Prediction horizon shapes representations in predictive learning

Aviv Ratzon; Omri Barak

arxiv: 2511.09290 · v2 · submitted 2025-11-12 · 💻 cs.LG · q-bio.NC

Prediction horizon shapes representations in predictive learning

Aviv Ratzon , Omri Barak This is my paper

Pith reviewed 2026-05-17 23:26 UTC · model grok-4.3

classification 💻 cs.LG q-bio.NC

keywords prediction horizonpredictive learninglatent geometryimplicit biasesstructured representationsworld modelsmachine learning

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The pith

Increasing the prediction horizon in learning tasks leads models to recover the latent geometry of the environment via their implicit biases.

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

The paper seeks to explain why predictive learning produces structured representations in some cases but not others. It focuses on the prediction horizon as the factor that alters the underlying structure of the optimization problem. In a minimal setting this structural shift combines with the model's built-in biases to favor solutions that match the true geometry of the task. The same pattern appears when the approach is applied to nonlinear networks and richer data. Understanding this link supplies a direct way to anticipate when prediction-based training will yield useful internal models of the world.

Core claim

Increasing the prediction horizon fundamentally shapes the effective structure of the learning problem. In a minimal setting the model's implicit biases interact with this structural change to recover the latent geometry of the task, as demonstrated both theoretically and empirically. The same phenomena persist when the results are extended to nonlinear architectures and more complex datasets.

What carries the argument

The interaction between a model's implicit biases and the structural change induced by a longer prediction horizon.

If this is right

Longer horizons cause predictive models to develop internal representations that reflect the underlying geometry rather than superficial correlations.
Short horizons allow the model to satisfy the objective with unstructured or shortcut solutions.
The recovered geometry appears as a direct consequence of the changed problem structure interacting with existing biases.
The structuring effect transfers from minimal linear cases to nonlinear networks and realistic datasets.

Where Pith is reading between the lines

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

Practitioners could select prediction horizons to promote desired internal structures without altering model architecture or adding explicit regularizers.
The same horizon-dependent mechanism may account for why certain sequence models or reinforcement-learning agents acquire spatial or causal representations.
If the effect scales, horizon length becomes a tunable lever for shaping representations in large-scale predictive training.

Load-bearing premise

The mechanism identified in the minimal setting continues to operate in nonlinear architectures and complex datasets.

What would settle it

Train a linear model on a simple dynamical system to predict future states at different horizons and test whether the learned weights encode the true latent positions or velocities only for sufficiently long horizons.

Figures

Figures reproduced from arXiv: 2511.09290 by Aviv Ratzon, Omri Barak.

**Figure 2.** Figure 2: Top: the first two principal components of hidden activations for networks trained on single-step [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Analyzing the singular values and vectors from the OLS estimator and the model’s effective [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Results for the task with two independent environments. Data are projected onto the first two [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Training a deep nonlinear network on a predictive task with observations generated from a piece [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Top: latent activations of the encoder module. In the multi-step setting with [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

read the original abstract

Predictive learning has emerged as a central paradigm for training models across diverse data domains and is increasingly viewed as a foundation for modern artificial intelligence. A common intuition for this success is that accurate prediction requires models to capture the underlying dynamics of the environment, leading to the emergence of structured world models. However, predictive learning does not universally yield such representations, and a mechanistic account of when and why it does remains incomplete. In this work, we identify the prediction horizon as a critical, but often implicit, component of predictive learning objectives. We show that increasing the prediction horizon fundamentally shapes the effective structure of the learning problem. In a minimal setting, we demonstrate both theoretically and empirically that the model's implicit biases interact with this structural change to recover the latent geometry of the task. We then extend these empirical results to nonlinear architectures and more complex datasets, where similar phenomena persist. These findings provide a principled explanation for the emergence of structured representations in predictive learning paradigms and clarify the conditions under which such representations should be expected.

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 shows that longer prediction horizons reshape the learning problem so implicit biases recover latent geometry, with a clean minimal case and some empirical carry-over.

read the letter

The main point to take away is that prediction horizon length is not neutral: it alters the structure of what the model is optimizing, and in a minimal linear setting this interacts with the model's biases to recover the task's latent geometry. That link is the new piece. They derive it theoretically and back it with targeted experiments in the simple case, which gives the claim some real footing rather than just post-hoc observation. The extension to nonlinear models and richer datasets is where the work gets more provisional. The phenomena appear to hold, but the paper does not appear to supply a proof or tight ablation that the same bias-structure interaction remains the dominant driver once feature learning and optimization dynamics enter the picture. If other mechanisms take over, the result becomes an interesting correlation rather than the mechanistic account advertised. The citation pattern looks standard for the area and does not seem to overclaim prior work. No obvious circularity in the minimal derivation, though the complex-data section would benefit from clearer controls on post-hoc choices. This is worth bringing to a reading group for anyone working on predictive objectives or world-model emergence. The minimal case is clean enough to discuss productively even if the generalization needs more work. I would send it out for peer review; the core observation is sharp enough to justify referee time, with the expectation that the nonlinear extension gets tightened.

