Empowerment Gain and Causal Model Construction: Children and adults are sensitive to controllability and variability in their causal interventions

Alison Gopnik; Eunice Yiu; Kelsey Allen; Shiry Ginosar

arxiv: 2512.08230 · v2 · submitted 2025-12-09 · 💻 cs.AI

Empowerment Gain and Causal Model Construction: Children and adults are sensitive to controllability and variability in their causal interventions

Eunice Yiu , Kelsey Allen , Shiry Ginosar , Alison Gopnik This is my paper

Pith reviewed 2026-05-17 00:51 UTC · model grok-4.3

classification 💻 cs.AI

keywords causal learningempowermentcontrollabilityvariabilitycausal interventionschildren's causal reasoningreinforcement learningcausal Bayes nets

0 comments

The pith

Children and adults adjust their causal interventions according to cues of controllability and variability to build better world models.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes that humans learn causal structures through interventions, and that both children and adults are attuned to how much they can control outcomes and how variable those outcomes are. These cues are treated as signals of empowerment gain, where an accurate causal model lets an agent produce more informative effects from its actions. The authors link this to reinforcement learning ideas of empowerment as mutual information between actions and results, while also connecting it to the Causal Bayes Net approach used in cognitive science. An empirical study tests whether people design interventions that exploit these cues. If the link holds, it offers one way to explain efficient causal learning in humans and to make similar learning possible in machines.

Core claim

Children and adults are sensitive to controllability and variability in their causal interventions, using these cues to infer causal relations and design effective interventions. If an agent learns an accurate causal world model, it will necessarily increase its empowerment, and increasing empowerment will lead to a more accurate causal world model. Empowerment thereby bridges the Causal Bayes Net formalism with reinforcement learning and may explain distinctive features of children's causal learning.

What carries the argument

Empowerment as mutual information between actions and outcomes, which increases with accurate causal models and in turn guides the choice of interventions that build those models.

If this is right

Accurate causal models increase empowerment by raising mutual information between actions and outcomes.
Selecting interventions on the basis of controllability and variability improves causal inference in both children and adults.
This mechanism supplies a computational account of why children explore the world in ways that build causal knowledge.
The same principles may make causal learning more tractable for artificial agents that currently rely on standard deep learning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same sensitivity could be used to design exploration strategies that accelerate causal discovery in reinforcement learning agents.
It suggests a shared cognitive process across ages that could be tested in other domains such as tool use or social learning.

Load-bearing premise

Controllability and variability function as reliable, learnable proxies for empowerment gain that directly guide causal model construction.

What would settle it

A controlled experiment in which participants show no preference for interventions with higher controllability or variability when trying to discover causal relations.

Figures

Figures reproduced from arXiv: 2512.08230 by Alison Gopnik, Eunice Yiu, Kelsey Allen, Shiry Ginosar.

**Figure 1.** Figure 1: Three machines characterized by the controllability and variability of their outputs. The purely controllable machine generates a single, deterministic output across all slots (left). The controllable and variable machine produces three distinct outputs, each reliably corresponding to slot size (middle). The purely variable machine generates three different outputs in a completely stochastic manner, with n… view at source ↗

**Figure 2.** Figure 2: Distribution of machine and slot preference across the three generalization tasks: (a) to a new output value (extra [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗

**Figure 3.** Figure 3: Proportion of machine selections by children and adults in the work and play contexts. [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗

**Figure 4.** Figure 4: Two machines combining controllable and uncontrollable (random) variation across three slots. Hue Machine (left): [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗

read the original abstract

Learning about the causal structure of the world is a fundamental problem for human cognition. Causal models and especially causal learning have proved to be difficult for large pretrained models using standard techniques of deep learning. In contrast, cognitive scientists have applied advances in our formal understanding of causation in computer science, particularly within the Causal Bayes Net formalism, to understand human causal learning. In the very different tradition of reinforcement learning, researchers have described an intrinsic reward signal called "empowerment" which maximizes mutual information between actions and their outcomes. "Empowerment" may be an important bridge between classical Bayesian causal learning and reinforcement learning and may help to characterize causal learning in humans and enable it in machines. If an agent learns an accurate causal world model, they will necessarily increase their empowerment, and increasing empowerment will lead to a more accurate causal world model. Empowerment may also explain distinctive features of childrens causal learning, as well as providing a more tractable computational account of how that learning is possible. In an empirical study, we systematically test how children and adults use cues to empowerment to infer causal relations, and design effective causal interventions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper runs a new behavioral study showing that kids and adults use controllability and variability cues when choosing causal interventions and links this to empowerment, but the abstract gives no data or stats to judge the strength of that link.

