Temporal Map Formation in the Barn Owl’s Brain

Barn owls provide an experimentally well-specified example of a temporal map, a neuronal representation of the outside world in the brain by means of time. Their laminar nucleus exhibits a place code of interaural time differences, a cue which is used to determine the azimuthal location of a sound stimulus, e.g., prey. We analyze a model of synaptic plasticity that explains the formation of such a representation in the young bird and show how in a large parameter regime a combination of local and nonlocal synaptic plasticity yields the temporal map as found experimentally. Our analysis includes the effect of nonlinearities as well as the influence of neuronal noise

Structure, Dynamics and Self-Organization in Recurrent Neural Networks: From Machine Learning to Theoretical Neuroscience

At a first glance, artificial neural networks, with engineered learning algorithms and carefully chosen nonlinearities, are nothing like the complicated self-organized spiking neural networks studied by theoretical neuroscientists. Yet, both adapt to their inputs, keep information from the past in their state space and are able of learning, implying that some information processing principles should be common to both. In this thesis we study those principles by incorporating notions of systems theory, statistical physics and graph theory into artificial neural networks and theoretical neuroscience models. % TO DO: What is different in this thesis? -> classical signal processing with complex systems on top The starting point for this thesis is \ac{RC}, a learning paradigm used both in machine learning\cite{jaeger2004harnessing} and in theoretical neuroscience\cite{maass2002real}. A neural network in \ac{RC} consists of two parts, a reservoir – a directed and weighted network of neurons that projects the input time series onto a high dimensional space – and a readout which is trained to read the state of the neurons in the reservoir and combine them linearly to give the desired output. In classical \ac{RC}, the reservoir is randomly initialized and left untrained, which alleviates the training costs in comparison to other recurrent neural networks. However, this lack of training implies that reservoirs are not adapted to specific tasks and thus their performance is often lower than that of other neural networks. Our contribution has been to show how knowledge about a task can be integrated into the reservoir architecture, so that reservoirs can be tailored to specific problems without training. We do this design by identifying two features that are useful for machine learning: the memory of the reservoir and its power spectra. First we show that the correlations between neurons limit the capacity of the reservoir to retain traces of previous inputs, and demonstrate that those correlations are controlled by moduli of the eigenvalues of the adjacency matrix of the reservoir. Second, we prove that when the reservoir resonates at the frequencies that are present on the desired output signal, the performance of the readout increases. Knowing the features of the reservoir dynamics that we need, the next question is how to impose them. The simplest way to design a network with that resonates at a certain frequency is by adding cycles, which act as feedback loops, but this also induces correlations and hence memory modifications. To disentangle the frequencies and the memory design, we studied how the addition of cycles modifies the eigenvalues in the adjacency matrix of the network. Surprisingly, the shape of the eigenvalues is quite beautiful \cite{aceituno2019universal} and can be characterized using random matrix theory tools. Combining this knowledge with our result relating eigenvalues and correlations, we designed an heuristic that tailors reservoirs to specific tasks and showed that it improves upon state of the art \ac{RC} in three different machine learning tasks. Although this idea works in the machine learning version of \ac{RC}, there is one fundamental problem when we try to translate to the world of theoretical neuroscience: the proposed frequency adaptation requires prior knowledge of the task, which might not be plausible in a biological neural network. Therefore the following questions are whether those resonances can emerge by unsupervised learning, and which kind of learning rules would be required. Remarkably, these resonances can be induced by the well-known Spike Time-Dependent Plasticity (STDP) combined with homeostatic mechanisms. We show this by deriving two self-consistent equations: one where the activity of every neuron can be calculated from its synaptic weights and its external inputs and a second one where the synaptic weights can be obtained from the neural activity. By considering spatio-temporal symmetries in our inputs we obtained two families of solutions to those equations where a periodic input is enhanced by the neural network after STDP. This approach shows that periodic and quasiperiodic inputs can induce resonances that agree with the aforementioned \ac{RC} theory. Those results, although rigorous, are expressed on a language of statistical physics and cannot be easily tested or verified in real, scarce data. To make them more accessible to the neuroscience community we showed that latency reduction, a well-known effect of STDP\cite{song2000competitive} which has been experimentally observed \cite{mehta2000experience}, generates neural codes that agree with the self-consistency equations and their solutions. In particular, this analysis shows that metabolic efficiency, synchronization and predictions can emerge from that same phenomena of latency reduction, thus closing the loop with our original machine learning problem. To summarize, this thesis exposes principles of learning recurrent neural networks that are consistent with adaptation in the nervous system and also improve current machine learning methods. This is done by leveraging features of the dynamics of recurrent neural networks such as resonances and correlations in machine learning problems, then imposing the required dynamics into reservoir computing through control theory notions such as feedback loops and spectral analysis. Then we assessed the plausibility of such adaptation in biological networks, deriving solutions from self-organizing processes that are biologically plausible and align with the machine learning prescriptions. Finally, we relate those processes to learning rules in biological neurons, showing how small local adaptations of the spike times can lead to neural codes that are efficient and can be interpreted in machine learning terms