Is Generation Required for Data-Efficient Perception?

Bernhard Sch\"olkopf; Jack Brady; Simon Buchholz; Thomas Kipf; Wieland Brendel

REVIEW 4 major objections 5 minor 8 references

Is Generation Required for Data-Efficient Perception?

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Generation is required for data-efficient perception: only decoder-inversion guarantees compositional generalization.

desk verdict Worth engaging seriously, but the paper proves less than its 'cannot be achieved' language claims; the decoder/encoder asymmetry is real and new, while the infeasibility theorem is narrower than advertised. read the letter →

arxiv 2512.08854 v3 pith:JF5QB5PZ submitted 2025-12-09 cs.CV cs.LG

Jack Brady , Bernhard Schölkopf , Thomas Kipf , Simon Buchholz , Wieland Brendel This is my paper

classification cs.CVcs.LG MSC 68T07

keywords compositionalgeneralizationout-of-domaingenerativemodelsencoder-onlylearninginductivebiasidentifiabilityobject-centricrepresentationsdataefficiency

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to settle whether machine vision needs generative models to be data-efficient, and answers yes for compositional generalization. Assuming images are generated by a compositional function in the class F_int—slot-wise maps plus bounded polynomial interactions between slots—it shows that the inductive bias needed to generalize to unseen combinations of concepts is simple for a decoder to enforce but generally impossible for an encoder to enforce, because encoder constraints would require knowledge of the unseen image manifold. The theoretical core is that, when images live in a much higher-dimensional space than the latents, the local derivatives of the inverse generator are unconstrained: any Jacobian and Hessian can occur (Theorem 3.2), so no local regularizer or architecture can keep an encoder inside the good class. On photorealistic synthetic data, encoder-only models fail on out-of-domain combinations unless trained with large-scale pretraining, while generative models that constrain a decoder and invert it—by gradient search or generative replay—gain out-of-domain accuracy with no extra data. If the paper is right, the data efficiency of human perception points toward generative representations, and the scaling of non-generative models is buying generalization that structure could provide instead.

What carries the argument

The load-bearing object is the function class F_int (Eq. 2.7): diffeomorphisms that write an image as a sum of slot-wise functions plus polynomial cross-slot interaction terms of degree at most n. Its defining property—that cross-slot derivative tensors of order n+1 vanish, e.g. D_{z_k}D_{z_l} f = 0 for n=1—can be imposed on a decoder by a block-diagonal architecture or the regularizer in Eq. 3.2, and this is what guarantees the decoder identifies the ground-truth generator out-of-domain. The inverse class G_int lacks such global structure: Theorem 3.2 shows that in ambient image dimension dx ≥ dz^3, the Jacobian and Hessian of an inverse at a point can be arbitrary (up to a measure-zero set

What would settle it

Train an encoder-only model from scratch on PUG-Background (no large-scale pretraining, no decoder inversion, no added supervision) and reach near-perfect OOD accuracy on unseen animal–background pairs; the paper's position predicts this will fail except in the non-interacting n=0 case. Equivalently, exhibit any encoder inductive bias that provably keeps an encoder in G_int on OOD regions without access to X_OOD.

Watch

Extended reading notes

Core claim

The central claim is that under the compositional data-generating process used here, compositional generalization is achievable with principled inductive biases for generative methods and not for non-generative ones. A generative method learns a decoder that approximates the ground-truth generator; because the generator class F_int is characterized by block-diagonal derivative tensors (e.g., a zero cross-slot Hessian when interactions are first-order), the decoder can be constrained to F_int by architecture or a simple regularizer, and out-of-domain latents are then recovered by inverting this decoder. A non-generative method instead learns the inverse generator directly; the paper shows tha

Load-bearing premise

The argument assumes the ground-truth visual generator belongs to the function class F_int (slot-wise plus polynomial-interaction diffeomorphisms); if real images are generated by a broader class, the OOD identifiability guarantee and the decoder/encoder asymmetry can fail.