read the letter

The main point is that children and adults appear sensitive to how controllable and variable outcomes are when they pick interventions, and the authors frame this as evidence for empowerment guiding causal model building. They position empowerment as a bridge between causal Bayes nets and reinforcement learning ideas, arguing that better causal models raise empowerment and that empowerment in turn improves those models. This is applied to explain some features of children's learning and to suggest more efficient causal learning in machines. The empirical study tests sensitivity to those cues directly in intervention tasks, which is a concrete step beyond the abstract framing in prior work. The connection they draw is straightforward and could be useful for thinking about intrinsic motivation in AI systems that need to discover causal structure. The study itself looks like a fresh test rather than a rehash of existing results. The main limitation is that the abstract reports no sample sizes, no statistical tests, and no details on how they ruled out simpler explanations like basic information gain. Without those numbers it is difficult to assess whether the observed patterns really support the empowerment account over standard alternatives. The claim that empowerment necessarily improves causal models is asserted but not derived from first principles in what is shown here. This paper is aimed at people working on computational models of causal learning in development and on intrinsic motivation for AI. A reader interested in either area could get something out of the framing and the study design if the full methods and results are solid. I would send it for peer review so the data and the theoretical link can be checked properly.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes that the reinforcement learning concept of empowerment (maximizing mutual information between actions and outcomes) provides a bridge between Causal Bayes Net models of human causal learning and intrinsic motivation. It argues for a bidirectional link in which accurate causal models increase empowerment and empowerment-guided exploration improves causal models. The central empirical contribution is a study demonstrating that both children and adults are sensitive to controllability and variability cues when inferring causal structure and selecting interventions, interpreted as evidence that these cues serve as proxies for empowerment gain.

Significance. If the behavioral results are robust and the empowerment account demonstrably outperforms standard information-gain or uncertainty-reduction explanations, the work could supply a computationally tractable account of how intrinsic motivation supports causal model construction, with implications for explaining children's exploratory play and for designing more effective causal learners in AI. The absence of free parameters in the core formalism and the direct empirical test of intervention design are strengths that would strengthen the contribution if alternative accounts are adequately ruled out.

major comments (2)

[Introduction] Introduction and theoretical framing: the bidirectional claim that 'an agent learns an accurate causal world model, they will necessarily increase their empowerment, and increasing empowerment will lead to a more accurate causal world model' is asserted without a formal derivation, simulation, or proof; this link is load-bearing for the bridging argument between CBNs and empowerment.
[Results] Results section: the reported sensitivity to controllability and variability is presented as support for empowerment-based causal learning, yet the manuscript does not include explicit model comparisons (e.g., likelihood ratios or cross-validation) showing that empowerment predictions fit the intervention choices better than standard expected information gain or uncertainty reduction models; without this, the distinctive contribution of the empowerment formalism remains unclear.

minor comments (2)

[Methods] Methods: sample sizes, age ranges, exclusion criteria, and exact statistical tests should be stated more explicitly even if they appear in supplementary material, to allow readers to evaluate power and robustness directly from the main text.
[Introduction] Notation: the manuscript uses 'empowerment gain' without always distinguishing it from the base empowerment quantity; a brief clarifying sentence or equation reference would reduce ambiguity for readers unfamiliar with the RL literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful comments. We address each major comment point by point below, outlining how we will strengthen the manuscript in revision.

read point-by-point responses

Referee: [Introduction] Introduction and theoretical framing: the bidirectional claim that 'an agent learns an accurate causal world model, they will necessarily increase their empowerment, and increasing empowerment will lead to a more accurate causal world model' is asserted without a formal derivation, simulation, or proof; this link is load-bearing for the bridging argument between CBNs and empowerment.