Referee Report

2 major / 2 minor

Summary. The paper claims that the prediction horizon is a critical but often implicit component of predictive learning objectives that fundamentally shapes the effective structure of the learning problem. In a minimal setting, theoretical derivation and empirical checks show that model implicit biases interact with this structural change to recover the latent geometry of the task. The authors then extend these observations empirically to nonlinear architectures and more complex datasets, where similar phenomena are reported to persist, providing a mechanistic account for the emergence of structured representations.

Significance. If the result holds, the work supplies a principled explanation for when predictive learning yields structured world models rather than unstructured representations. The minimal-setting theoretical demonstration combined with empirical checks is a positive feature; the extension to nonlinear models and complex data, if mechanistically grounded, would clarify conditions under which such representations should be expected across domains.

major comments (2)

The central claim requires that the bias-structure interaction derived in the minimal setting remains operative in nonlinear architectures. The manuscript reports empirical persistence but provides no analysis (e.g., ablation on optimization dynamics or feature-learning effects) demonstrating that the minimal-setting mechanism dominates rather than being superseded by architecture-specific factors. This is load-bearing for the generalization stated in the abstract.
The theoretical demonstration in the minimal setting appears to rest on exact solvability or linearity assumptions. If these assumptions are violated under nonlinearity, the extension becomes an empirical correlation rather than a mechanistic account; a concrete test or counter-example analysis would be needed to bound the scope of the derivation.

minor comments (2)

Notation for the prediction horizon and implicit bias terms should be introduced with explicit definitions in the main text rather than relying on appendix cross-references.
Figure captions for the minimal-setting experiments could more explicitly state the controls used to isolate horizon length from other hyperparameters.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which help clarify the scope and strength of our claims. We address the major comments point by point below, and we plan to revise the manuscript accordingly to address the concerns raised.

read point-by-point responses

Referee: The central claim requires that the bias-structure interaction derived in the minimal setting remains operative in nonlinear architectures. The manuscript reports empirical persistence but provides no analysis (e.g., ablation on optimization dynamics or feature-learning effects) demonstrating that the minimal-setting mechanism dominates rather than being superseded by architecture-specific factors. This is load-bearing for the generalization stated in the abstract.

Authors: We acknowledge that the manuscript currently relies on empirical observation of similar phenomena in nonlinear architectures without detailed mechanistic analysis. To address this, we will add new experiments including ablations on optimization dynamics, such as tracking gradient norms and representation evolution during training, and feature-learning effects by comparing linear probes on intermediate layers. This will help demonstrate whether the minimal-setting mechanism remains dominant. revision: yes
Referee: The theoretical demonstration in the minimal setting appears to rest on exact solvability or linearity assumptions. If these assumptions are violated under nonlinearity, the extension becomes an empirical correlation rather than a mechanistic account; a concrete test or counter-example analysis would be needed to bound the scope of the derivation.

Authors: The theoretical results are derived in a minimal linear setting chosen for exact solvability to isolate the effect of the prediction horizon. We agree that bounding the scope is important. In the revision, we will include a discussion of the assumptions and provide a concrete analysis by considering a mildly nonlinear perturbation of the minimal model, where we can numerically verify the persistence of the bias-structure interaction, thus providing a test case for the transition to nonlinearity. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent minimal-setting analysis.

full rationale

The paper's core chain begins with an explicit analysis of how prediction horizon alters the effective structure of the learning objective in a minimal linear setting, deriving the interaction between implicit biases and this structure to recover latent geometry. This theoretical step uses standard dynamical systems and optimization arguments without reducing to fitted parameters renamed as predictions or self-citations that bear the load. Empirical extensions to nonlinear models and complex data are presented as observations of persistence rather than forced by construction. No self-definitional loops, ansatz smuggling, or uniqueness theorems imported from the authors' prior work appear in the load-bearing steps; the account remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the central claim rests on standard assumptions of predictive learning plus the novel claim that horizon length alters effective problem structure.

axioms (1)

domain assumption Models possess implicit biases that interact with changes in learning-problem structure.
Invoked to explain recovery of latent geometry in the minimal setting.

