Simultaneous unsupervised and supervised learning of cognitive functions in biologically plausible spiking neural networks

Simultaneous unsupervised and supervised learning of cognitive functions in biologically plausible spiking neural networks Trevor Bekolay (tbekolay@uwaterloo.ca) Carter Kolbeck (ckolbeck@uwaterloo.ca) Chris Eliasmith (celiasmith@uwaterloo.ca) Center for Theoretical Neuroscience, University of Waterloo 200 University Ave., Waterloo, ON N2L 3G1 Canada Abstract overcomes these limitations. Our approach 1) remains func- tional during online learning, 2) requires only two layers con- nected with simultaneous supervised and unsupervised learn- ing, and 3) employs spiking neuron models to reproduce cen- tral features of biological learning, such as spike-timing de- pendent plasticity (STDP). We present a novel learning rule for learning transformations of sophisticated neural representations in a biologically plau- sible manner. We show that the rule, which uses only infor- mation available locally to a synapse in a spiking network, can learn to transmit and bind semantic pointers. Semantic pointers have previously been used to build Spaun, which is currently the world’s largest functional brain model (Eliasmith et al., 2012). Two operations commonly performed by Spaun are semantic pointer binding and transmission. It has not yet been shown how the binding and transmission operations can be learned. The learning rule combines a previously proposed supervised learning rule and a novel spiking form of the BCM unsupervised learning rule. We show that spiking BCM in- creases sparsity of connection weights at the cost of increased signal transmission error. We also demonstrate that the com- bined learning rule can learn transformations as well as the supervised rule and the offline optimization used previously. We also demonstrate that the combined learning rule is more robust to changes in parameters and leads to better outcomes in higher dimensional spaces, which is critical for explaining cognitive performance on diverse tasks. Keywords: synaptic plasticity; spiking neural networks; unsu- pervised learning; supervised learning; Semantic Pointer Ar- chitecture; Neural Engineering Framework. Online learning with spiking neuron models faces signifi- cant challenges due to the temporal dynamics of spiking neu- rons. Spike rates cannot be used directly, and must be esti- mated with causal filters, producing a noisy estimate. When the signal being estimated changes, there is some time lag before the spiking activity reflects the new signal, resulting in situations during online learning in which the inputs and de- sired outputs are out of sync. Our approach is robust to these sources of noise, while only depending on quantities that are locally available to a synapse. Other techniques doing similar types of learning in spik- ing neural networks (e.g., SpikeProp [Bohte, Kok, & Poutre, 2002], ReSuMe [Ponulak, 2006]) can learn only simple op- erations, such as learning to spike at a specific time. Oth- ers (e.g., SORN [Lazar, Pipa, & Triesch, 2009], reservoir computing approaches [Paugam-Moisy, Martinez, & Bengio, 2008]) can solve complex tasks like classification, but it is not clear how these approaches can be applied to a general cogni- tive system. The functions learned by our approach are com- plex and have already been combined into a general cognitive system called the Semantic Pointer Architecture (SPA). Pre- viously, the SPA has been used to create Spaun, a brain model made up of 2.5 million neurons that can do eight diverse tasks (Eliasmith et al., 2012). Spaun accomplishes these tasks by transmitting and manipulating semantic pointers, which are compressed neural representations that carry surface seman- tic content, and can be decompressed to generate deep se- mantic content (Eliasmith, in press). Semantic pointers are composed to represent syntactic structure using a “binding” transformation, which compresses the information in two se- mantic pointers into a single semantic pointer. Such repre- sentations can be “collected” using superposition, and col- lections can participate in further bindings to generate deep structures. Spaun performs these transformations by using the Neural Engineering Framework (NEF; Eliasmith & An- derson, 2003) to directly compute static connection weights between populations. We show that our approach can learn to transmit, bind, and classify semantic pointers. In this paper, we demonstrate learning of cognitively rele- vant transformations of neural representations online and in a biologically plausible manner. We improve upon a tech- nique previously presented in MacNeil and Eliasmith (2011) by combining their error-minimization learning rule with an unsupervised learning rule, making it more biologically plau- sible and robust. There are three weaknesses with most previous attempts at combining supervised and unsupervised learning in artificial neural networks (e.g., Backpropagation [Rumelhart, Hinton, & Williams, 1986], Self-Organizing Maps [Kohonen, 1982], Deep Belief Networks [Hinton, Osindero, & Teh, 2006]). These approaches 1) have explicit offline training phases that are distinct from functional use of the network, 2) re- quire many layers with some layers connected with super- vised learning and others with unsupervised learning, and 3) use non-spiking neuron models. The approach proposed here BCM Bienenstock, Cooper, Munro learning rule; Eq (7) hPES Homeostatic Prescribed Error Sensitivity; Eq (9) NEF Neural Engineering Framework; see Theory PES Prescribed Error Sensitivity; Eq (6) SPA Semantic Pointer Architecture; see Theory STDP Spike-timing dependent plasticity (Bi & Poo, 2001)

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