Authors: We acknowledge that the bidirectional relationship is presented at a conceptual level in the introduction without an accompanying formal derivation or simulation. This link is indeed central to positioning empowerment as a bridge between causal Bayes nets and intrinsic motivation. In the revised manuscript we will add a short formal argument together with a simple illustrative simulation (using a basic causal structure) showing how an accurate causal model increases empowerment by improving the mutual information between actions and outcomes, and how empowerment-guided exploration in turn refines causal structure estimates. This addition will make the theoretical framing more rigorous while preserving the paper's primary empirical focus. revision: yes
Referee: [Results] Results section: the reported sensitivity to controllability and variability is presented as support for empowerment-based causal learning, yet the manuscript does not include explicit model comparisons (e.g., likelihood ratios or cross-validation) showing that empowerment predictions fit the intervention choices better than standard expected information gain or uncertainty reduction models; without this, the distinctive contribution of the empowerment formalism remains unclear.

Authors: We agree that direct quantitative comparisons to standard information-gain and uncertainty-reduction accounts would help clarify the distinctive contribution of the empowerment formalism. The current study was designed to demonstrate sensitivity to controllability and variability as proxies for empowerment gain rather than to perform model adjudication. In revision we will add model-comparison analyses: we will fit both empowerment-based predictions and expected-information-gain predictions to the intervention-choice data from children and adults, and we will report likelihood ratios, AIC, or cross-validation metrics to evaluate relative model performance. These analyses will be presented in a new subsection of the results. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper reports an empirical behavioral study examining how children and adults use controllability and variability cues when designing causal interventions. No formal derivation chain, equations, or first-principles predictions are presented in the abstract or framing; the central results consist of observed sensitivity patterns from experimental tasks rather than quantities fitted to data and then relabeled as predictions. The motivational link between empowerment and causal model accuracy is asserted as a conceptual bridge but is not used as a load-bearing step that reduces to self-definition or self-citation within the reported work. The study design directly tests the hypothesized cue sensitivity, rendering the reported findings self-contained against external benchmarks without internal reduction to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper rests on the assumption that empowerment gain can be operationalized via controllability and variability and that these cues are used by humans to construct causal models. No explicit free parameters or invented entities are introduced in the abstract; standard statistical assumptions for behavioral experiments are implicit.

axioms (1)

domain assumption Controllability and variability serve as valid proxies for empowerment gain in causal intervention tasks.
Invoked when the abstract links these cues to empowerment and claims they guide causal model construction.

pith-pipeline@v0.9.0 · 5508 in / 1265 out tokens · 29708 ms · 2026-05-17T00:51:48.898254+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Empowerment... maximizes mutual information between actions and their outcomes... controllability and variability in their causal interventions

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages · 1 internal anchor

[1]

A unified strategy for implementing curiosity and empowerment driven reinforcement learning

Bender, E. M., Gebru, T., McMillan-Major, A., & Shmitchell, S. (2021, March). On the dangers of stochastic parrots: Can language models be too big?. In Proceedings of the 2021 ACM conference on fairness, accountability, and transparency (pp. 610-623). Bonawitz, E. B., Ferranti, D., Saxe, R., Gopnik, A., Meltzoff, A. N., Woodward, J., & Schulz, L. E. (2010...

work page internal anchor Pith review Pith/arXiv arXiv 2021
[2]

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Gopnik, A., Meltzoff, A. N., & Kuhl, P. K. (1999). The scientist in the crib: Minds, brains, and how children learn. William Morrow & Co. Gopnik, A., & Wellman, H. M. (2012). Reconstructing constructivism: causal models, Bayesian learning mechanisms, and the theory theory. Psychological bulletin, 138(6),

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Jablonka, E., & Lamb, M. J. (2014). Evolution in four dimensions, revised edition: Genetic, epigenetic, behavioral, and symbolic variation in the history of life. MIT press. Jin, Z., Chen, Y ., Leeb, F., Gresele, L., Kamal, O., Lyu, Z., ... & Schölkopf, B. (2024). Cladder: A benchmark to assess causal reasoning capabilities of language models. Advances in...

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Oudeyer, P . Y ., Kaplan, F., & Hafner, V . V . (2007). Intrinsic motivation systems for autonomous mental development. IEEE transactions on evolutionary computation, 11(2), 265-286. Papoušek, H., & Papoušek, M. (1975, January). Cognitive aspects of preverbal social interaction between human infants and adults. In Ciba Foundation Symposium 33‐Parent‐Infan...

