Encoding time in neural dynamic regimes with distinct computational tradeoffs

Converging evidence suggests the brain encodes time in dynamic patterns of neural activity, including neural sequences, ramping activity, and complex dynamics. Most temporal tasks, however, require more than just encoding time, and can have distinct computational requirements including the need to exhibit temporal scaling, generalize to novel contexts, or robustness to noise. It is not known how neural circuits can encode time and satisfy distinct computational requirements, nor is it known whether similar patterns of neural activity at the population level can exhibit dramatically different computational or generalization properties. To begin to answer these questions, we trained RNNs on two timing tasks based on behavioral studies. The tasks had different input structures but required producing identically timed output patterns. Using a novel framework we quantified whether RNNs encoded two intervals using either of three different timing strategies: scaling, absolute, or stimulus-specific dynamics. We found that similar neural dynamic patterns at the level of single intervals, could exhibit fundamentally different properties, including, generalization, the connectivity structure of the trained networks, and the contribution of excitatory and inhibitory neurons. Critically, depending on the task structure RNNs were better suited for generalization or robustness to noise. Further analysis revealed different connection patterns underlying the different regimes. Our results predict that apparently similar neural dynamic patterns at the population level (e.g., neural sequences) can exhibit fundamentally different computational properties in regards to their ability to generalize to novel stimuli and their robustness to noise—and that these differences are associated with differences in network connectivity and distinct contributions of excitatory and inhibitory neurons. We also predict that the task structure used in different experimental studies accounts for some of the experimentally observed variability in how networks encode time.     

Information storage matrices in neural networks

A new neural network model with feedback based on the concept of information storage matrices is proposed. This model is similar to the Hopfield and spectral type neural networks but has a more general structure. The presentation gives a fully developed theory for first-order networks, including results on the formation of fixed points and their domains of attraction. These results are used to determine, in deterministic sense, the information storage capacity. The algorithm is applied to the DNA sequencing problem. It is demonstrated how a hidden genetic information in an arbitrary long DNA strand can be extracted.     

Information processing in social insect networks

Investigating local-scale interactions within a network makes it possible to test hypotheses about the mechanisms of global network connectivity and to ask whether there are general rules underlying network function across systems. Here we use motif analysis to determine whether the interactions within social insect colonies resemble the patterns exhibited by other animal associations or if they exhibit characteristics of biological regulatory systems. Colonies exhibit a predominance of feed-forward interaction motifs, in contrast to the densely interconnected clique patterns that characterize human interaction and animal social networks. The regulatory motif signature supports the hypothesis that social insect colonies are shaped by selection for network patterns that integrate colony functionality at the group rather than individual level, and demonstrates the utility of this approach for analysis of selection effects on complex systems across biological levels of organization.     

Persistent activity in neural networks with dynamic synapses

Persistent activity states (attractors), observed in several neocortical areas after the removal of a sensory stimulus, are believed to be the neuronal basis of working memory. One of the possible mechanisms that can underlie persistent activity is recurrent excitation mediated by intracortical synaptic connections. A recent experimental study revealed that connections between pyramidal cells in prefrontal cortex exhibit various degrees of synaptic depression and facilitation. Here we analyze the effect of synaptic dynamics on the emergence and persistence of attractor states in interconnected neural networks. We show that different combinations of synaptic depression and facilitation result in qualitatively different network dynamics with respect to the emergence of the attractor states. This analysis raises the possibility that the framework of attractor neural networks can be extended to represent time-dependent stimuli.     

Functional nodes in dynamic neural networks for bioprocess modelling

This contribution presents a novel method for the direct integration of a-priori knowledge in a neural network and its application for the online determination of a secondary metabolite during industrial yeast fermentation. Hereby, existing system knowledge is integrated in an artificial neural network (ANN) by means of 'functional nodes'. A generalized backpropagation algorithm is presented. For illustration, a set of ordinary differential equations describing the diacetyl formation and degradation during the cultivation is incorporated in a functional node and integrated in a dynamic feedforward neural network in a hybrid manner. The results show that a hybrid modelling approach exploiting available a-priori knowledge and experimental data can considerably outperform a pure data-based modelling approach with respect to robustness, generalization and necessary amount of training data. The number of training sets were decreased by 50%, obtaining the same accuracy as in a conventional approach. All incorrect decisions, according to defined cost criteria obtained with the conventional ANN, were avoided.     

Prediction of membrane protein types by means of wavelet analysis and cascaded neural networks

In this study, membrane proteins were classified using the information hidden in their sequences. It was achieved by applying the wavelet analysis to the sequences and consequently extracting several features, each of them revealing a proportion of the information content present in the sequence. The resultant features were made normalized and subsequently fed into a cascaded model developed in order to reduce the effect of the existing bias in the dataset, rising from the difference in size of the membrane protein classes. The results indicate an improvement in prediction accuracy of the model in comparison with similar works. The application of the presented model can be extended to other fields of structural biology due to its efficiency, simplicity and flexibility.     

