What Should Embeddings Embed? Autoregressive Models Represent Latent Generating Distributions

Autoregressive language models have demonstrated a remarkable ability to extract latent structure from text. The embeddings from large language models have been shown to capture aspects of the syntax and semantics of language. But what {\em should} embeddings represent? We connect the autoregressive prediction objective to the idea of constructing predictive sufficient statistics to summarize the information contained in a sequence of observations, and use this connection to identify three settings where the optimal content of embeddings can be identified: independent identically distributed data, where the embedding should capture the sufficient statistics of the data; latent state models, where the embedding should encode the posterior distribution over states given the data; and discrete hypothesis spaces, where the embedding should reflect the posterior distribution over hypotheses given the data. We then conduct empirical probing studies to show that transformers encode these three kinds of latent generating distributions, and that they perform well in out-of-distribution cases and without token memorization in these settings.

Analyzing the Benefits of Prototypes for Semi-Supervised Category Learning

Categories can be represented at different levels of abstraction, from prototypes focused on the most typical members to remembering all observed exemplars of the category. These representations have been explored in the context of supervised learning, where stimuli are presented with known category labels. We examine the benefits of prototype-based representations in a less-studied domain: semi-supervised learning, where agents must form unsupervised representations of stimuli before receiving category labels. We study this problem in a Bayesian unsupervised learning model called a variational auto-encoder, and we draw on recent advances in machine learning to implement a prior that encourages the model to use abstract prototypes to represent data. We apply this approach to image datasets and show that forming prototypes can improve semi-supervised category learning. Additionally, we study the latent embeddings of the models and show that these prototypes allow the models to form clustered representations without supervision, contributing to their success in downstream categorization performance.

Using Contrastive Learning with Generative Similarity to Learn Spaces that Capture Human Inductive Biases

Humans rely on strong inductive biases to learn from few examples and abstract useful information from sensory data. Instilling such biases in machine learning models has been shown to improve their performance on various benchmarks including few-shot learning, robustness, and alignment. However, finding effective training procedures to achieve that goal can be challenging as psychologically-rich training data such as human similarity judgments are expensive to scale, and Bayesian models of human inductive biases are often intractable for complex, realistic domains. Here, we address this challenge by introducing a Bayesian notion of generative similarity whereby two datapoints are considered similar if they are likely to have been sampled from the same distribution. This measure can be applied to complex generative processes, including probabilistic programs. We show that generative similarity can be used to define a contrastive learning objective even when its exact form is intractable, enabling learning of spatial embeddings that express specific inductive biases. We demonstrate the utility of our approach by showing how it can be used to capture human inductive biases for geometric shapes, and to better distinguish different abstract drawing styles that are parameterized by probabilistic programs.

Deep de Finetti: Recovering Topic Distributions from Large Language Models

Large language models (LLMs) can produce long, coherent passages of text, suggesting that LLMs, although trained on next-word prediction, must represent the latent structure that characterizes a document. Prior work has found that internal representations of LLMs encode one aspect of latent structure, namely syntax; here we investigate a complementary aspect, namely the document's topic structure. We motivate the hypothesis that LLMs capture topic structure by connecting LLM optimization to implicit Bayesian inference. De Finetti's theorem shows that exchangeable probability distributions can be represented as a mixture with respect to a latent generating distribution. Although text is not exchangeable at the level of syntax, exchangeability is a reasonable starting assumption for topic structure. We thus hypothesize that predicting the next token in text will lead LLMs to recover latent topic distributions. We examine this hypothesis using Latent Dirichlet Allocation (LDA), an exchangeable probabilistic topic model, as a target, and we show that the representations formed by LLMs encode both the topics used to generate synthetic data and those used to explain natural corpus data.

Transport Score Climbing: Variational Inference Using Forward KL and Adaptive Neural Transport

Variational inference often minimizes the "reverse" Kullbeck-Leibler (KL) KL(q||p) from the approximate distribution q to the posterior p. Recent work studies the "forward" KL KL(p||q), which unlike reverse KL does not lead to variational approximations that underestimate uncertainty. This paper introduces Transport Score Climbing (TSC), a method that optimizes KL(p||q) by using Hamiltonian Monte Carlo (HMC) and a novel adaptive transport map. The transport map improves the trajectory of HMC by acting as a change of variable between the latent variable space and a warped space. TSC uses HMC samples to dynamically train the transport map while optimizing KL(p||q). TSC leverages synergies, where better transport maps lead to better HMC sampling, which then leads to better transport maps. We demonstrate TSC on synthetic and real data. We find that TSC achieves competitive performance when training variational autoencoders on large-scale data.

Variational Combinatorial Sequential Monte Carlo Methods for Bayesian Phylogenetic Inference

Bayesian phylogenetic inference is often conducted via local or sequential search over topologies and branch lengths using algorithms such as random-walk Markov chain Monte Carlo (MCMC) or Combinatorial Sequential Monte Carlo (CSMC). However, when MCMC is used for evolutionary parameter learning, convergence requires long runs with inefficient exploration of the state space. We introduce Variational Combinatorial Sequential Monte Carlo (VCSMC), a powerful framework that establishes variational sequential search to learn distributions over intricate combinatorial structures. We then develop nested CSMC, an efficient proposal distribution for CSMC and prove that nested CSMC is an exact approximation to the (intractable) locally optimal proposal. We use nested CSMC to define a second objective, VNCSMC which yields tighter lower bounds than VCSMC. We show that VCSMC and VNCSMC are computationally efficient and explore higher probability spaces than existing methods on a range of tasks.