Publication
ALDER: Discovering the Laws of a World by Acting in It
Teng Cao; Yu Deng; Quentin Delfosse; Kristian Kersting
In: Computing Research Repository eprint Journal (CoRR), Vol. abs/2609.33728, Pages 1-27, a, 2026.
Abstract
Reliable world models should not only predict future states but express how actions
change the world in an explicit, transparent and testable form, such as equations.
Yet methods that rely on a fixed set of trajectories cannot distinguish equally good
competing hypotheses, while searches over a fixed set of predefined candidates
cannot discover equations outside the initial hypothesis space. We introduce
ALDER (Action-guided Law Discovery, Evaluation, and Revision), a method that
actively proposes novel experiments to test and revise models. Specifically, ALDER
proposes parametric equations; a numerical optimizer fits their coefficients; an
independent verifier tests these candidates on held-out data. To distinguish between
competing valid hypotheses, a cost- and safety-aware selector queries interventions,
in the form of novel experiments. The resulting counterexamples update the
evidence ledger and guide the next structural revision, while incompatible laws
are discarded. Across an in-house benchmark, ODE equation discovery tasks,
and robotic experiments, ALDER discovers laws beyond its initial formula set,
repairs failed model proposals, distinguishes fixed candidate models with fewer
interactions, and improves out-of-distribution prediction. Furthermore, given a
current state and a target, ALDER selects control actions by solving the inverse
problem defined by its validated world model. Together, these results show that
explicit equation-based world models can be tested and revised through interaction,
then naturally used to guide goal-directed control.