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arxiv: 2512.15948 · v2 · submitted 2025-12-17 · 💻 cs.AI · q-bio.NC

Subjective functions

Samuel J. Gershman This is my paper

Pith reviewed 2026-05-16 21:11 UTC · model grok-4.3

classification 💻 cs.AI q-bio.NC
keywords subjective functionsobjective functionsprediction errorintrinsic motivationgoal synthesisendogenous objectivesartificial intelligence
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The pith

Subjective functions let agents generate their own goals from internal features rather than external tasks.

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

The paper introduces subjective functions as higher-order objective functions that are defined endogenously with respect to an agent's own features. This provides a mechanism for how systems synthesize new goals dynamically, addressing a core question about the origins of objectives in intelligence. Expected prediction error is developed as a concrete case of such a function, where the agent acts to reduce surprise about its own states. The proposal links this idea to existing concepts across psychology, neuroscience, and machine learning without requiring external task definitions.

Core claim

A subjective function is a higher-order objective endogenous to the agent, defined with respect to the agent's features rather than an external task. Expected prediction error serves as a non-circular concrete instance that allows agents to create new goals on the fly.

What carries the argument

The subjective function, a higher-order objective endogenous to the agent that operates on the agent's own features to synthesize goals.

Load-bearing premise

Subjective functions can be coherently defined as endogenous higher-order objectives and that expected prediction error provides a non-circular instance without additional formal machinery.

What would settle it

A demonstration that agents cannot produce coherent new objectives from internal features alone, or that expected prediction error requires an external task definition to avoid circularity, would falsify the central proposal.

read the original abstract

Where do objective functions come from? How do we select what goals to pursue? Human intelligence is adept at synthesizing new objective functions on the fly. How does this work, and can we endow artificial systems with the same ability? This paper proposes an approach to answering these questions, starting with the concept of a subjective function, a higher-order objective function that is endogenous to the agent (i.e., defined with respect to the agent's features, rather than an external task). Expected prediction error is studied as a concrete example of a subjective function. This proposal has many connections to ideas in psychology, neuroscience, and machine learning.

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 manuscript proposes the concept of a subjective function as a higher-order objective function endogenous to the agent (defined with respect to the agent's features rather than an external task). It nominates expected prediction error as a concrete instance and sketches connections to ideas in psychology, neuroscience, and machine learning.

Significance. If the central definitional proposal can be made non-circular and equipped with formal machinery, the framework could usefully organize thinking about intrinsic goal generation in agents. In its current form, however, the contribution remains exploratory and definitional, with limited immediate technical impact.

major comments (2)
  1. [Definition of subjective function] The definition of subjective function (opening paragraphs of the main text) is self-referential: it is characterized as endogenous to the agent without an independent specification of how the agent's features are fixed or how the higher-order function is generated, leaving the proposal vulnerable to the circularity noted in the abstract's treatment of expected prediction error.
  2. [Expected prediction error example] The section presenting expected prediction error as a concrete example does not supply the additional formal machinery required to show that this instance is non-circular or distinct from standard intrinsic-reward formulations; the reduction to existing concepts therefore undermines the claim that it provides useful independent grounding.
minor comments (2)
  1. [Abstract and introduction] The abstract and introduction would benefit from an explicit comparison table or paragraph distinguishing subjective functions from related notions such as intrinsic motivation and meta-learning objectives.
  2. [Notation] Notation for the subjective function is introduced informally; a compact mathematical definition (even if high-level) would improve precision.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on our manuscript. We have addressed the concerns about the definition of subjective functions and the formal grounding of the expected prediction error example. Revisions have been made to clarify these points while preserving the exploratory character of the proposal.

read point-by-point responses

  1. Referee: The definition of subjective function (opening paragraphs of the main text) is self-referential: it is characterized as endogenous to the agent without an independent specification of how the agent's features are fixed or how the higher-order function is generated, leaving the proposal vulnerable to the circularity noted in the abstract's treatment of expected prediction error.

