arxiv: 2605.07724 · v1 · submitted 2026-05-08 · 💻 cs.LG · cs.AI

Recognition: 2 theorem links

· Lean Theorem

Curated Synthetic Data Doesn't Have to Collapse: A Theoretical Study of Generative Retraining with Pluralistic Preferences

Ali Falahati , Mohammad Mohammadi Amiri , Kate Larson , Lukasz Golab

Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:27 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords generative modelsmodel collapsesynthetic datarecursive trainingpreference aggregationNash bargainingalignmentdiversity

0 comments

The pith

Recursive training with multiple reward functions converges to a diverse stable distribution instead of collapsing.

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

The paper shows that collapse onto narrow outputs during recursive retraining of generative models is not inevitable when curation draws on several distinct reward signals rather than a single fixed one. It formalizes the process as a dynamical system under heterogeneous preferences and proves convergence, under stated conditions, to a limiting distribution that spreads probability mass across competing high-reward regions. This distribution preserves diversity and satisfies a weighted Nash bargaining solution, which the authors present as a formal account of how pluralistic values can be aggregated in self-improving loops. A sympathetic reader would care because the result supplies a theoretical alternative to the common requirement of injecting real data to maintain output variety.

Core claim

When synthetic outputs are curated according to a single reward, recursive retraining collapses to a narrow set of high-reward samples. With multiple reward functions the dynamics instead converge to a stable distribution that allocates positive probability across several high-reward modes, preserves diversity, and coincides with the weighted Nash bargaining solution among the preference functions.

What carries the argument

The weighted Nash bargaining solution, which the authors prove is the unique limiting distribution of the recursive training dynamics driven by heterogeneous preferences.

If this is right

The model allocates probability mass across multiple competing high-reward regions instead of concentrating on one.
Diversity is preserved without external real-data injection.
Value aggregation across preferences receives an exact characterization as a weighted Nash bargaining outcome.
The limiting distribution is stable and satisfies the bargaining axioms for the given set of reward functions.

Where Pith is reading between the lines

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

Practitioners could test the result by training small models with deliberately conflicting rewards and measuring output entropy after many retraining cycles.
The framework suggests that multi-objective alignment problems might be solvable inside synthetic loops if the preference set is sufficiently pluralistic.
The same convergence argument could be examined in settings with noisy or time-varying rewards to see whether the bargaining solution remains attractive.
It links synthetic-data collapse to classic questions in multi-objective optimization and social choice theory.

Load-bearing premise

That the recursive training process can be formalized so that its dynamics admit a stable distribution under the stated conditions with multiple reward functions.

What would settle it

Simulate the recursive process with two or more distinct reward functions on a small generative model and check whether the output distribution stabilizes at the predicted weighted Nash bargaining allocation rather than collapsing to a single mode.

Figures

Figures reproduced from arXiv: 2605.07724 by Ali Falahati, Kate Larson, Lukasz Golab, Mohammad Mohammadi Amiri.

**Figure 1.** Figure 1: Overview of pluralistic curation. At each retraining step, the generative model samples candidates from its current distribution. A reward function is chosen at random r1 with probability q, or r2 with probability 1 − q and one candidate is selected. The model is then retrained to maximize the likelihood of this curated sample. Over time, this alternating selection drives the model toward a stable mixture … view at source ↗

**Figure 2.** Figure 2: Synthetic Dataset Pluralistic curation (top) vs. single-reward retraining (bottom) on a two-mode Gaussian mixture with means at µ1 = (2, 2) and µ2 = (8, 8). Bottom plots track expected rewards (left) and reward variances (right) across retraining steps. following lemma addresses this gap: when q dominates leakage, the basin mass is eventually bounded away from both 0 and 1. Lemma 3.5 (Uniform non-collapse … view at source ↗

**Figure 3.** Figure 3: Final distributions and reward variances under pluralistic curation across varying mode distances. Same synthetic two-mode Gaussian-mixture setting as [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Entropy over training iterations on CIFAR-10 for different retraining configurations. (Left) two-preference retraining under varying reward ratios (Right) balanced multi-preference retraining with 1 to 5 preferences. Under the same outside-gap and cross-basin leakage controls, mass concentrates on ∪iSi,ε and limit weights are controlled by leakage, approaching {qi} in the vanishingleakage regime. Details… view at source ↗

