Photonic Delay Systems as Machine Learning Implementations

Nonlinear photonic delay systems present interesting implementation platforms for machine learning models. They can be extremely fast, offer great degrees of parallelism and potentially consume far less power than digital processors. So far they have been successfully employed for signal processing using the Reservoir Computing paradigm. In this paper we show that their range of applicability can be greatly extended if we use gradient descent with backpropagation through time on a model of the system to optimize the input encoding of such systems. We perform physical experiments that demonstrate that the obtained input encodings work well in reality, and we show that optimized systems perform significantly better than the common Reservoir Computing approach. The results presented here demonstrate that common gradient descent techniques from machine learning may well be applicable on physical neuro-inspired analog computers

Bayesian Recurrent Neural Network Models for Forecasting and Quantifying Uncertainty in Spatial-Temporal Data

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep learning models have become more common, RNNs have been used to forecast increasingly complicated systems. Dynamical spatio-temporal processes represent a class of complex systems that can potentially benefit from these types of models. Although the RNN literature is expansive and highly developed, uncertainty quantification is often ignored. Even when considered, the uncertainty is generally quantified without the use of a rigorous framework, such as a fully Bayesian setting. Here we attempt to quantify uncertainty in a more formal framework while maintaining the forecast accuracy that makes these models appealing, by presenting a Bayesian RNN model for nonlinear spatio-temporal forecasting. Additionally, we make simple modifications to the basic RNN to help accommodate the unique nature of nonlinear spatio-temporal data. The proposed model is applied to a Lorenz simulation and two real-world nonlinear spatio-temporal forecasting applications

Intrinsically-generated fluctuating activity in excitatory-inhibitory networks

Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in networks of deterministic, but randomly connected rate units. How this type of intrinsi- cally generated fluctuations appears in more realistic networks of spiking neurons has been a long standing question. To ease the comparison between rate and spiking networks, recent works investigated the dynami- cal regimes of randomly-connected rate networks with segregated excitatory and inhibitory populations, and firing rates constrained to be positive. These works derived general dynamical mean field (DMF) equations describing the fluctuating dynamics, but solved these equations only in the case of purely inhibitory networks. Using a simplified excitatory-inhibitory architecture in which DMF equations are more easily tractable, here we show that the presence of excitation qualitatively modifies the fluctuating activity compared to purely inhibitory networks. In presence of excitation, intrinsically generated fluctuations induce a strong increase in mean firing rates, a phenomenon that is much weaker in purely inhibitory networks. Excitation moreover induces two different fluctuating regimes: for moderate overall coupling, recurrent inhibition is sufficient to stabilize fluctuations, for strong coupling, firing rates are stabilized solely by the upper bound imposed on activity, even if inhibition is stronger than excitation. These results extend to more general network architectures, and to rate networks receiving noisy inputs mimicking spiking activity. Finally, we show that signatures of the second dynamical regime appear in networks of integrate-and-fire neurons

Model-free reconstruction of neuronal network connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the effective network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (e.g., bursting or non-bursting). We thus demonstrate how conditioning with respect to the global mean activity improves the performance of our method. [...] Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good reconstruction of the network clustering coefficient, allowing to discriminate between weakly or strongly clustered topologies, whereas on the other hand an approach based on cross-correlations would invariantly detect artificially high levels of clustering. Finally, we present the applicability of our method to real recordings of in vitro cortical cultures. We demonstrate that these networks are characterized by an elevated level of clustering compared to a random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted for publicatio

Oscillations, metastability and phase transitions in brain and models of cognition

Neuroscience is being practiced in many different forms and at many different organizational levels of the Nervous System. Which of these levels and associated conceptual frameworks is most informative for elucidating the association of neural processes with processes of Cognition is an empirical question and subject to pragmatic validation. In this essay, I select the framework of Dynamic System Theory. Several investigators have applied in recent years tools and concepts of this theory to interpretation of observational data, and for designing neuronal models of cognitive functions. I will first trace the essentials of conceptual development and hypotheses separately for discerning observational tests and criteria for functional realism and conceptual plausibility of the alternatives they offer. I will then show that the statistical mechanics of phase transitions in brain activity, and some of its models, provides a new and possibly revealing perspective on brain events in cognition

Scaling of a large-scale simulation of synchronous slow-wave and asynchronous awake-like activity of a cortical model with long-range interconnections

Cortical synapse organization supports a range of dynamic states on multiple spatial and temporal scales, from synchronous slow wave activity (SWA), characteristic of deep sleep or anesthesia, to fluctuating, asynchronous activity during wakefulness (AW). Such dynamic diversity poses a challenge for producing efficient large-scale simulations that embody realistic metaphors of short- and long-range synaptic connectivity. In fact, during SWA and AW different spatial extents of the cortical tissue are active in a given timespan and at different firing rates, which implies a wide variety of loads of local computation and communication. A balanced evaluation of simulation performance and robustness should therefore include tests of a variety of cortical dynamic states. Here, we demonstrate performance scaling of our proprietary Distributed and Plastic Spiking Neural Networks (DPSNN) simulation engine in both SWA and AW for bidimensional grids of neural populations, which reflects the modular organization of the cortex. We explored networks up to 192x192 modules, each composed of 1250 integrate-and-fire neurons with spike-frequency adaptation, and exponentially decaying inter-modular synaptic connectivity with varying spatial decay constant. For the largest networks the total number of synapses was over 70 billion. The execution platform included up to 64 dual-socket nodes, each socket mounting 8 Intel Xeon Haswell processor cores @ 2.40GHz clock rates. Network initialization time, memory usage, and execution time showed good scaling performances from 1 to 1024 processes, implemented using the standard Message Passing Interface (MPI) protocol. We achieved simulation speeds of between 2.3x10^9 and 4.1x10^9 synaptic events per second for both cortical states in the explored range of inter-modular interconnections.Comment: 22 pages, 9 figures, 4 table