The ability to predict future states of the world is essential for planning behavior, and it is arguably a central pillar of intelligence.  In the field of sensory neuroscience, "predictive coding" -- the notion that circuits in cerebral actively predict their own activity -- has been an influential theoretical framework for understanding visual cortex.  In my talk, I will bring together the idea of predictive coding with modern tools of machine learning to build practical, working vision models that predict their inputs in both space and time. These networks learn to predict future frames in a video sequence, with each layer in the network making local predictions and only forwarding deviations from those predictions to subsequent network layers. We show that these networks are able to robustly learn to predict the movement of synthetic (rendered) objects, and that in doing so, the networks learn internal representations that are useful for decoding latent object parameters (e.g. pose) that support object recognition with fewer training views. We also show that these networks can scale to complex natural image streams (car-mounted camera videos), capturing key aspects of both egocentric movement and the movement of objects in the visual scene, and generalizing well across video datasets. These results suggest that prediction represents a powerful framework for unsupervised learning, allowing for implicit learning of object and scene structure.  At the same time, we find that models trained for prediction also recapitulate a wide variety of findings in neuroscience and psychology, providing a touch point between deep learning and empirical neuroscience data.

Session Chair: Christos Papadimitriou

In recent years (deep) neural networks got the most prominent models for supervised machine learning tasks. They are usually trained based on stochastic gradient descent where backpropagation is used for the gradient calculation. While this leads to efficient training, it is not very plausible from a biological perspective.

We show that Langevin Markov chain Monte Carlo inference in an energy-based model with latent variables has the property that the early steps of inference, starting from a stationary point, correspond to propagating error gradients into internal layers, similar to backpropagation. Backpropagated error gradients correspond to temporal derivatives with respect to the activation of hidden units. These lead to a weight update proportional to the product of the presynaptic firing rate and the temporal rate of change of the postsynaptic firing rate. Simulations and a theoretical argument suggest that this rate-based update rule is consistent with those associated with spike-timing-dependent plasticity. These ideas could be an element of a theory for explaining how brains perform credit assignment in deep hierarchies as efficiently as backpropagation does, with neural computation corresponding to both approximate inference in continuous-valued latent variables and error backpropagation, at the same time.

Session Chair: Murray Sherman

Synaptic connections between neurons in the brain are dynamic because of continuously ongoing spine dynamics, axonal sprouting, and other processes. In fact, it was recently shown that the spontaneous synapse-autonomous component of spine dynamics is at least as large as the component that depends on the history of pre- and postsynaptic neural activity. These data are inconsistent with common models for network plasticity, and raise the questions how neural circuits can maintain a stable computational function in spite of these continuously ongoing processes, and what functional uses these ongoing processes might have. I will present a general theoretical framework that allows us to answer these questions. Our results indicate that spontaneous synapse-autonomous processes, in combination with reward signals such as dopamine, can explain the capability of networks of neurons in the brain to configure themselves for specific computational tasks, and to compensate automatically for later changes in the network or task.
On a more general level, the novel framework allows us to analyze synaptic plasticity and network rewiring from the viewpoint of stochastic optimization and sampling methods. As an example, I will show that the framework is also applicable to artificial neural networks, which provides as a side-effect new and effective brain-inspired methods for deep learning. 

References:

Kappel, D., Habenschuss, S., Legenstein, R., & Maass, W. (2015). Network plasticity as Bayesian inference. PLoS computational biology, 11(11), e1004485.

Kappel, D., Legenstein, R., Habenschuss, S., Hsieh, M., & Maass, W. (2018). A dynamic connectome supports the emergence of stable computational function of neural circuits through reward-based learning. arXiv preprint arXiv:1704.04238.

Bellec, G., Kappel, D., Maass, W., & Legenstein, R. (2017). Deep Rewiring: Training very sparse deep networks. arXiv preprint arXiv:1711.05136.

This talk will describe my recent work with Cameron Musco and Merav Parter, on studying neural networks from the perspective of the field of Distributed Algorithms.   In our project, we aim both to obtain interesting, elegant theoretical results, and also to draw relevant biological conclusions.

We base our work on simple Stochastic Spiking Neural Network (SSN) models, in which probabilistic neural components are organized into weighted directed graphs and execute in a synchronized fashion.  Our model captures the spiking behavior observed in real neural networks and reflects the widely accepted notion that spike responses, and neural computation in general, are inherently stochastic.  In most of our work so far, we have considered static networks, but the model would allow us to also consider learning by means of weight adjustments.