**Figure 5.** Figure 5: Evolution of output length entropy for text with GPT2. Two-preference retraining under varying preferred length distances. (Lipman et al., 2022; Shaul et al., 2023; Tong et al., 2023). The initial model is pretrained on all 50,000 training images from CIFAR-10. At each retraining iteration, we generate 5 · 104 samples from the current model. From these, we retain 2.5 · 103 samples using a discrete K-BT mo… view at source ↗

read the original abstract

Recursive retraining of generative models poses a critical representation challenge: when synthetic outputs are curated based on a fixed reward signal, the model tends to collapse onto a narrow set of outputs that over-optimize that objective. Prior work suggests that such collapse is unavoidable without adding real data into the mix. We revisit this conclusion from an alignment perspective and show that collapse can be mitigated through curation based on multiple reward functions. We formalize the dynamics of recursive training under heterogeneous preferences and prove that, under certain conditions, the model converges to a stable distribution that allocates probability mass across competing high-reward regions. The limiting distribution preserves diversity and provably satisfies a weighted Nash bargaining solution, offering a formal interpretation of value aggregation in synthetic retraining loops.

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 recursive retraining of generative models on synthetic data curated via a single fixed reward leads to collapse, but curation based on multiple heterogeneous reward functions can mitigate this. It formalizes the recursive dynamics under pluralistic preferences and proves that, under certain conditions on the rewards and update rules, the process converges to a unique stable distribution that spreads probability mass across competing high-reward modes, preserves diversity, and coincides with a weighted Nash bargaining solution.

Significance. If the derivation is rigorous, the result supplies a formal mechanism by which pluralistic curation prevents collapse without external real data, while supplying a game-theoretic interpretation of value aggregation in alignment loops. This could inform the design of retraining pipelines that maintain output diversity under competing objectives.

major comments (2)

[Theorem 1 / dynamical-system formalization] The abstract and the statement of the main theorem invoke 'certain conditions' on the reward functions and the update rule that guarantee convergence and uniqueness of the limiting distribution. These conditions are load-bearing for the central claim yet are not enumerated or shown to be minimal; without an explicit list (e.g., Lipschitz continuity of rewards, contraction properties of the curation map, or boundedness of the preference weights), it is impossible to assess whether the result survives approximate sampling or finite model capacity.
[Section 3 (dynamics) and proof of Theorem 1] The update rule that maps the current generative distribution to the next one via curation of synthetic samples under multiple rewards is never written as an explicit operator (e.g., no equation of the form P_{t+1} = T(P_t, R_1, …, R_k)). Consequently the proof that the fixed point satisfies the weighted Nash bargaining axioms cannot be verified for independence from self-referential parameter fitting.

minor comments (2)

[Notation section] Define all symbols appearing in the dynamical equations at first use; several preference-weight and reward-normalization constants are introduced without prior definition.
[Related-work paragraph] Add a short paragraph contrasting the derived limiting distribution with the single-reward collapse results cited in the introduction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation of the paper's significance and for the constructive comments that highlight opportunities to improve clarity and rigor. We address each major comment below and will revise the manuscript to incorporate the suggested changes.

read point-by-point responses

Referee: [Theorem 1 / dynamical-system formalization] The abstract and the statement of the main theorem invoke 'certain conditions' on the reward functions and the update rule that guarantee convergence and uniqueness of the limiting distribution. These conditions are load-bearing for the central claim yet are not enumerated or shown to be minimal; without an explicit list (e.g., Lipschitz continuity of rewards, contraction properties of the curation map, or boundedness of the preference weights), it is impossible to assess whether the result survives approximate sampling or finite model capacity.

Authors: We agree that the conditions should be stated explicitly. In the revised manuscript we will insert a dedicated subsection (new Section 2.3) that enumerates all standing assumptions: (i) each reward R_i is continuous and bounded; (ii) the curation operator is a contraction mapping in total variation with modulus strictly less than one; (iii) preference weights w_i > 0 sum to one; and (iv) the model class is sufficiently expressive to contain the fixed point. We will also add a remark discussing robustness under approximate sampling via concentration bounds and will explicitly note that finite-capacity effects remain outside the current infinite-capacity analysis. revision: yes
Referee: [Section 3 (dynamics) and proof of Theorem 1] The update rule that maps the current generative distribution to the next one via curation of synthetic samples under multiple rewards is never written as an explicit operator (e.g., no equation of the form P_{t+1} = T(P_t, R_1, …, R_k)). Consequently the proof that the fixed point satisfies the weighted Nash bargaining axioms cannot be verified for independence from self-referential parameter fitting.