Targeted maximum likelihood estimation for dynamic treatment regimes in sequentially randomized controlled trials

Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the search for optimized treatment regimes in ongoing treatment settings. Analyzing data for multiple time-point treatments with a view toward optimal treatment regimes is of interest in many types of afflictions: HIV infection, Attention Deficit Hyperactivity Disorder in children, leukemia, prostate cancer, renal failure, and many others. Methods for analyzing data from SRCTs exist but they are either inefficient or suffer from the drawbacks of estimating equation methodology. We describe an estimation procedure, targeted maximum likelihood estimation (TMLE), which has been fully developed and implemented in point treatment settings, including time to event outcomes, binary outcomes and continuous outcomes. Here we develop and implement TMLE in the SRCT setting. As in the former settings, the TMLE procedure is targeted toward a pre-specified parameter of the distribution of the observed data, and thereby achieves important bias reduction in estimation of that parameter. As with the so-called Augmented Inverse Probability of Censoring Weight (A-IPCW) estimator, TMLE is double-robust and locally efficient. We report simulation results corresponding to two data-generating distributions from a longitudinal data structure.     

Training feedforward neural networks with dynamic particle swarm optimisation

Particle swarm optimisation has been successfully applied to train feedforward neural networks in static environments. Many real-world problems to which neural networks are applied are dynamic in the sense that the underlying data distribution changes over time. In the context of classification problems, this leads to concept drift where decision boundaries may change over time. This article investigates the applicability of dynamic particle swarm optimisation algorithms as neural network training algorithms under the presence of concept drift.     

Information maintenance and statistical dependence reduction in simple neural networks

This study compares the ability of excitatory, feed-forward neural networks to construct good transformations on their inputs. The quality of such a transformation is judged by the minimization of two information measures: the information loss of the transformation and the statistical dependency of the output. The networks that are compared differ from each other in the parametric properties of their neurons and in their connectivity. The particular network parameters studied are output firing threshold, synaptic connectivity, and associative modification of connection weights. The network parameters that most directly affect firing levels are threshold and connectivity. Networks incorporating neurons with dynamic threshold adjustment produce better transformations. When firing threshold is optimized, sparser synaptic connectivity produces a better transformation than denser connectivity. Associative modification of synaptic weights confers only a slight advantage in the construction of optimal transformations. Additionally, our research shows that some environments are better suited than others for recoding. Specifically, input environments high in statistical dependence, i.e. those environments most in need of recoding, are more likely to undergo successful transformations.     

Some new stability properties of dynamic neural networks with different time-scales

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of these networks to be stable. The main contribution of the paper is that Lyapunov function and singularly perturbed technique are combined to access several new stable properties of different time-scales neural networks. Exponential stability and asymptotic stability are obtained by sector and bound conditions. Compared to other papers, these conditions are simpler. Numerical examples are given to demonstrate the effectiveness of the theoretical results.     

Information processing in echo state networks at the edge of chaos

We investigate information processing in randomly connected recurrent neural networks. It has been shown previously that the computational capabilities of these networks are maximized when the recurrent layer is close to the border between a stable and an unstable dynamics regime, the so called edge of chaos. The reasons, however, for this maximized performance are not completely understood. We adopt an information-theoretical framework and are for the first time able to quantify the computational capabilities between elements of these networks directly as they undergo the phase transition to chaos. Specifically, we present evidence that both information transfer and storage in the recurrent layer are maximized close to this phase transition, providing an explanation for why guiding the recurrent layer toward the edge of chaos is computationally useful. As a consequence, our study suggests self-organized ways of improving performance in recurrent neural networks, driven by input data. Moreover, the networks we study share important features with biological systems such as feedback connections and online computation on input streams. A key example is the cerebral cortex, which was shown to also operate close to the edge of chaos. Consequently, the behavior of model systems as studied here is likely to shed light on reasons why biological systems are tuned into this specific regime.     

