Large Associative Memory Problem in Neurobiology and Machine Learning

Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological, since it seemingly requires the existence of many-body synaptic junctions between the neurons. We show that these models are effective descriptions of a more microscopic (written in terms of biological degrees of freedom) theory that has additional (hidden) neurons and only requires two-body interactions between them. For this reason our proposed microscopic theory is a valid model of large associative memory with a degree of biological plausibility. The dynamics of our network and its reduced dimensional equivalent both minimize energy (Lyapunov) functions. When certain dynamical variables (hidden neurons) are integrated out from our microscopic theory, one can recover many of the models that were previously discussed in the literature, e.g. the model presented in ''Hopfield Networks is All You Need'' paper. We also provide an alternative derivation of the energy function and the update rule proposed in the aforementioned paper and clarify the relationships between various models of this class.

Local Unsupervised Learning for Image Analysis

Local Hebbian learning is believed to be inferior in performance to end-to-end training using a backpropagation algorithm. We question this popular belief by designing a local algorithm that can learn convolutional filters at scale on large image datasets. These filters combined with patch normalization and very steep non-linearities result in a good classification accuracy for shallow networks trained locally, as opposed to end-to-end. The filters learned by our algorithm contain both orientation selective units and unoriented color units, resembling the responses of pyramidal neurons located in the cytochrome oxidase 'interblob' and 'blob' regions in the primary visual cortex of primates. It is shown that convolutional networks with patch normalization significantly outperform standard convolutional networks on the task of recovering the original classes when shadows are superimposed on top of standard CIFAR-10 images. Patch normalization approximates the retinal adaptation to the mean light intensity, important for human vision. We also demonstrate a successful transfer of learned representations between CIFAR-10 and ImageNet 32x32 datasets. All these results taken together hint at the possibility that local unsupervised training might be a powerful tool for learning general representations (without specifying the task) directly from unlabeled data.

Unsupervised Learning by Competing Hidden Units

It is widely believed that the backpropagation algorithm is essential for learning good feature detectors in early layers of artificial neural networks, so that these detectors are useful for the task performed by the higher layers of that neural network. At the same time, the traditional form of backpropagation is biologically implausible. In the present paper we propose an unusual learning rule, which has a degree of biological plausibility, and which is motivated by Hebb's idea that change of the synapse strength should be local - i.e. should depend only on the activities of the pre and post synaptic neurons. We design a learning algorithm that utilizes global inhibition in the hidden layer, and is capable of learning early feature detectors in a completely unsupervised way. These learned lower layer feature detectors can be used to train higher layer weights in a usual supervised way so that the performance of the full network is comparable to the performance of standard feedforward networks trained end-to-end with a backpropagation algorithm.