Editorial extensions

If this is right

If the central claim is correct, encoder-only (non-generative) vision models cannot be made to generalize compositionally by better inductive biases alone; improvements will continue to demand larger pretraining corpora or added supervision.
Generative methods that constrain a decoder to F_int and invert it can improve out-of-domain accuracy on unseen concept combinations without any additional data, relying only on gradient search and generative replay.
The n=0 special case (concepts that never interact, such as non-occluding objects) is the predicted exception: encoder-only methods should generalize OOD here, and the experiments confirm near-perfect OOD accuracy across all tested encoders.
The theory provides a formal grounding for the long-standing conjecture that generalization is easier in the causal direction (generating an image from latents) than in the anti-causal direction (inferring latents from an image).
Human perceptual data efficiency could be explained by the brain solving an inverse-generation problem rather than learning a direct feedforward encoder, which is why a child can recognize a penguin in a desert after seeing each in other settings.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial extension: the entire asymmetry is conditional on the assumption that natural images are generated by F_int; if real-world generation involves higher-order or non-polynomial interactions outside this class, the feasibility gap between encoders and decoders could shrink or reverse—the paper acknowledges this limitation.
Editorial extension: Theorem 3.2 and the density result in the appendix suggest a concrete test for future work: search for encoder architectures that are expressive enough to invert F_int but are not closed under addition and not dense in continuous functions; if such a class exists, it might provide the principled encoder inductive bias the paper argues is impossible.
Editorial extension: the two inversion strategies are complementary—replay works when slots can be recombined into novel scenes, search works when they cannot—so a model that routes between them (or uses search to generate replay data) may scale the approach toward natural images, where slots are less well-separated.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short take: this is a genuine contribution with an overstated central claim. The novel part is the local structure analysis of the inverse class G_int — Lemma 3.1 and Theorem 3.2 show that in high ambient dimension, pointwise first and second derivatives of a left inverse are essentially unconstrained, while the decoder-side constraint (Eq. 3.1/3.2) is simple and axis-aligned. That asymmetry is real and worth writing down. The empirical comparison on PUG is consistent with the story: non-generative encoders often fail OOD unless heavily pretrained, and decoder search/replay helps. The n=0 control is a nice check, and the paper is honest enough to show non-generative methods succeeding there.

What the paper does well: it states its assumptions openly, including the F_int premise, and the proofs in the appendix look coherent to me — standard calculus and linear algebra, not hand-waving. The empirical setup is a reasonable first test even if limited to synthetic data.

Where it overreaches: the jump from Theorem 3.2 to "generally infeasible" for encoder inductive biases. The theorem rules out local pointwise derivative regularizers; it does not rule out global architectural biases or non-local regularizers like smoothness or invertibility penalties. The Appendix A.2 argument for architectural constraints assumes G_enc is closed under addition and coordinate projections — a ViT plus slot encoder is neither. So the strong "cannot be achieved" language in the title and intro is not actually proven for practical encoder families. What the paper establishes is better stated as: no general principled way to enforce G_int on encoders is known, and the known local constraints are manifold-dependent. That weaker claim is still interesting. Also, the F_int assumption is the load-bearing premise, and the limitations section honestly flags that the results may fail outside it; the headline goes beyond what the paper itself is willing to defend.

Empirically, selecting the best configuration per model and omitting error bars makes the comparison weaker than it could be — that's fixable. The self-cited prior theorem (Brady et al. 2025) is the foundation, so independent scrutiny of that result would raise confidence, but self-citation by itself is not the issue.

Bottom line: this deserves a serious referee and likely publication after revision, with claims tempered to "no principled inductive bias known" rather than "cannot be achieved," and with empirical reporting cleaned up. I'd bring it to reading group — it will generate good debate — and I'd cite it as the formal statement of the decoder/encoder asymmetry, not as a proof that generation is required.

Referee Report

4 major / 5 minor

Summary. The paper asks whether compositional generalization, as a hallmark of human data efficiency, can be guaranteed in non-generative (encoder-only) perceptual systems or only in generative systems that invert a learned decoder. Under a compositional latent-variable model with generators in the polynomial interaction class F_int (Brady et al., 2025), the authors argue that: (i) guaranteeing OOD generalization requires constraining the decoder to F_int or the encoder to its inverse class G_int; (ii) constraining a decoder is straightforward via architecture or derivative regularization (e.g., Eq. 3.2), whereas constraining an encoder is claimed to be generally infeasible because it would require knowledge of unobserved OOD manifold geometry; (iii) this asymmetry is supported by Theorem 3.2 showing local freedom of a left inverse's Jacobian and Hessian when d_x ≥ d_z^3, and by Appendix A.2 density results under closure assumptions on the encoder class; and (iv) experiments on PUG datasets show non-generative methods need large-scale pretraining or favorable structure (PUG-Object), while generative methods improve OOD accuracy via gradient search and replay. The central reading is that compositional generalization cannot be achieved in non-generative methods through inductive bias but can be achieved in generative methods by constraining and inverting a decoder.