Flexible vowel recognition by the generation of dynamic coherence in oscillator neural networks: speaker-independent vowel recognition

We propose a new model for speaker-independent vowel recognition which uses the flexibility of the dynamic linking that results from the synchronization of oscillating neural units. The system consists of an input layer and three neural layers, which are referred to as the A-, B- and C-centers. The input signals are a time series of linear prediction (LPC) spectrum envelopes of auditory signals. At each time-window within the series, the A-center receives input signals and extracts local peaks of the spectrum envelope, i.e., formants, and encodes them into local groups of independent oscillations. Speaker-independent vowel characteristics are embedded as a connection matrix in the B-center according to statistical data of Japanese vowels. The associative interaction in the B-center and reciprocal interaction between the A- and B-centers selectively activate a vowel as a global synchronized pattern over two centers. The C-center evaluates the synchronized activities among the three formant regions to give the selective output of the category among the five Japanese vowels. Thus, a flexible ability of dynamical linking among features is achieved over the three centers. The capability in the present system was investigated for speaker-independent recognition of Japanese vowels. The system demonstrated a remarkable ability for the recognition of vowels very similar to that of human listeners, including misleading vowels. In addition, it showed stable recognition for unsteady input signals and robustness against background noise. The optimum condition of the frequency of oscillation is discussed in comparison with stimulus-dependent synchronizations observed in neurophysiological experiments of the cortex. Received: 20 July 1993/Accepted in revised form: 22 December 1993     

Information processing in large-scale cerebral networks: the causal connectivity approach

Today, cognitive functions are considered to be the offspring of the activity of large-scale networks of functionally interconnected cerebral regions. The interpretation of cerebral activation data provided by functional imaging has therefore recently moved to the search for the effective connectivity of activated regions, which aims at understanding the role of anatomical links in the activation propagation. Our assumption is that only causal connectivity can offer a real understanding of the links between brain and mind. Causal connectivity is based on the anatomical connection pattern, the information processing within cerebral regions and the causal influences that connected regions exert on each other. In our approach, the information processing within a region is implemented by a causal network of functional primitives, which are the interpretation of integrated biological properties. Our choice of a qualitative representation of information reflects the fact that cerebral activation data are only the approximate view, provided by imaging techniques, of the real cerebral activity. This explicit modeling approach allows the formulation and the simulation of functional and physiological assumptions about activation data. Two alternative models explaining results of the striate cortex activation described by Fox and Raichle (Fox PT, Raichle ME (1984) J. Neurophysiol 51:1109–1120; Fox PT, Raichle ME (1985) Ann Neurol 17:303–305) are provided as an example of our approach. Received: 22 December 1998 / Accepted in revised form: 23 June 1999     

Characterizing multistationarity regimes in biochemical reaction networks

Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.     

Exact results for the average dynamic behavior of some non-linear neural networks

We have studied the global dynamic behavior of neural-like networks of synchronous threshold elements by writing a master equation as a function of parameter values using statistical methods. Exact results for highly connected networks and no correlation are obtained, showing that in this case (contrary to previous results) the average activity can only display simple stable behaviour, the sole exception being special cases of a slow passage through a tangent bifurcation, and a limit cycle of length two. By introducing an appropriate probabilistic hypothesis, we also study the average activity and correlation for highly connected networks with the topology of a (Cayley) tree. In this case the dynamic is ruled by a pair of coupled equations linking activity and correlation, and the tendency is for the correlation to dispappear over time. However, under reasonable biological conditions, this tendency will be extremely slow, giving rise to a region of pseudo-stability.     

Optimization of chemical libraries by neural networks

Neural networks are finding ever-more applications in the design of combinatorial libraries. These can be divided into two types: Kohonen (self-organizing) maps, and feed-forward networks. While the number of applications is currently quite limited, a rapid increase in publications in this area can be expected in the next few years from the rapid development of general combinatorial chemistry technology.     

Sensory processing by neural circuits in Caenorhabditis elegans

The anatomical and developmental constancy of Caenorhabditis elegans belies the complexity of its numerically small nervous system. Indeed, there is an increased appreciation of C. elegans as an organism to study systems level questions. Many recent studies focus on the circuits that control locomotion, egg-laying, and male mating behaviors and their modulation by multiple sensory stimuli.     

Reward ignorant modeling of dynamic treatment regimes

Personalized medicine optimizes patient outcome by tailoring treatments to patient‐level characteristics. This approach is formalized by dynamic treatment regimes (DTRs): decision rules that take patient information as input and output recommended treatment decisions. The DTR literature has seen the development of increasingly sophisticated causal inference techniques that attempt to address the limitations of our typically observational datasets. Often overlooked, however, is that in practice most patients may be expected to receive optimal or near‐optimal treatment, and so the outcome used as part of a typical DTR analysis may provide limited information. In light of this, we propose considering a more standard analysis: ignore the outcome and elicit an optimal DTR by modeling the observed treatment as a function of relevant covariates. This offers a far simpler analysis and, in some settings, improved optimal treatment identification. To distinguish this approach from more traditional DTR analyses, we term it reward ignorant modeling, and also introduce the concept of multimethod analysis, whereby different analysis methods are used in settings with multiple treatment decisions. We demonstrate this concept through a variety of simulation studies, and through analysis of data from the International Warfarin Pharmacogenetics Consortium, which also serve as motivation for this work.