Authors: We acknowledge the presentational omission. In the revision we will define the operator explicitly in Section 3 as P_{t+1} = T(P_t; {R_i}_{i=1}^k, w), where T is the map that draws synthetic samples from P_t, scores them under each R_i, and produces the next distribution via the weighted pluralistic aggregation rule. The proof of Theorem 1 will be reorganized to first derive that any fixed point of T satisfies the variational first-order condition equivalent to the weighted Nash bargaining solution, then establish uniqueness and global convergence from the contraction property. The derivation relies solely on the variational characterization of T and does not involve self-referential parameter fitting. revision: yes

Circularity Check

0 steps flagged

No circularity; convergence result derived from formalized dynamics without reduction to inputs or self-citation

full rationale

The paper formalizes recursive retraining dynamics under multiple reward functions and proves convergence to a limiting distribution satisfying a weighted Nash bargaining solution under explicitly stated conditions. No load-bearing step reduces by construction to a fitted parameter, self-referential definition, or prior self-citation; the stable distribution and diversity preservation are outputs of the proof rather than inputs. The analysis is self-contained against the dynamical system model with no renaming of known results or smuggled ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on an unstated formalization of recursive training dynamics and on unspecified conditions that enable convergence; these are domain assumptions whose details are not supplied in the abstract.

axioms (2)

domain assumption Recursive training dynamics under heterogeneous preferences can be formalized as a dynamical system that admits a stable limiting distribution.
The proof of convergence presupposes this formalization.
ad hoc to paper Certain conditions on the reward functions and update rules guarantee convergence to the claimed distribution.
The abstract invokes these conditions without enumerating them.

pith-pipeline@v0.9.0 · 5435 in / 1239 out tokens · 44678 ms · 2026-05-11T02:27:15.812817+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.

pt+1(x) = pt(x) (q H^K,r1_pt(x) + (1-q) H^K,r2_pt(x)) ... large-K limit H^∞,r_p(x) = e^{r(x)} / E_p[e^{r(y)}]
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

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

limiting mixture satisfies weighted Nash bargaining solution ... u1(pα)−d1^q (u2(pα)−d2)^{1-q} maximized at α=q

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

113 extracted references · 113 canonical work pages · 13 internal anchors

[2]

2016 , eprint=

Pointer Sentinel Mixture Models , author=. 2016 , eprint=

work page 2016
[3]

Advances in Neural Information Processing Systems , volume=

Deep reinforcement learning from human preferences , author=. Advances in Neural Information Processing Systems , volume=

work page
[4]

Advances in Neural Information Processing Systems , volume=

Fine-grained human feedback gives better rewards for language model training , author=. Advances in Neural Information Processing Systems , volume=

work page
[6]

2006 , publisher=

Pattern Recognition and Machine Learning , author=. 2006 , publisher=

work page 2006
[7]

Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks

Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks , author=. arXiv preprint arXiv:1511.06434 , year=

work page internal anchor Pith review arXiv
[8]

2009 , institution=

Learning Multiple Layers of Features from Tiny Images , author=. 2009 , institution=

work page 2009
[9]

International Conference on Learning Representations (ICLR) , year=

Very Deep Convolutional Networks for Large-Scale Image Recognition , author=. International Conference on Learning Representations (ICLR) , year=

work page
[10]

Analyzing and improving the image quality of stylegan

Karras, Tero and Laine, Samuli and Aila, Timo , title =. arXiv preprint arXiv:1912.04958 , year =

work page arXiv 1912
[11]

Hierarchical Text-Conditional Image Generation with CLIP Latents

Hierarchical text-conditional image generation with clip latents , author=. arXiv preprint arXiv:2204.06125 , volume=

work page internal anchor Pith review Pith/arXiv arXiv
[12]

Make-A-Video: Text-to-Video Generation without Text-Video Data

Make-a-video: Text-to-video generation without text-video data , author=. arXiv preprint arXiv:2209.14792 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[13]

Advances in Neural Information Processing Systems , volume=

Efficient spatially sparse inference for conditional GANs and diffusion models , author=. Advances in Neural Information Processing Systems , volume=

work page
[14]

Advances in Neural Information Processing Systems , volume=

Language models are few-shot learners , author=. Advances in Neural Information Processing Systems , volume=

work page
[15]

GPT-4 Technical Report

OpenAI , title =. arXiv preprint arXiv:2303.08774 , year =

work page internal anchor Pith review Pith/arXiv arXiv
[16]

, title =

Torralba, Antonio and Efros, Alexei A. , title =. CVPR , year =

work page
[17]

