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cc18:relational-networks-for-goal-directed-sensory-motor-task:overview

Abstract

Recent advances in conventional machine learning approaches to construct autonomous intelligent systems still lag behind biological computing architectures in terms of power consumption and computational versatility. Major differences between networks trained using standard machine learning techniques compared to their biological counterparts are the degree of recurrence and general objective to approximate a given input-output function rather than generic relations between quantities.

This motivates us to explore and build biologically inspired computing architectures, which focus on relation, rather than function approximation, by exploiting temporal properties of spiking neurons. This spiking network architecture can be implemented on dedicated “neuromorphic” hardware which optimally exploits the computational properties of spiking neurons. We will build a (relatively) simple spiking neuronal network implementing a goal-directed state-to-action mapping (SAG) unit. As a core architecture, we will use a three-way relation network proposed by [1]. However, we would like to translate the rate-coding scheme into spike time coding scheme to exploit the spatio-temporal sparsity of the network.

The aim of this workshop is to implement and test a “hard-wired” version of this relational network on a neuromorphic processor (e.g. the DYNAP-SE chip), encoding behavior (i.e. mapping the Stimulus position to the Pointer position) of an “agent” for various goals: (a) following the stimulus, (b) avoiding the stimulus, © keeping a fixed distance to the stimulus.

Workshop description

1. Motivation

Despite recent advances in machine learning approaches to build intelligent systems, biological neural structures still outperform any artificial systems in terms of computational versatility and power consumption. This motivates us to explore and build biologically inspired adaptive computing architectures, exploiting properties of spiking neurons, including dedicated “neuromorphic” [2] hardware. In particular, we aim to explore the functional property of biological structures of representing the relations between its bidirectionally coupled units rather than learning (feedforward) functions.

2. Proposed solution

We will build a (relatively) simple spiking neuronal network implementing a goal-directed state-to-action mapping (SAG) unit. As a core architecture, we will use a three-way relation network proposed by Peter Diehl [1] (see Fig 1 on the left). This unit consists of four recurrently connected populations of neurons (nodes), three of which represent one-dimensional variables and the fourth one encodes a relation between them (e.g. A + B - C = 0). A crucial step in translating the proposed architecture in [1] to our specified task (see below) is to change the input from a rate encoded Poisson spike train representing a certain value, to a spatially arranged winner-takes-all (WTA) population where the position of an active neuron represents its value independent of the rate of activity.

To achieve the aforementioned mapping and regarding the goal-driven motor control task we are trying to solve in this workgroup, node S would represent sensory input, node A would represent action and node G would represent the goal, currently selected as “relevant”. Unlike S and A, G would only have discrete values (G1, G2, etc.), determining a concrete relation between S and A for any given G. This totally agrees with examples of relations in Diehl’s work, except that instead of a plane in a 3D {S, A, G} space we will see A(S) lines in discrete G-planes (see Fig 1 on the right).

The aim of this workshop is to implement and test a “hard-wired” version of this relational network on the DYNAP-SE [3] chip, encoding behavior (i.e. mapping the stimulus position to the pointer position) of an “agent” for various goals: (a) following the stimulus, (b) avoiding the stimulus, © keeping a fixed distance to the stimulus. As a result, we will get a working building block for a scalable hierarchical network of cooperative controllers [4], simultaneously operating on various levels of abstraction of states, actions, and goals.

3. Anticipated challenges

Since in the original model all weights were converging to the desired state by STDP learning, here we will have to clarify the exact wiring between nodes to introduce the relations by hand. The trickiest part would be to understand what happens in the hidden population H, which actually encodes our three-way relation.

Another significant constraint is caused by the DYNAP-SE chip limitations, which, due to its architecture restricts the number of incoming synapses per neuron to 64 in total and possible weight values to four. Finally, tuning the populations’ excitation versus inhibition parameters to achieve stable and robust Winner-take-all behavior will also be a challenge.

4. Expected working steps

1. Using Brian2 simulator (and, possibly, ncs_brian library [5]), flash out the connectivity of a network of AdExp-Leaky-Integrate-and-Fire neurons, having 256 neurons in populations S, A and H each, and 30 neurons in population G. Each population should consist of sparsely connected 80% of excitatory and 20% inhibitory neurons. Input and output should be coded as localized Gaussian peaks of population activity, which allows us to detach the encoded value from the population firing rate. In case it will not be possible to derive the connectivity analytically, the network should be trained with samples of the A(S,G) relation shown on Figure 1.

2. Once the connectivity is established, it should be mapped onto the DYNAP-SE chip. Given the provided input for S and G populations, A population should exhibit an adequate response regardless of possible noise and single faulty neurons or synapses.

Figure 1: LEFT PANEL: Adapted figure from [1] showing a scheme of a three-way relational network. Yellow circles represent populations of LIF-neurons, blue circles represent inputs (given two input the network infers the remaining one). Blue arrows depict the direction of connections, emphasizing recurrent connectivity. For convenience of the “hard-wired” hardware implementation, the size of the S, A and H populations will be reduced to 256 neurons. The size of the G population will be reduced to 30 neurons. RIGHT PANEL: An example of state-to-action mapping for three various goals: (i) following the stimulus (G1), (ii) avoiding the stimulus (ii), © keeping a fixed distance from the stimulus (G3)

References:

[1] P. U. Diehl and M. Cook, “Learning and inferring relations in cortical networks,” arXiv preprint arXiv:1608.08267, 2016.

[2] E. Chicca, F. Stefanini, C. Bartolozzi, and G. Indiveri, “Neuromorphic electronic circuits for building autonomous cognitive systems,” Proceedings of the IEEE, vol. 102, no. 9, pp. 1367– 1388, 2014.

[3] S. Moradi, N. Qiao, F. Stefanini, and G. Indiveri, “A scalable multicore architecture with heterogeneous memory structures for dynamic neuromorphic asynchronous processors (dynaps),” IEEE Transactions on Biomedical Circuits and Systems, 2017.

[4] J. J. Buhmann, Networks of Cooperative Controllers for Distributed and Hierarchical Decision Making. PhD thesis, ETH Zurich, 2017.

[5] NCS_brian library is available at https://code.ini.uzh.ch/ncs/libs/ncs_brian

cc18/relational-networks-for-goal-directed-sensory-motor-task/overview.txt · Last modified: 2019/05/16 20:20 (external edit)