  Recent works such as VisProg and ViperGPT have smartly composed foundation
models for visual reasoning-using large language models (LLMs) to produce
programs that can be executed by pre-trained vision-language models. However,
they operate in limited domains, such as 2D images, not fully exploiting the
generalization of language: abstract concepts like "left" can also be grounded
in 3D, temporal, and action data, as in moving to your left. This limited
generalization stems from these inference-only methods' inability to learn or
adapt pre-trained models to a new domain. We propose the Logic-Enhanced
Foundation Model (LEFT), a unified framework that learns to ground and reason
with concepts across domains with a differentiable, domain-independent,
first-order logic-based program executor. LEFT has an LLM interpreter that
outputs a program represented in a general, logic-based reasoning language,
which is shared across all domains and tasks. LEFT's executor then executes the
program with trainable domain-specific grounding modules. We show that LEFT
flexibly learns concepts in four domains: 2D images, 3D scenes, human motions,
and robotic manipulation. It exhibits strong reasoning ability in a wide
variety of tasks, including those that are complex and not seen during
training, and can be easily applied to new domains.
