Learning Cognitive Maps from Transformer Representations for Efficient Planning in Partially Observed Environments

Despite their stellar performance on a wide range of tasks, including in-context tasks only revealed during inference, vanilla transformers and variants trained for next-token predictions (a) do not learn an explicit world model of their environment which can be flexibly queried and (b) cannot be used for planning or navigation. In this paper, we consider partially observed environments (POEs), where an agent receives perceptually aliased observations as it navigates, which makes path planning hard. We introduce a transformer with (multiple) discrete bottleneck(s), TDB, whose latent codes learn a compressed representation of the history of observations and actions. After training a TDB to predict the future observation(s) given the history, we extract interpretable cognitive maps of the environment from its active bottleneck(s) indices. These maps are then paired with an external solver to solve (constrained) path planning problems. First, we show that a TDB trained on POEs (a) retains the near perfect predictive performance of a vanilla transformer or an LSTM while (b) solving shortest path problems exponentially faster. Second, a TDB extracts interpretable representations from text datasets, while reaching higher in-context accuracy than vanilla sequence models. Finally, in new POEs, a TDB (a) reaches near-perfect in-context accuracy, (b) learns accurate in-context cognitive maps (c) solves in-context path planning problems.

Graphical Models with Attention for Context-Specific Independence and an Application to Perceptual Grouping

Discrete undirected graphical models, also known as Markov Random Fields (MRFs), can flexibly encode probabilistic interactions of multiple variables, and have enjoyed successful applications to a wide range of problems. However, a well-known yet little studied limitation of discrete MRFs is that they cannot capture context-specific independence (CSI). Existing methods require carefully developed theories and purpose-built inference methods, which limit their applications to only small-scale problems. In this paper, we propose the Markov Attention Model (MAM), a family of discrete MRFs that incorporates an attention mechanism. The attention mechanism allows variables to dynamically attend to some other variables while ignoring the rest, and enables capturing of CSIs in MRFs. A MAM is formulated as an MRF, allowing it to benefit from the rich set of existing MRF inference methods and scale to large models and datasets. To demonstrate MAM's capabilities to capture CSIs at scale, we apply MAMs to capture an important type of CSI that is present in a symbolic approach to recurrent computations in perceptual grouping. Experiments on two recently proposed synthetic perceptual grouping tasks and on realistic images demonstrate the advantages of MAMs in sample-efficiency, interpretability and generalizability when compared with strong recurrent neural network baselines, and validate MAM's capabilities to efficiently capture CSIs at scale.

Query Training: Learning and inference for directed and undirected graphical models

Probabilistic graphical models (PGMs) provide a compact representation of knowledge that can be queried in a flexible way: after learning the parameters of a graphical model, new probabilistic queries can be answered at test time without retraining. However, learning undirected graphical models is notoriously hard due to the intractability of the partition function. For directed models, a popular approach is to use variational autoencoders, but there is no systematic way to choose the encoder architecture given the PGM, and the encoder only amortizes inference for a single probabilistic query (i.e., new queries require separate training). We introduce Query Training (QT), a systematic method to turn any PGM structure (directed or not, with or without hidden variables) into a trainable inference network. This single network can approximate any inference query. We demonstrate experimentally that QT can be used to learn a challenging 8-connected grid Markov random field with hidden variables and that it consistently outperforms the state-of-the-art AdVIL when tested on three undirected models across multiple datasets.

Learning undirected models via query training

Typical amortized inference in variational autoencoders is specialized for a single probabilistic query. Here we propose an inference network architecture that generalizes to unseen probabilistic queries. Instead of an encoder-decoder pair, we can train a single inference network directly from data, using a cost function that is stochastic not only over samples, but also over queries. We can use this network to perform the same inference tasks as we would in an undirected graphical model with hidden variables, without having to deal with the intractable partition function. The results can be mapped to the learning of an actual undirected model, which is a notoriously hard problem. Our network also marginalizes nuisance variables as required. We show that our approach generalizes to unseen probabilistic queries on also unseen test data, providing fast and flexible inference. Experiments show that this approach outperforms or matches PCD and AdVIL on 9 benchmark datasets.

Learning higher-order sequential structure with cloned HMMs

Variable order sequence modeling is an important problem in artificial and natural intelligence. While overcomplete Hidden Markov Models (HMMs), in theory, have the capacity to represent long-term temporal structure, they often fail to learn and converge to local minima. We show that by constraining HMMs with a simple sparsity structure inspired by biology, we can make it learn variable order sequences efficiently. We call this model cloned HMM (CHMM) because the sparsity structure enforces that many hidden states map deterministically to the same emission state. CHMMs with over 1 billion parameters can be efficiently trained on GPUs without being severely affected by the credit diffusion problem of standard HMMs. Unlike n-grams and sequence memoizers, CHMMs can model temporal dependencies at arbitrarily long distances and recognize contexts with 'holes' in them. Compared to Recurrent Neural Networks and their Long Short-Term Memory extensions (LSTMs), CHMMs are generative models that can natively deal with uncertainty. Moreover, CHMMs return a higher-order graph that represents the temporal structure of the data which can be useful for community detection, and for building hierarchical models. Our experiments show that CHMMs can beat n-grams, sequence memoizers, and LSTMs on character-level language modeling tasks. CHMMs can be a viable alternative to these methods in some tasks that require variable order sequence modeling and the handling of uncertainty.

Generative Shape Models: Joint Text Recognition and Segmentation with Very Little Training Data

We demonstrate that a generative model for object shapes can achieve state of the art results on challenging scene text recognition tasks, and with orders of magnitude fewer training images than required for competing discriminative methods. In addition to transcribing text from challenging images, our method performs fine-grained instance segmentation of characters. We show that our model is more robust to both affine transformations and non-affine deformations compared to previous approaches.