Significance. The question addressed is important and timely: it connects a long-standing cognitive-science hypothesis about perception-as-inversion with modern object-centric representation learning. If the central asymmetry were fully established, the paper would provide a principled argument against encoder-only inductive biases for compositional generalization and would support generative approaches such as decoder inversion, gradient search, and replay. The paper has notable strengths: it formalizes the problem within the F_int/G_int framework; it gives concrete derivative-based regularizers for decoders; it provides an explicit theorem (Theorem 3.2) on local derivative freedom; and it tests the claims on a controlled, photorealistic benchmark with multiple pretrained encoders and both generative and non-generative training regimes. The empirical n=0 control (PUG-Object) is a useful falsification probe. However, the theoretical results as stated do not support the paper's strongest claim of general infeasibility of encoder inductive biases, and there is a mismatch between the theorem's dimension regime and the experiments. With substantial revision of the claims and additional theory or exp

major comments (4)

[Sec. 5 vs Theorem 3.2] The experimental setup does not satisfy the main theorem's dimension assumption. Theorem 3.2 requires d_x ≥ d_z^3, but the models use 3 slots of dimension 64, so d_z = 192, and images are 224×224×3, so d_x = 150,528. Since 192^3 = 7,077,888 > 150,528, the theorem does not apply to the experiments. The remark after Lemma A.5 suggests the expected threshold is d_x ≥ d_z(d_z+1)/2, which would be satisfied, but that is a remark, not a proved theorem. Please either prove the result under the weaker threshold and use it to ground the experiments, or clearly state that the experiments probe a regime beyond the proved range. As written, the empirical asymmetry is not covered by the formal result.
[Sec. 3.1, Theorem 3.2 and Takeaways] Theorem 3.2 establishes local freedom of Dg(x0) and D^2 g_l(x0) at a single point x0, for almost every Jacobian A, under d_x ≥ d_z^3. This rules out pointwise first- and second-order derivative regularizers applied independently at each point, but it does not rule out architectural inductive biases that constrain the global function class, nor non-local regularizers (e.g., invertibility penalties, sparsity in a learned basis, smoothness over neighborhoods, or multi-point constraints). The 'Takeaways' paragraph in Sec. 3.1 and the abstract's 'generally infeasible using regularization or architectural constraints' is therefore an extrapolation. The manuscript should either narrow the claim to local, pointwise, derivative-based inductive biases, or provide an additional theorem covering the broader classes of encoder constraints that are claimed to be infeasible.
[Appendix A.2] The architecture-level results assume properties that standard neural encoders do not satisfy. Theorem A.8 and Corollary A.11 require G_enc to be closed under addition and, for d_x > d_z, under coordinate projections. The function class of a fixed architecture such as the ViT+slot encoder used in Sec. 5 is not closed under addition: the sum of two such functions is generally not representable by the same fixed architecture. Coordinate projection closure is also not a natural property of attention-based encoders. Hence the density/universality results do not apply to the encoder classes of practical interest. The conclusion that 'it is challenging to find natural function classes G_enc' is plausible, but it is not proved for the architectures used in the paper. Please state the closure assumptions explicitly in the main text and explain which practical classes satisfy them, or reframe the
[Sec. 2, Eq. (2.7) and Sec. 7, Limitations] The central claim is conditional on the ground-truth generator belonging to F_int, the polynomial-interaction class in Eq. (2.7). The manuscript states 'we assume that ground-truth generators f belong to F_int' without independent justification, and Sec. 7 acknowledges that results may fail outside F_int. Since Eq. (2.5) is itself imported from prior work (Brady et al., 2025), the entire asymmetry between decoder and encoder biases is a conditional theorem. This is acceptable as a contribution, but the abstract and title ('Generation is Required...') present the conclusion as unconditional. Please state the F_int condition in the abstract, and discuss the scope of the claim. The n=0 case in Fig. 6C is especially relevant: within the paper's own framework, non-generative encoders achieve near-perfect OOD generalization on PUG-Object, so the blanket statement that non-generative methods ca

minor comments (5)

