arXiv subjects

T. Anderson Keller

Publications and source records attributed to T. Anderson Keller.

22 records · Page 2Linked to original sources

arXiv2022

Topographic VAEs learn Equivariant Capsules

In this work we seek to bridge the concepts of topographic organization and equivariance in neural networks. To accomplish this, we introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. Furthermore, through topographic organization over time (i.e. temporal coherence), we demonstrate how predefined latent space transformation operators can be encouraged for observed transformed input sequences -- a primitive form of unsupervised learned equivariance. We demonstrate that this model successfully learns sets of approximately equivariant features (i.e. "capsules") directly from sequences and achieves higher likelihood on correspondingly transforming test sequences. Equivariance is verified quantitatively by measuring the approximate commutativity of the inference network and the sequence transformations. Finally, we demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks.

cs.LG↗

arXiv2021

Modeling Category-Selective Cortical Regions with Topographic Variational Autoencoders

Category-selectivity in the brain describes the observation that certain spatially localized areas of the cerebral cortex tend to respond robustly and selectively to stimuli from specific limited categories. One of the most well known examples of category-selectivity is the Fusiform Face Area (FFA), an area of the inferior temporal cortex in primates which responds preferentially to images of faces when compared with objects or other generic stimuli. In this work, we leverage the newly introduced Topographic Variational Autoencoder to model the emergence of such localized category-selectivity in an unsupervised manner. Experimentally, we demonstrate our model yields spatially dense neural clusters selective to faces, bodies, and places through visualized maps of Cohen's d metric. We compare our model with related supervised approaches, namely the Topographic Deep Artificial Neural Network (TDANN) of Lee et al., and discuss both theoretical and empirical similarities. Finally, we show preliminary results suggesting that our model yields a nested spatial hierarchy of increasingly abstract categories, analogous to observations from the human ventral temporal cortex.

q-bio.NC↗

arXiv2021

Self Normalizing Flows

Efficient gradient computation of the Jacobian determinant term is a core problem in many machine learning settings, and especially so in the normalizing flow framework. Most proposed flow models therefore either restrict to a function class with easy evaluation of the Jacobian determinant, or an efficient estimator thereof. However, these restrictions limit the performance of such density models, frequently requiring significant depth to reach desired performance levels. In this work, we propose Self Normalizing Flows, a flexible framework for training normalizing flows by replacing expensive terms in the gradient by learned approximate inverses at each layer. This reduces the computational complexity of each layer's exact update from $\mathcal{O}(D^3)$ to $\mathcal{O}(D^2)$, allowing for the training of flow architectures which were otherwise computationally infeasible, while also providing efficient sampling. We show experimentally that such models are remarkably stable and optimize to similar data likelihood values as their exact gradient counterparts, while training more quickly and surpassing the performance of functionally constrained counterparts.

cs.LG↗

arXiv2018

Fast Weight Long Short-Term Memory

Associative memory using fast weights is a short-term memory mechanism that substantially improves the memory capacity and time scale of recurrent neural networks (RNNs). As recent studies introduced fast weights only to regular RNNs, it is unknown whether fast weight memory is beneficial to gated RNNs. In this work, we report a significant synergy between long short-term memory (LSTM) networks and fast weight associative memories. We show that this combination, in learning associative retrieval tasks, results in much faster training and lower test error, a performance boost most prominent at high memory task difficulties.

cs.NE↗