes: selection of stored solutions and evolutionary search for novel solutions. During the replication of candidate solutions attractor networks occasionally produce recombinant patterns, increasing variation on which selection can act. Combinatorial search acts on multiplying units (activity patterns) with hereditary variation and novel variants appear due to (i) noisy recall of patterns from the attractor networks, (ii) noise during transmission of candidate solutions as messages between networks, and, (iii) spontaneously generated, untrained patterns in spurious attractors. Conclusions: Attractor dynamics of recurrent neural networks can be used to model Darwinian search. The proposed architecture can be used for fast search among stored solutions (by selection) and for evolutionary search when novel candidate solutions are generated in successive iterations. Since all the suggested components are present in advanced nervous systems, we hypothesize that the brain could implement a truly evolutionary combinatorial search system, capable of generating novel variants.

Spike Code Flow in Cultured Neuronal Networks

We observed spike trains produced by one-shot electrical stimulation with 8 × 8 multielectrodes in cultured neuronal networks. Each electrode accepted spikes from several neurons. We extracted the short codes from spike trains and obtained a code spectrum with a nominal time accuracy of 1%. We then constructed code flow maps as movies of the electrode array to observe the code flow of “1101” and “1011,” which are typical pseudorandom sequence such as that we often encountered in a literature and our experiments. They seemed to flow from one electrode to the neighboring one and maintained their shape to some extent. To quantify the flow, we calculated the “maximum cross-correlations” among neighboring electrodes, to find the direction of maximum flow of the codes with lengths less than 8. Normalized maximum cross-correlations were almost constant irrespective of code. Furthermore, if the spike trains were shuffled in interval orders or in electrodes, they became significantly small. Thus, the analysis suggested that local codes of approximately constant shape propagated and conveyed information across the network. Hence, the codes can serve as visible and trackable marks of propagating spike waves as well as evaluating information flow in the neuronal network.

Simulation of Code Spectrum and Code Flow of Cultured Neuronal Networks

It has been shown that, in cultured neuronal networks on a multielectrode, pseudorandom-like sequences (codes) are detected, and they flow with some spatial decay constant. Each cultured neuronal network is characterized by a specific spectrum curve. That is, we may consider the spectrum curve as a “signature” of its associated neuronal network that is dependent on the characteristics of neurons and network configuration, including the weight distribution. In the present study, we used an integrate-and-fire model of neurons with intrinsic and instantaneous fluctuations of characteristics for performing a simulation of a code spectrum from multielectrodes on a 2D mesh neural network. We showed that it is possible to estimate the characteristics of neurons such as the distribution of number of neurons around each electrode and their refractory periods. Although this process is a reverse problem and theoretically the solutions are not sufficiently guaranteed, the parameters seem to be consistent with those of neurons. That is, the proposed neural network model may adequately reflect the behavior of a cultured neuronal network. Furthermore, such prospect is discussed that code analysis will provide a base of communication within a neural network that will also create a base of natural intelligence.

Capture of fixation by rotational flow; a deterministic hypothesis regarding scaling and stochasticity in fixational eye movements

Visual scan paths exhibit complex, stochastic dynamics. Even during visual fixation, the eye is in constant motion. Fixational drift and tremor are thought to reflect fluctuations in the persistent neural activity of neural integrators in the oculomotor brainstem, which integrate sequences of transient saccadic velocity signals into a short term memory of eye position. Despite intensive research and much progress, the precise mechanisms by which oculomotor posture is maintained remain elusive. Drift exhibits a stochastic statistical profile which has been modeled using random walk formalisms. Tremor is widely dismissed as noise. Here we focus on the dynamical profile of fixational tremor, and argue that tremor may be a signal which usefully reflects the workings of oculomotor postural control. We identify signatures reminiscent of a certain flavor of transient neurodynamics; toric traveling waves which rotate around a central phase singularity. Spiral waves play an organizational role in dynamical systems at many scales throughout nature, though their potential functional role in brain activity remains a matter of educated speculation. Spiral waves have a repertoire of functionally interesting dynamical properties, including persistence, which suggest that they could in theory contribute to persistent neural activity in the oculomotor postural control system. Whilst speculative, the singularity hypothesis of oculomotor postural control implies testable predictions, and could provide the beginnings of an integrated dynamical framework for eye movements across scales.

Perception and self-organized instability

This paper considers state-dependent dynamics that mediate perception in the brain. In particular, it considers the formal basis of self-organized instabilities that enable perceptual transitions during Bayes-optimal perception. The basic phenomena we consider are perceptual transitions that lead to conscious ignition (Dehaene and Changeux, 2011) and how they depend on dynamical instabilities that underlie chaotic itinerancy (Breakspear, 2001; Tsuda, 2001) and self-organized criticality (Beggs and Plenz, 2003; Plenz and Thiagarajan, 2007; Shew et al., 2011). Our approach is based on a dynamical formulation of perception as approximate Bayesian inference, in terms of variational free energy minimization. This formulation suggests that perception has an inherent tendency to induce dynamical instabilities (critical slowing) that enable the brain to respond sensitively to sensory perturbations. We briefly review the dynamics of perception, in terms of generalized Bayesian filtering and free energy minimization, present a formal conjecture about self-organized instability and then test this conjecture, using neuronal (numerical) simulations of perceptual categorization.

Free energy, value, and attractors

It has been suggested recently that action and perception can be understood as minimising the free energy of sensory samples. This ensures that agents sample the environment to maximise the evidence for their model of the world, such that exchanges with the environment are predictable and adaptive. However, the free energy account does not invoke reward or cost-functions from reinforcement-learning and optimal control theory. We therefore ask whether reward is necessary to explain adaptive behaviour. The free energy formulation uses ideas from statistical physics to explain action in terms of minimising sensory surprise. Conversely, reinforcement-learning has its roots in behaviourism and engineering and assumes that agents optimise a policy to maximise future reward. This paper tries to connect the two formulations and concludes that optimal policies correspond to empirical priors on the trajectories of hidden environmental states, which compel agents to seek out the (valuable) states they expect to encounter.