[Title] The title in the preprint header is typeset as 'GENERATION ISREQUIRED FORDATA-EFFICIENT PERCEPTION'; fix the spacing.
[Sec. 3.1, n=0 paragraph] The condition '|D_zk fi(z)| · |D_zl fi(z)| = 0' is written without norms or a formal definition of fi as a coordinate function. Please define the notation precisely or refer to the original definition in Brady et al. (2023).
[Sec. 5.2, PUG-Texture replay] The statement that replay 'cannot be applied' on PUG-Texture because slots capture objects/backgrounds and 'cannot be trivially recomposed' is unclear. It would help to explain why the slot recombination used for PUG-Background does not transfer to animal–texture composition, e.g., because texture is a property of the object slot rather than an independent slot.
[Acknowledgments] The name appears misspelled: 'Thaddäus Wiedmer' should likely be 'Thaddäus Wiedemer' (matching reference [Wiedemer et al., 2024]).
[Sec. 2, notation] The sets Z_S, Z_ID, Z_OOD are used interchangeably with the latent space Z; please define Z as the image of the generator or clarify the domain/codomain conventions so that Eq. (2.4) is unambiguous.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the derivation is conditional on an imported function-class assumption, and the central asymmetry rests on new local-derivative theorems rather than on a fitted value or a definitional reduction.

full rationale

The paper's theoretical claim is conditional: it assumes the ground-truth generator belongs to F_int (Eq. 2.7), a class imported from the authors' prior work Brady et al. (2025). This is a load-bearing self-citation, but it is a stated mathematical characterization with stated assumptions and does not itself assume the paper's conclusion that generation is required. The OOD-identifiability guarantee (Eq. 2.5) is a property of F_int established in the cited prior theorem; the paper does not re-derive it from its own target claim, and the class choice is presented as an assumption ('we assume that ground-truth generators f belong to F_int') rather than as a prediction. The decoder regularizer Eq. (3.2) is simply the defining block-diagonal derivative condition of F_int, so saying decoder constraints are straightforward is a consequence of the class definition; this is not disguised as an empirical prediction. The infeasibility claim for encoders rests on Theorem 3.2 and Appendix A.2, which show pointwise derivative freedom and a density result under an addition-closure assumption that the paper explicitly acknowledges is not satisfied by fixed neural architectures ('For functions implemented by neural networks with fixed architecture this is in general not true'). This is a scope or overreach concern, not a circular reduction: the theorem does not assume that all encoder inductive biases fail. The empirical sections report measured OOD accuracies rather than fitting a parameter and then presenting the same quantity as a prediction. The replay objective (Eq. 4.4) and the decoder interaction regularizer (Eq. B.1) are reused from prior work by the same group, but they are methods used in experiments, not evidence that presupposes the conclusion. The paper's own Limitations section explicitly concedes that results 'may, in principle, fail to generalize to function classes associated with other settings'. No equation in the paper reduces to its inputs by construction, and no fitted parameter is renamed as a prediction. The self-citations are real, potentially load-bearing, mathematical results, but they are not circular reductions; the central derivation has independent content.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper's central claim rests on the F_int modeling assumption imported from the authors' prior work, on a global-extension step in the proof of Theorem 3.2, and on restrictive structural assumptions in Appendix A.2. No entirely new physical or mathematical entities are postulated. Free parameters are limited to empirical hyperparameters; the theoretical result is parameter-free.

free parameters (4)

decoder interaction regularizer weight = 0.01
Appendix B.1: regularizes cross-attention so pixels attend to at most one slot, enforcing decoder behavior close to F_int; hand-chosen and directly shapes the generative advantage.
VAE beta (KL weight) = 0.005 or 0.001
Appendix B.2: KL weight chosen per experiment; affects slot representation quality and downstream readout.
search entropy regularizer weight = 10 or 50
Appendix B.2: added during gradient-based search to keep optimized latents near classifier-supported regions; hand-chosen per dataset.
search optimization iterations = 300/500 (PUG-Background), 700 (PUG-Texture)
Appendix B.2: budget for Eq. 4.3 inversion; chosen per dataset and affects OOD search quality.

assumptions (5)

domain assumption Ground-truth generators f belong to F_int, the polynomial-interaction class in Eq. (2.7).
Section 2: 'we assume that ground-truth generators f belong to F_int'. This is the key modeling assumption that makes OOD identifiability (Eq. 2.5) possible. If natural image generation lies outside F_int, the paper's theoretical comparison loses its basis.
domain assumption F_int is the largest function class satisfying Eq. (2.5) (Brady et al. 2025, Thm 4.4).
The paper imports this theorem from its own prior work without proof. The largest-class property is used to argue F_int is the relevant setting for compositional generalization.
standard math Global extension of local left inverses is possible via tubular neighborhoods and partition of unity.
Appendix A.1, proof of Theorem 3.2: after constructing a local left inverse, the authors say standard techniques extend it globally. This requires f's image to admit a tubular neighborhood, which is not established for all non-proper polynomial generators in F_int.
ad hoc to paper Encoder classes of interest are closed under addition and coordinate projections, or are dense via Stone-Weierstrass.
Appendix A.2: Theorem A.8 and Corollary A.11 rely on G_enc being a vector-space-like class. The paper concedes fixed neural-network architectures are generally not closed under addition, so this assumption limits the generality of the infeasibility conclusion.
domain assumption Eq. (2.1) is the right formalization of perception, and compositional generalization is defined by slot-wise recombinations in Eq. (2.4).
Section 2: perception is treated as inverting the ground-truth generator up to slot-wise bijections, and OOD is defined as unseen Cartesian products of slot sets. Task-based perception is argued to be a special case, which is reasonable but not fully explored.

