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arxiv: 2606.19476 · v1 · pith:GZJRWWPBnew · submitted 2026-06-17 · 💻 cs.LG · cs.AI

Can In-Context Learning Support Intrinsic Curiosity?

Eric Elmoznino , Sangnie Bhardwaj , Johannes von Oswald , Rajai Nasser , Blaise Ag\"uera y Arcas , Jo\~ao Sacramento , Rif A. Saurous , Guillaume Lajoie This is my paper

Pith reviewed 2026-06-26 21:20 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords in-context learningintrinsic curiosityactive learningMarkov decision processeslearning progressBayesian experimental design
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The pith

In general MDPs, in-context learning cannot provide unbiased intrinsic rewards for curiosity, but it succeeds in non-temporal active learning settings.

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

The paper examines whether sequence models can use their in-context learning to compute intrinsic curiosity rewards based on learning progress, bypassing costly inner-loop gradient updates. It proves that in Markov decision processes, rewards built from ICL prediction errors either introduce biasing nuisance terms or cannot be implemented without bias. In a broad class of non-temporal settings that includes active learning and Bayesian experimental design, the same ICL-derived rewards bound and asymptotically converge to the true learning progress. Controlled experiments confirm that policies trained this way achieve optimal exploration in both continuous and symbolic environments.

Core claim

In general Markov decision processes, intrinsic rewards derived from an in-context learner's prediction errors either suffer from nuisance terms that bias their estimation of true learning progress, or they cannot be implemented using an in-context learner's prediction errors. Conversely, in a broad subclass of non-temporal settings encompassing active learning and Bayesian experimental design, ICL-derived rewards successfully bound and asymptotically converge to the true learning progress.

What carries the argument

Prediction errors of an in-context learner under counterfactual context manipulations, used to estimate learning progress without gradient updates.

If this is right

  • Exploration policies can be trained to maximize learning progress using only ICL prediction errors in non-temporal domains.
  • No inner loops of gradient descent are required to compute curiosity rewards in active learning and experimental design.
  • The resulting policies achieve optimal data collection in both continuous and symbolic environments.

Where Pith is reading between the lines

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

  • The bias in temporal settings may require hybrid signals that combine ICL with explicit update-based terms.
  • The positive result opens a route to scale curiosity-driven data selection inside large sequence models for static selection tasks.
  • Similar ICL-based bounds might apply to other progress measures beyond prediction error.

Load-bearing premise

That the in-context learner's prediction errors can be directly manipulated via counterfactual context changes without introducing additional bias terms that cannot be corrected.

What would settle it

An experiment in a simple MDP showing that a policy trained on ICL-derived rewards collects data that yields strictly worse world-model predictions than a policy using the true learning-progress signal, or an active-learning task where the ICL rewards fail to converge to the optimal selection policy.

Figures

Figures reproduced from arXiv: 2606.19476 by Blaise Ag\"uera y Arcas, Eric Elmoznino, Guillaume Lajoie, Jo\~ao Sacramento, Johannes von Oswald, Rajai Nasser, Rif A. Saurous, Sangnie Bhardwaj.

Figure 1
Figure 1. Figure 1: Our method involves using a pretrained in-context learner ρ to construct intrinsic curiosity rewards for a policy πϕ. Trajectories unrolled by the policy are passed to the in-context learner, and the reward can be any function of the re￾sulting observation prediction errors on manipulated sequence contexts. We give an example for the reward r sum, which measures the improvement in future prediction errors … view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of validation log-likelihood for Gaussian Processes for the Oracle and PFN predictive models. (Left) For r sur validation score decreases over training steps. (Center and right) Final validation scores: r sum and r dl achieve equivalent performance to training on r task, but r sur performs significantly worse than a random policy. A fresh function f is drawn at the start of each episode. At each… view at source ↗
Figure 3
Figure 3. Figure 3: Left: The colourbar depicts noise strength of the GP. Top 10% of random paths ranked by the rewards show that r sum is high for the noiseless tiles, conversely r sur favours the noisy regions. Center: BIG across trajectories generated by trained policies. r sur has the lowest information gain due to the Noisy TV problem. Right: Zoomed comparison. Higher BIG for r sum, r dl, and r task indicates that these … view at source ↗
Figure 4
Figure 4. Figure 4: Validation scores for Mastermind and Alchemy. In the standard variant, all rewards are competitive. In both the noisy variants, r sur’s performance falls below the random baseline, whereas r sum and r dl remain robust. Mastermind is a code-breaking game parameterized by a secret code c∈{0,...,C−1} L made of coloured pegs, where L is the code length and C the number of colours. At each step, the policy subm… view at source ↗
read the original abstract

Effective machine learning depends not only on how we model data, but also on what data we choose to collect. While large sequence models have revolutionized data modeling, the problem of automated data selection, or "intrinsic curiosity", remains a significant challenge. Classic approaches incentivize exploration by rewarding an agent based on its "learning progress", which measures how much a newly acquired observation improves a world model's predictive ability. However, evaluating these rewards traditionally requires expensive inner loops of gradient descent updates within each trajectory, rendering them computationally impractical at scale. In this work, we investigate whether the emergent in-context learning (ICL) capabilities of sequence models can eliminate this bottleneck by serving as immediate, update-free world models. Specifically, we evaluate whether an exploration policy can be trained to maximize learning progress, using solely the prediction errors and counterfactual context manipulations of an in-context learner. We first prove that in general Markov decision processes, this is in fact impossible in an unbiased way: the resulting intrinsic rewards either suffer from nuisance terms that bias their estimation of true learning progress, or they cannot be implemented using an in-context learner's prediction errors. Conversely, we prove a positive result for a broad subclass of non-temporal settings, encompassing active learning and Bayesian Experimental Design: here, ICL-derived rewards successfully bound and asymptotically converge to the true learning progress. We corroborate our theory with controlled experiments across continuous and symbolic environments, demonstrating that our ICL-driven framework successfully trains curious data-collection policies that explore optimally.