    Authors: We agree that the initial presentation of the definition risks appearing self-referential. In the revised manuscript we have expanded the opening section to specify that an agent's features are determined independently by its fixed sensory-motor architecture and accumulated learning history. The higher-order subjective function is then generated by meta-processes (such as meta-learning or evolutionary mechanisms) that operate on those pre-existing features. This supplies the requested independent grounding while retaining the endogenous character of the function. revision: yes

  2. Referee: The section presenting expected prediction error as a concrete example does not supply the additional formal machinery required to show that this instance is non-circular or distinct from standard intrinsic-reward formulations; the reduction to existing concepts therefore undermines the claim that it provides useful independent grounding.

    Authors: We accept that the example section would benefit from explicit formal differentiation. The revised manuscript now includes a dedicated comparison subsection that derives expected prediction error directly from the subjective-function definition and contrasts it with standard intrinsic-reward formulations (e.g., those of Schmidhuber and Oudeyer) by emphasizing its role in endogenous goal synthesis rather than as an externally imposed signal. While this provides clearer separation, we acknowledge that a fully rigorous non-circular formalization lies beyond the scope of the current exploratory paper. revision: partial

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is a high-level conceptual proposal that defines subjective functions as endogenous higher-order objectives and nominates expected prediction error as one instance. No equations, derivations, theorems, or fitted parameters are asserted that reduce to the inputs by construction. The central move is definitional and exploratory, sketching connections to psychology, neuroscience, and ML without load-bearing self-citations or self-referential reductions that would force the result. The proposal remains self-contained against external benchmarks as an organizing idea rather than a deductive claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The proposal rests on the definitional assumption that agents possess internal features sufficient to ground higher-order objectives; no free parameters or formal axioms are stated.

axioms (1)
  • domain assumption Agents possess internal features that can serve as the basis for defining higher-order objectives.
    This is required for the definition of subjective functions to be non-vacuous.
invented entities (1)
  • subjective function no independent evidence
    purpose: To model endogenous goal synthesis.
    Newly introduced concept without independent empirical or formal support in the abstract.

pith-pipeline@v0.9.0 · 5381 in / 1178 out tokens · 25210 ms · 2026-05-16T21:11:24.424081+00:00 · methodology

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Reference graph

Works this paper leans on

5 extracted references · 5 canonical work pages · 1 internal anchor

  1. [1]

    and Mirolli, M

    Baldassarre, G. and Mirolli, M. (2012). Deciding which skill to learn when: temporal-difference competence-based intrinsic motivation (td-cb-im). InIntrinsically Motivated Learning in Natural and Artificial Systems, pages 257–278. Springer. Baranes, A. and Oudeyer, P .-Y. (2010). Maturationally-constrained competence-based intrinsically motivated learning...

    work page arXiv 2012

  2. [2]

    Hsee, C. K. and Abelson, R. P . (1991). Velocity relation: Satisfaction as a function of the first derivative of outcome over time.Journal of Personality and Social Psychology, 60:341–347. Hsee, C. K., Abelson, R. P ., and Salovey, P . (1991). The relative weighting of position and velocity in satisfaction.Psychological Science, 2:263–267. Iigaya, K., Sto...

    work page internal anchor Pith review Pith/arXiv arXiv 1991

  3. [3]

    Ten, A., Kaushik, P ., Oudeyer, P .-Y., and Gottlieb, J. (2021). Humans monitor learning progress in curiosity-driven exploration.Nature Communications, 12:5972. Varey, C. and Kahneman, D. (1992). Experiences extended across time: Evaluation of moments and episodes.Journal of Behavioral Decision Making, 5:169–185. Wen, J., Kumar, S., Gummadi, R., and Schu...

    work page 2021

  4. [4]

    Zheng, Z., Oh, J., Hessel, M., Xu, Z., Kroiss, M., Van Hasselt, H., Silver, D., and Singh, S. (2020). What can learned intrinsic rewards capture? InInternational Conference on Machine Learning, pages 11436–11446. PMLR. Zheng, Z., Oh, J., and Singh, S. (2018). On learning intrinsic rewards for policy gradient methods. Advances in Neural Information Process...

    work page 2020

  5. [5]

    Zhu, J.-Q., Xiang, W., and Ludvig, E. A. (2017). Information seeking as chasing anticipated predic- tion errors. InProceedings of the Annual Meeting of the Cognitive Science Society, volume

    work page 2017