Specifically, we consider the implementation of various algorithmic primitives using stochastic SNNs.  We first consider a basic symmetry-breaking task that has been well studied in the computational neuroscience community:  the Winner-Take-All  (WTA)  problem.  WTA is believed to serve as a basic building block for many other tasks, such as learning, pattern recognition, and clustering.  In a simple version of the problem, we are given neurons with identical firing rates, and want to select a distinguished one.  Our main contribution is the explicit construction of a simple and efficient WTA network containing only two inhibitory neurons; our construction uses the stochastic behavior of SNNs in an essential way.  We give a complete proof of correctness and analysis of convergence time, using distributed algorithms proof methods.  In related results, we give an optimization of the simple two-inhibitor network that achieves better convergence time at the cost of more inhibitory neurons.  We also give lower bound results that show inherent limitations on the convergence time achievable with small numbers of inhibitory neurons.

We also consider the use of stochastic behavior in neural algorithms for Similarity Testing (ST).   In this problem, the network is supposed to distinguish, with high reliability, between input vectors that are identical and input vectors that are significantly different.  We construct a compact stochastic network that solves the ST problem, based on randomly sampling positions in the vectors.  At the heart of our solution is the design of a compact and fast-converging neural Random Access Memory (neuro-RAM)  mechanism.

In this talk, I will describe our SNN model and our work on Winner-Take-All, in some detail.  I will also summarize our work on Similarity Testing, discuss some important general issues such as compositionality, and suggest directions for future work.

Building a microscopically accurate model of a system as complex as a brain or even a single cell is hardly possible, and arguably not very useful. Can we use modern machine learning approaches to automate finding predictive phenomenological dynamical models of time series measured in experiments? I will discuss our approach to the problem, implemented as a software Package SirIsaac. I will show how the method performs in various synthetic test cases, as well as on building (and interpreting) a dynamical model of a reflexive escape from a painful stimulus by C. elegans.

Recent understanding of our nervous system reveals that sensory organs are optimized for efficient uptake of information from the environment to the brain. While bulk of the energy consumed in this process is to generate asynchronous action potentials for signal communication, evolutionary pressure has further optimized on this mode of communication within the brain for efficient representation and processing of information. We will explore this link between energy and information to reveal some of the mechanisms, circuits and energy efficient codes in the brain. The implications of this link will be important to consider for the design of neuromorphic systems of the future.

We investigate neural circuits in the exacting setting that (i) the acquisition of a piece of knowledge can occur from a single interaction, (ii) the result of each such interaction is a rapidly evaluatable subcircuit, (iii) hundreds of thousands of such subcircuits can be acquired in sequence without substantially degrading the earlier ones, and (iv) recall can be in the form of a rapid evaluation of a composition of subcircuits that have been so acquired at arbitrary different earlier times.

We develop a complexity theory, in terms of asymptotically matching upper and lower bounds, on the capacity of a neural network for executing, in this setting, the following action, which we call association: Each action sets up a subcircuit so that the excitation of a chosen set of neurons A will in future cause the excitation of another chosen set B. A succession of experiences, possibly over a lifetime, results in the realization of a complex set of subcircuits. The composability requirement constrains the model to ensure that, for each association as realized by a subcircuit, the excitation in the triggering set of neurons A is quantitatively similar to that in the triggered set B, and also that the unintended excitation in the rest of the system is negligible. These requirements ensure that chains of associations can be triggered.

We first analyze what we call the Basic Mechanism, which uses only direct connections between neurons in the triggering set A and the target set B. We consider random networks of n neurons with expected number d of connections to and from each. We show that in the composable context capacity growth is limited by d^2, a severe limitation if the network is sparse, as it is in cortex. We go on to study the Expansive Mechanism, that additionally uses intermediate relay neurons which have high synaptic weights. For this mechanism we show that the capacity can grow as dn, to within logarithmic factors. From these two results it follows that in the composable regime, for the realistic estimate of d being the square root of n, optimal superlinear capacity in terms of the neuron numbers can be realized by the Expansive Mechanism, instead of the linear order n to which the Basic Mechanism is limited.

Reference: L.G Valiant, Capacity of Neural Networks for Lifelong Learning of Composable Tasks,  Proc. 58th Annual IEEE Symposium on Foundations of Computer Science, October 15 - 17, 2017, Berkeley, California , 367-378 (2017).