LETTER Communicated by Aapo Hyvarinen Learning Slowness in a Sparse Model of Invariant Feature Detection Thusitha N. Chandrapala tnc@ust.hk Bertram E. Shi eebert@ee.ust.hk Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR Primary visual cortical complex cells are thought to serve as invariant fea- ture detectors and to provide input to higher cortical areas. We propose a single model for learning the connectivity required by complex cells that integrates two factors that have been hypothesized to play a role in the development of invariant feature detectors: temporal slowness and sparsity. This model, the generative adaptive subspace self-organizing map (GASSOM), extends Kohonen’s adaptive subspace self-organizing map (ASSOM) with a generative model of the input. Each observation is assumed to be generated by one among many nodes in the network, each being associated with a different subspace in the space of all obser- vations. The generating nodes evolve according to a first-order Markov chain and generate inputs that lie close to the associated subspace. This model differs from prior approaches in that temporal slowness is not an externally imposed criterion to be maximized during learning but, rather, an emergent property of the model structure as it seeks a good model of the input statistics. Unlike the ASSOM, the GASSOM does not require an explicit segmentation of the input training vectors into separate episodes. This enables us to apply this model to an unlabeled naturalistic image sequence generated by a realistic eye movement model. We show that the emergence of temporal slowness within the model improves the invari- ance of feature detectors trained on this input. 1 Introduction Many neurons in the visual cortex can be thought of as invariant feature detectors: they exhibit selectivity along certain stimulus dimensions and invariance along others. Processing in the visual cortex is often thought to be hierarchical, with neurons in higher areas elaborating on sensory repre- sentations encoded by lower areas. Neurons in higher areas are generally selective to more complex stimuli. For example, neurons in the inferior tem- poral (IT) cortex respond selectively to complex objects like faces (Perrett, Neural Computation 27, 1496–1529 (2015) c  2015 Massachusetts Institute of Technology doi:10.1162/NECO_a_00743