Infinite Ends from Finite Samples: Open-Ended Goal Inference as Top-Down Bayesian Filtering of Bottom-Up Proposals

TL;DR

This paper tackles open-ended goal inference by proposing open-ended SIPS, a sequential Monte Carlo algorithm that unites top-down Bayesian inverse planning with bottom-up subgoal-based proposals. By sampling plausible goals from co-occurring subgoals (e.g., using a character-level $n$-gram model) and filtering them via a Bayesian posterior over goals given observed actions, the approach achieves efficient, near-human inferences in a fast, open-ended setting. Empirical results on Block Words show open-ended SIPS matching or exceeding exact Bayesian inference in predictive metrics while using far fewer computational resources, with strong alignment to human step-by-step reasoning and robust performance across garden-path and irrational-alternative scenarios. The work underscores the value of integrating bottom-up cues with top-down planning to explain the speed, accuracy, and generality of human theory-of-mind, and points to future directions in domain adaptation and human-informed priors for broader applicability.

Abstract

The space of human goals is tremendously vast; and yet, from just a few moments of watching a scene or reading a story, we seem to spontaneously infer a range of plausible motivations for the people and characters involved. What explains this remarkable capacity for intuiting other agents' goals, despite the infinitude of ends they might pursue? And how does this cohere with our understanding of other people as approximately rational agents? In this paper, we introduce a sequential Monte Carlo model of open-ended goal inference, which combines top-down Bayesian inverse planning with bottom-up sampling based on the statistics of co-occurring subgoals. By proposing goal hypotheses related to the subgoals achieved by an agent, our model rapidly generates plausible goals without exhaustive search, then filters out goals that would be irrational given the actions taken so far. We validate this model in a goal inference task called Block Words, where participants try to guess the word that someone is stacking out of lettered blocks. In comparison to both heuristic bottom-up guessing and exact Bayesian inference over hundreds of goals, our model better predicts the mean, variance, efficiency, and resource rationality of human goal inferences, achieving similar accuracy to the exact model at a fraction of the cognitive cost, while also explaining garden-path effects that arise from misleading bottom-up cues. Our experiments thus highlight the importance of uniting top-down and bottom-up models for explaining the speed, accuracy, and generality of human theory-of-mind.

Figures (10)

• Figure 1: Illustration of open-ended goal inference in Block Words via particle filtering. Initially, i is stacked on n, leading pink to be proposed as a goal. In the next step, however, t is stacked on p. This makes pink much less likely after reweighting, and hence removed after resampling.
• Figure 2: Human similarity and accuracy of goal inference models, measured in terms of (a) IoU with mean human inferences, and (b) average goal accuracy. Each bar corresponds to a model (and sample size $N$), while each column is a condition. We computed human-human IoU through repeated sampling of 50-50 splits. Error bars denote 95% confidence intervals.
• Figure 3: Step-by-step inference results on two illustrative Block Words scenarios. On the left, we show the sequence of actions, and on the right, the 5 most probable goals at each step for humans and our models ($N=2$ for the sampling-based methods), averaged across humans and algorithm runs (error bars reflect the standard error). In (a), only the bottom-up proposal fails to infer that m being stacked on f at $t=10$ implies that make and fake are less likely than take. In (b), both open-ended SIPS and humans exhibit sticky inferences at $t=8$, assigning high weight to atom and custom as guesses as a result of the garden path trajectory. In contrast, the bottom-up proposal displays a recency bias since it does not store previous guesses.
• Figure 4: Response variance, sample efficiency, and cognitive cost trade-offs vs. humans. Ribbons show 10th-90th quantiles.
• Figure A1: Interface for our open-ended goal inference task.