The primate visual system learns to recognize the true direction of pattern motion using local detectors only capable of detecting the component of motion perpendicular the orientation of the moving edge. A multilayer feedforward network model similar to Linsker's model was presented with input patterns each consisting of randomly oriented contours moving in a particular direction. Input layer units are granted component direction and speed tuning curves similar to those recorded from neurons in primate visual area VI that project to area MT. The network is trained on many such patterns until most weights saturate. A proportion of the units in the second layer solve the aperture problem (e.g., show the to gratings), same direction-tuning curve peak resembling pattern-direction selective neurons, which ftrst appear inareaMT.

Sereno, 1987) showed that a feedforward network with area VI-like input-layer units and a Hebb rule can develop area MT-like second layer units that solve the aperture problem for pattern motion. The present study extends this earlier work to more complex motions. Saito et al. (1986) showed that neurons with large receptive fields in macaque visual area MST are sensitive to different senses of rotation and dilation, irrespective of the receptive field location of the movement singularity. A network with an MT-like second layer was trained and tested on combinations of rotating, dilating, and translating patterns. Third-layer units learn to detect specific senses of rotation or dilation in a position-independent fashion, despite having position-dependent direction selectivity within their receptive fields.

Motivated by biological considerations, we study sparse neural maps from an input layer to a target layer with sparse activity, and specifically the problem of storing $K$ input-target associations $(x,y)$, or memories, when the target vectors $y$ are sparse. We mathematically prove that $K$ undergoes a phase transition and that in general, and somewhat paradoxically, sparsity in the target layers increases the storage capacity of the map. The target vectors can be chosen arbitrarily, including in random fashion, and the memories can be both encoded and decoded by networks trained using local learning rules, including the simple Hebb rule. These results are robust under a variety of statistical assumptions on the data. The proofs rely on elegant properties of random polytopes and sub-gaussian random vector variables. Open problems and connections to capacity theories and polynomial threshold maps are discussed.

Uncertainty is omnipresent when we perceive or interact with our environment, and the Bayesian framework provides computational methods for dealing with it. Mathematical models for Bayesian decision making typically require datastructures that are hard to implement in neural networks. This article shows that even the simplest and experimentally best supported type of synaptic plasticity, Hebbian learning, in combination with a sparse, redundant neural code, can in principle learn to infer optimal Bayesian decisions. We present a concrete Hebbian learning rule operating on log-probability ratios. Modulated by reward-signals, this Hebbian plasticity rule also provides a new perspective for understanding how Bayesian inference could support fast reinforcement learning in the brain. In particular we show that recent experimental results by Yang and Shadlen [1] on reinforcement learning of probabilistic inference in primates can be modeled in this way.

In the mammalian visual cortex, orientation-selective'simple cells' which detect straight lines may be adapted to detect curved lines instead. We test a biologically plausible, Hebbian, single-neuron model, which learns oriented receptive fields upon exposure to unstructured (noise) input and maintains orientation selectivity upon exposure to edges or bars of all orientations and positions. This model can also learn arc-shaped receptive fields upon exposure to an environment of only circular rings. Thus, new experiments which try to induce an abnormal (curved) receptive field may provide insight into the plasticity of simple cells. The model suggests that exposing cells to only a single spatial frequency may induce more striking spatial frequency and orientation dependent effects than heretofore observed.

In the mammalian visual cortex, orientation-selective'simple cells' which detect straight lines may be adapted to detect curved lines instead. We test a biologically plausible, Hebbian, single-neuron model, which learns oriented receptive fields upon exposure to unstructured (noise) input and maintains orientation selectivity upon exposure to edges or bars of all orientations and positions. This model can also learn arc-shaped receptive fields upon exposure to an environment of only circular rings. Thus, new experiments which try to induce an abnormal (curved) receptive field may provide insight into the plasticity of simple cells. The model suggests that exposing cells to only a single spatial frequency may induce more striking spatial frequency and orientation dependent effects than heretofore observed.

In the mammalian visual cortex, orientation-selective'simple cells' which detect straight lines may be adapted to detect curved lines instead. We test a biologically plausible, Hebbian, single-neuron model, which learns oriented receptive fields upon exposure to unstructured (noise)input and maintains orientation selectivity upon exposure to edges or bars of all orientations and positions. This model can also learn arc-shaped receptive fields upon exposure to an environment of only circular rings. Thus, new experiments which try to induce an abnormal (curved) receptive field may provide insightinto the plasticity of simple cells. The model suggests that exposing cells to only a single spatial frequency may induce more striking spatial frequency and orientation dependent effects than heretofore observed.