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Pith. "Pith review of Is Generation Required for Data-Efficient Perception?." pith.science (2026). https://pith.science/paper/JF5QB5PZ

@misc{pith2026251208854,
  author       = {Pith},
  title        = {Pith review of: Is Generation Required for Data-Efficient Perception?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JF5QB5PZ}},
  note         = {Machine review of arXiv:2512.08854}
}

read the original abstract

It has been hypothesized that achieving the data efficiency of human visual perception requires a generative approach in which internal representations result from inverting a decoder. Yet today's most successful vision models are non-generative, relying on an encoder that maps images to representations without decoder inversion. This raises the question of whether generation is necessary for data-efficient machine perception. To address this, we study to what extent generative and non-generative methods can achieve compositional generalization, a hallmark of human data efficiency. Under a compositional generative process, we formally characterize the inductive biases required for compositional generalization in decoder-based (generative) and encoder-based (non-generative) methods. We show theoretically that the inductive biases required for an encoder are substantially more complex and generally infeasible to impose explicitly through architectural constraints or regularization. By contrast, the decoder biases take a simple form that can be enforced directly. These results suggest that compositional generalization may be substantially easier to achieve through a generative paradigm of learning and inverting a decoder rather than learning an encoder directly. We examine our theoretical findings empirically by training a range of generative and non-generative methods on synthetic image data. We find that non-generative methods often fail to generalize compositionally and require large-scale pretraining to improve generalization. By comparison, generative methods yield gains in generalization without requiring additional data.

Figures

Figures reproduced from arXiv: 2512.08854 by the authors.

**Figure 1.** Generative vs. non-generative compositional generalization. We assume in-domain (ID) and out-of-domain (OOD) images arise from a latent variable model through an unknown compositional generator f ∈ Fint, with inverse g ∈ Gint. Guaranteeing compositional generalization for a generative approach requires constraining a decoder such that fˆ ∈ Fint, and for a non-generative approach, an encoder such that gˆ ∈ Gint (Sec.… view at source ↗

**Figure 2.** Visualization of a data generating process with in- and out-of-domain regions. Compositional generalization. We now formalize compositional generalization. Informally, compositional generalization is the ability to perceive OOD images containing unseen concept combinations (e.g. “penguin” and “desert” in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Structure of a data manifold X and latent manifold Z. Thus, when dx ≫ dz, D2g and Dg can be arbitrary matrices (up to a set of measure 0). We emphasize that this result applies to Fint with arbitrary interaction degree n ≥ 1 and any slot dimensions. However, the structure expressed in Eq. (3.3) does not vanish entirely from g. Instead, it persists, but only for the restriction of g to the data manifold X . Specifi… view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Approaches for inverting a generator out-of-domain. Left. Visualization of gradient-based search to invert a decoder fˆ out-of-domain, with initialization given by an encoder gˆ. Right. Visualization of generative replay in which an encoder is trained on OOD images gen…

**Figure 5.** Figure 5: ID and OOD images from each dataset used in our experiments. Datasets. To evaluate compositional generalization, we require datasets that can be partitioned into ID and OOD regions containing unseen concept combinations. To this end, we leverage PUG (Bordes et al., 202…

**Figure 6.** Figure 6: OOD performance for non-generative methods. We report OOD performance across three dataset splits for non-generative methods trained with and without supervision and with differing ViTs. On PUG-Background (A.), we see that strong OOD performance generally emerges only …

**Figure 7.** Figure 7: OOD performance for generative methods. We report OOD performance on PUG-Background and PUG-Texture for unsupervised VAEs which leverage replay (Sec. 4.2) and search (Sec. 4.1) trained with differing ViT encoders. On PUG-Background (A.), we observe a significant increa…

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Works this paper leans on

8 extracted references · 3 linked inside Pith

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Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.

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The classG enc is closed under addition, i.e., forg 1,g 2 ∈ Genc alsog 1 +g 2 ∈ Genc

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