The dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is achieved through token masking: looping over the vocabulary and excluding non-conforming tokens. There are two important problems with this approach. (i) Evaluating the constraint on every token can be prohibitively expensive -- LM vocabularies often exceed $100,000$ tokens. (ii) LCD can distort the global distribution over strings, sampling tokens based only on local information, even if they lead down dead-end paths. This work introduces a new algorithm that addresses both these problems. First, to avoid evaluating a constraint on the full vocabulary at each step of generation, we propose an adaptive rejection sampling algorithm that typically requires orders of magnitude fewer constraint evaluations. Second, we show how this algorithm can be extended to produce low-variance, unbiased estimates of importance weights at a very small additional cost -- estimates that can be soundly used within previously proposed sequential Monte Carlo algorithms to correct for the myopic behavior of local constraint enforcement. Through extensive empirical evaluation in text-to-SQL, molecular synthesis, goal inference, pattern matching, and JSON domains, we show that our approach is superior to state-of-the-art baselines, supporting a broader class of constraints and improving both runtime and performance. Additional theoretical and empirical analyses show that our method's runtime efficiency is driven by its dynamic use of computation, scaling with the divergence between the unconstrained and constrained LM, and as a consequence, runtime improvements are greater for better models.

Active inference is a formal approach to study cognition based on the notion that adaptive agents can be seen as engaging in a process of approximate Bayesian inference, via the minimisation of variational and expected free energies. Minimising the former provides an account of perceptual processes and learning as evidence accumulation, while minimising the latter describes how agents select their actions over time. In this way, adaptive agents are able to maximise the likelihood of preferred observations or states, given a generative model of the environment. In the literature, however, different strategies have been proposed to describe how agents can plan their future actions. While they all share the notion that some kind of expected free energy offers an appropriate way to score policies, sequences of actions, in terms of their desirability, there are different ways to consider the contribution of past motor experience to the agent's future behaviour. In some approaches, agents are assumed to know their own actions, and use such knowledge to better plan for the future. In other approaches, agents are unaware of their actions, and must infer their motor behaviour from recent observations in order to plan for the future. This difference reflects a standard point of departure in two leading frameworks in motor control based on the presence, or not, of an efference copy signal representing knowledge about an agent's own actions. In this work we compare the performances of action-aware and action-unaware agents in two navigations tasks, showing how action-unaware agents can achieve performances comparable to action-aware ones while at a severe disadvantage.

Objective: Sparse Bayesian learning provides an effective scheme to solve the high-dimensional problem in brain signal decoding. However, traditional assumptions regarding data distributions such as Gaussian and binomial are potentially inadequate to characterize the noisy signals of brain activity. Hence, this study aims to propose a robust sparse Bayesian learning framework to address noisy highdimensional brain activity decoding. Methods: Motivated by the commendable robustness of the minimum error entropy (MEE) criterion for handling complex data distributions, we proposed an MEE-based likelihood function to facilitate the accurate inference of sparse Bayesian learning in analyzing noisy brain datasets. Results: Our proposed approach was evaluated using two high-dimensional brain decoding tasks in regression and classification contexts, respectively. The experimental results showed that, our approach can realize superior decoding metrics and physiological patterns than the conventional and state-of-the-art methods. Conclusion: Utilizing the proposed MEE-based likelihood model, sparse Bayesian learning is empowered to simultaneously address the challenges of noise and high dimensionality in the brain decoding task. Significance: This work provides a powerful tool to realize robust brain decoding, advancing biomedical engineering applications such as brain-computer interface.

Deep directed generative models with energy-based probability estimation.

Monte Carlo (MC) integration is the de facto method for approximating the predictive distribution of Bayesian neural networks (BNNs).

This problem is known as location parameter estimation in the statistics literature.