pith-pipeline@v0.9.0 · 5465 in / 1181 out tokens · 47196 ms · 2026-05-17T23:26:27.752418+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 echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

the matrix X⊤X has a block structure consisting of two diagonal blocks and two off-diagonal band matrices. The width of these bands grows linearly with the prediction horizon A
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

deeper networks bias the solution toward lower-rank approximations of the hard-margin solution at the cost of smaller margins

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

Works this paper leans on

7 extracted references · 7 canonical work pages · 4 internal anchors

[1]

The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks

Jonathan Frankle and Michael Carbin. The lottery ticket hypothesis: Finding sparse, trainable neural net- works.arXiv preprint arXiv:1803.03635,

work page internal anchor Pith review Pith/arXiv arXiv
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Gradient descent aligns the layers of deep linear networks

Ziwei Ji and Matus Telgarsky. Gradient descent aligns the layers of deep linear networks.arXiv preprint arXiv:1810.02032,

work page internal anchor Pith review Pith/arXiv arXiv
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Sequential predictive learning is a unifying theory for hippocampal representation and replay.bioRxiv, pages 2024– 04,

Daniel Levenstein, Aleksei Efremov, Roy Henha Eyono, Adrien Peyrache, and Blake Richards. Sequential predictive learning is a unifying theory for hippocampal representation and replay.bioRxiv, pages 2024– 04,

work page 2024
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Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning

William Lotter, Gabriel Kreiman, and David Cox. Deep predictive coding networks for video prediction and unsupervised learning.arXiv preprint arXiv:1605.08104,

work page internal anchor Pith review Pith/arXiv arXiv
[5]

arXiv preprint arXiv:1906.05890 , year=

Kaifeng Lyu and Jian Li. Gradient descent maximizes the margin of homogeneous neural networks.arXiv preprint arXiv:1906.05890,

work page arXiv 1906
[6]

Understanding deep learning requires rethinking generalization

Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization.arXiv preprint arXiv:1611.03530,

work page internal anchor Pith review Pith/arXiv arXiv
[7]

Error bars are standard deviation obtained by bootstrapping

As shown,A thresh scales linearly withS, supporting the claim that the prediction horizon required for latent state extraction grows proportionally with the environment size. Error bars are standard deviation obtained by bootstrapping. A.1 Code Availability Code for running the simulations and generating the figures is attached to this submission. A publi...

work page 2020

[1] [1]

The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks

Jonathan Frankle and Michael Carbin. The lottery ticket hypothesis: Finding sparse, trainable neural net- works.arXiv preprint arXiv:1803.03635,

work page internal anchor Pith review Pith/arXiv arXiv

[2] [2]

Gradient descent aligns the layers of deep linear networks

Ziwei Ji and Matus Telgarsky. Gradient descent aligns the layers of deep linear networks.arXiv preprint arXiv:1810.02032,

work page internal anchor Pith review Pith/arXiv arXiv

[3] [3]

Sequential predictive learning is a unifying theory for hippocampal representation and replay.bioRxiv, pages 2024– 04,

Daniel Levenstein, Aleksei Efremov, Roy Henha Eyono, Adrien Peyrache, and Blake Richards. Sequential predictive learning is a unifying theory for hippocampal representation and replay.bioRxiv, pages 2024– 04,

work page 2024

[4] [4]

Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning

William Lotter, Gabriel Kreiman, and David Cox. Deep predictive coding networks for video prediction and unsupervised learning.arXiv preprint arXiv:1605.08104,

work page internal anchor Pith review Pith/arXiv arXiv

[5] [5]

arXiv preprint arXiv:1906.05890 , year=

Kaifeng Lyu and Jian Li. Gradient descent maximizes the margin of homogeneous neural networks.arXiv preprint arXiv:1906.05890,

work page arXiv 1906

[6] [6]

Understanding deep learning requires rethinking generalization

Chiyuan Zhang, Samy Bengio, Moritz Hardt, Benjamin Recht, and Oriol Vinyals. Understanding deep learning requires rethinking generalization.arXiv preprint arXiv:1611.03530,

work page internal anchor Pith review Pith/arXiv arXiv

[7] [7]

Error bars are standard deviation obtained by bootstrapping

As shown,A thresh scales linearly withS, supporting the claim that the prediction horizon required for latent state extraction grows proportionally with the environment size. Error bars are standard deviation obtained by bootstrapping. A.1 Code Availability Code for running the simulations and generating the figures is attached to this submission. A publi...

work page 2020