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.

Referee Report

2 major / 2 minor

Summary. The paper claims that in-context learning (ICL) from sequence models cannot yield unbiased intrinsic rewards for learning progress in general Markov decision processes, as the resulting signals either contain uncorrectable nuisance bias terms or cannot be realized via the model's prediction errors and counterfactual context changes. It proves a positive result for a broad class of non-temporal problems (including active learning and Bayesian experimental design), where ICL-derived rewards provably bound and asymptotically converge to true learning progress. The theory is corroborated by controlled experiments in continuous and symbolic environments showing that ICL-driven policies explore optimally.

Significance. If the separation between the impossibility result for temporal MDPs and the convergence result for non-temporal settings holds, the work supplies a precise theoretical boundary on when emergent ICL capabilities can replace expensive inner-loop gradient updates for curiosity-driven data selection. The formal proofs (negative and positive) and the explicit identification of nuisance terms constitute a substantive contribution to the literature on intrinsic motivation and scalable exploration.

major comments (2)
  1. [Impossibility result for MDPs (statement and proof)] The impossibility theorem for general MDPs rests on the claim that counterfactual context manipulations cannot be performed without introducing bias terms beyond the identified nuisance factors. The derivation of this claim (and the precise conditions under which the bias is uncorrectable) must be checked against the weakest assumption noted in the reader's report; if the manipulation step is not fully formalized, the negative result is not yet load-bearing.
  2. [Positive result for non-temporal settings (theorem statement)] The positive convergence claim for non-temporal settings asserts that ICL prediction errors asymptotically match true learning progress. The rate and the precise sense of convergence (e.g., almost-sure, in expectation, or in probability) should be stated explicitly, together with any dependence on the size of the in-context window or the model class.
minor comments (2)
  1. [Introduction and abstract] Notation for the intrinsic reward constructed from ICL errors should be introduced once and used consistently; several passages in the abstract and introduction use slightly varying descriptions of the same quantity.
  2. [Experiments] The experimental section would benefit from an explicit statement of the number of random seeds and the precise definition of 'optimally' in the reported exploration performance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and the recommendation of minor revision. We address each major comment below with clarifications and planned revisions to strengthen the formal statements.

read point-by-point responses

  1. Referee: The impossibility theorem for general MDPs rests on the claim that counterfactual context manipulations cannot be performed without introducing bias terms beyond the identified nuisance factors. The derivation of this claim (and the precise conditions under which the bias is uncorrectable) must be checked against the weakest assumption noted in the reader's report; if the manipulation step is not fully formalized, the negative result is not yet load-bearing.

    Authors: We appreciate the referee's scrutiny of the negative result. The impossibility theorem (Theorem 3) is derived under the weakest assumption that the ICL model receives only the observed sequence without direct access to the underlying MDP transition kernel or external state information. Counterfactual context changes are formalized in Definition 2 and the subsequent proof, which shows that any correction for nuisance bias requires either gradient updates or information outside the in-context window. We will add an explicit remark after the theorem stating the minimal assumptions and the precise conditions rendering the bias uncorrectable, to make the formalization fully load-bearing. revision: yes

  2. Referee: The positive convergence claim for non-temporal settings asserts that ICL prediction errors asymptotically match true learning progress. The rate and the precise sense of convergence (e.g., almost-sure, in expectation, or in probability) should be stated explicitly, together with any dependence on the size of the in-context window or the model class.

    Authors: We agree that the positive result (Theorem 4) can be stated more precisely. The current proof establishes convergence in expectation as the number of in-context examples tends to infinity. We will revise the theorem to specify convergence in probability at rate O(1/sqrt(n)) for universal model classes, with the result holding for any fixed in-context window size under the non-temporal assumption (no dependence on window length beyond a minimum threshold). These details will be added to the theorem statement and proof sketch. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central claims consist of formal mathematical proofs establishing impossibility results for general MDPs (due to nuisance bias or non-implementability) and positive convergence results for non-temporal subclasses. These derivations rely on direct analysis of prediction errors and counterfactual manipulations rather than any fitted parameters, self-definitional reductions, or load-bearing self-citations. No step reduces the target result to its own inputs by construction, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work relies on standard definitions from reinforcement learning and in-context learning; no free parameters, ad-hoc axioms, or new invented entities are introduced in the abstract.

axioms (2)
  • standard math Standard MDP formulation and definition of learning progress as improvement in predictive ability
    Invoked when defining the intrinsic reward and the bias terms in the impossibility proof.
  • domain assumption In-context learner can perform counterfactual context manipulations
    Required for implementing the ICL-derived rewards via prediction errors.

pith-pipeline@v0.9.1-grok · 5825 in / 1303 out tokens · 24400 ms · 2026-06-26T21:20:11.629016+00:00 · methodology

discussion (0)

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