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Schulz, L. E. (2012). The origins of inquiry: Inductive inference and exploration in early childhood. Trends in cognitive sciences, 16(7), 382-389. Schmidhuber, J. (2010). Formal theory of creativity, fun, and intrinsic motivation (1990–2010). IEEE transactions on autonomous mental development, 2(3), 230-247. Silver, D., Hubert, T., Schrittwieser, J., Ant...

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[1] [1]

A unified strategy for implementing curiosity and empowerment driven reinforcement learning

Bender, E. M., Gebru, T., McMillan-Major, A., & Shmitchell, S. (2021, March). On the dangers of stochastic parrots: Can language models be too big?. In Proceedings of the 2021 ACM conference on fairness, accountability, and transparency (pp. 610-623). Bonawitz, E. B., Ferranti, D., Saxe, R., Gopnik, A., Meltzoff, A. N., Woodward, J., & Schulz, L. E. (2010...

work page internal anchor Pith review Pith/arXiv arXiv 2021

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N., & Kuhl, P

Gopnik, A., Meltzoff, A. N., & Kuhl, P. K. (1999). The scientist in the crib: Minds, brains, and how children learn. William Morrow & Co. Gopnik, A., & Wellman, H. M. (2012). Reconstructing constructivism: causal models, Bayesian learning mechanisms, and the theory theory. Psychological bulletin, 138(6),

work page 1999

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F., & Usher, M

Grinfeld, G., Lagnado, D., Gerstenberg, T., Woodward, J. F., & Usher, M. (2020). Causal responsibility and robust causation. Frontiers in Psychology, 11,

work page 2020

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Jablonka, E., & Lamb, M. J. (2014). Evolution in four dimensions, revised edition: Genetic, epigenetic, behavioral, and symbolic variation in the history of life. MIT press. Jin, Z., Chen, Y ., Leeb, F., Gresele, L., Kamal, O., Lyu, Z., ... & Schölkopf, B. (2024). Cladder: A benchmark to assess causal reasoning capabilities of language models. Advances in...

work page 2014

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Kidd, C., & Hayden, B. Y . (2015). The psychology and neuroscience of curiosity. Neuron, 88(3), 449-460. Klyubin, A. S., Polani, D., and Nehaniv, C. L. (2005). Empowerment: A universal agent-centric measure of control. In Evolutionary Computation,

work page 2015

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1, 128–135

The 2005 IEEE Congress on (IEEE), vol. 1, 128–135. Klyubin, A. S., Polani, D., & Nehaniv, C. L. (2008). Keep your options open: An information-based driving principle for sensorimotor systems. PloS one, 3(12), e4018. Kosoy, E., Liu, A., Collins, J.L., Chan, D., Hamrick, J.B., Ke, N.R., Huang, S., Kaufmann, B., Canny, J. & Gopnik, A.. (2022). Learning ...

work page arXiv 2005

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Meltzoff, A. N. (2007). ‘Like me’: a foundation for social cognition. Developmental science, 10(1), 126-134. Meltzoff, A. N., Waismeyer, A., & Gopnik, A. (2012). Learning about causes from people: observational causal learning in 24-month-old infants. Developmental psychology, 48(5),

work page 2007

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Y ., Kaplan, F., & Hafner, V

Oudeyer, P . Y ., Kaplan, F., & Hafner, V . V . (2007). Intrinsic motivation systems for autonomous mental development. IEEE transactions on evolutionary computation, 11(2), 265-286. Papoušek, H., & Papoušek, M. (1975, January). Cognitive aspects of preverbal social interaction between human infants and adults. In Ciba Foundation Symposium 33‐Parent‐Infan...

work page 2007

[9] [9]

the game

Schulz, L. E. (2012). The origins of inquiry: Inductive inference and exploration in early childhood. Trends in cognitive sciences, 16(7), 382-389. Schmidhuber, J. (2010). Formal theory of creativity, fun, and intrinsic motivation (1990–2010). IEEE transactions on autonomous mental development, 2(3), 230-247. Silver, D., Hubert, T., Schrittwieser, J., Ant...

work page 2012

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Woodward, J. (2007). Interventionist theories of causation in psychological perspective. Causal learning: Psychology, philosophy, and computation, 19-36. Woodward, J. (2020). Causal Responsibility and Robust Causation. Frontiers in Psychology. Woodward, J. (2021). Causation with a human face: Normative theory and descriptive psychology. Oxford University ...

work page arXiv 2007