ACM Computing Surveys (CSUR) , volume=

A survey on bias and fairness in machine learning , author=. ACM Computing Surveys (CSUR) , volume=. 2021 , publisher=

work page 2021
[18]

FAccT , year =

Buolamwini, Joy and Gebru, Timnit , title =. FAccT , year =

work page
[19]

and Gebru, Timnit and McMillan-Major, Angelina and Shmitchell, Shmargaret , title =

Bender, Emily M. and Gebru, Timnit and McMillan-Major, Angelina and Shmitchell, Shmargaret , title =. FAccT , year =

work page
[24]

Proceedings of the ACM on Human-Computer Interaction , volume =

Miceli, Milagros and Posada, Julian and Yang, Tianling , title =. Proceedings of the ACM on Human-Computer Interaction , volume =

work page
[25]

and Suri, Siddharth , title =

Gray, Mary L. and Suri, Siddharth , title =

work page
[26]

FAccT , pages =

Denton, Emily and Hanna, Alex and Amironesei, Razvan and Smart, Andrew and Nicole, Hilary , title =. FAccT , pages =

work page
[27]

, title =

Sambasivan, Nithya and Kapania, Nishant and Highfill, Hannah and Akrong, Diana and Paritosh, Praveen and Aroyo, Lora M. , title =. CHI , pages =

work page
[28]

Advances in neural information processing systems , volume=

Fine-tuning language models to find agreement among humans with diverse preferences , author=. Advances in neural information processing systems , volume=

work page
[29]

International Conference on Machine Learning , pages=

Wasserstein generative adversarial networks , author=. International Conference on Machine Learning , pages=. 2017 , organization=

work page 2017
[30]

NIPS Tutorial , year=

NIPS 2016 tutorial: Generative adversarial networks , author=. NIPS Tutorial , year=

work page 2016
[31]

IEEE Transactions on Neural Networks and Learning Systems , volume=

Training generative adversarial networks via stochastic Nash games , author=. IEEE Transactions on Neural Networks and Learning Systems , volume=. 2021 , publisher=

work page 2021
[32]

arXiv preprint arXiv:1810.05221 , year=

Mdgan: Boosting anomaly detection using multi-discriminator generative adversarial networks , author=. arXiv preprint arXiv:1810.05221 , year=

work page arXiv
[33]

Artificial Intelligence Review , volume=

Games of GANs: Game-theoretical models for generative adversarial networks , author=. Artificial Intelligence Review , volume=. 2023 , publisher=

work page 2023
[34]

Patterns , volume=

Multi-objective latent space optimization of generative molecular design models , author=. Patterns , volume=. 2024 , publisher=

work page 2024
[35]

arXiv preprint arXiv:2011.10134 , year=

Provable multi-objective reinforcement learning with generative models , author=. arXiv preprint arXiv:2011.10134 , year=

work page arXiv 2011
[36]

Advances in Neural Information Processing Systems , volume=

Mcl-gan: Generative adversarial networks with multiple specialized discriminators , author=. Advances in Neural Information Processing Systems , volume=

work page
[37]

International Conference on Machine Learning , pages=

Multi-objective training of generative adversarial networks with multiple discriminators , author=. International Conference on Machine Learning , pages=. 2019 , organization=

work page 2019
[38]

European Conference on Computer Vision , pages=

Sharegpt4v: Improving large multi-modal models with better captions , author=. European Conference on Computer Vision , pages=. 2024 , organization=

work page 2024
[39]

arXiv preprint arXiv:2403.00000 , year=

Bias-aware data curation for generative models , author=. arXiv preprint arXiv:2403.00000 , year=

work page arXiv
[40]

Advances in Neural Information Processing Systems , volume=

Generative adversarial nets , author=. Advances in Neural Information Processing Systems , volume=

work page
[41]

Unrolled generative adversarial networks

Unrolled generative adversarial networks , author=. arXiv preprint arXiv:1611.02163 , year=

work page arXiv
[42]

Advances in Neural Information Processing Systems , volume=

Improved training of Wasserstein GANs , author=. Advances in Neural Information Processing Systems , volume=

work page
[43]

Advances in Neural Information Processing Systems , volume=

Improved techniques for training GANs , author=. Advances in Neural Information Processing Systems , volume=

work page
[44]

Spectral Normalization for Generative Adversarial Networks

Spectral normalization for generative adversarial networks , author=. arXiv preprint arXiv:1802.05957 , year=

work page Pith review arXiv
[45]

Conditional Generative Adversarial Nets

Conditional generative adversarial nets , author=. arXiv preprint arXiv:1411.1784 , year=

work page internal anchor Pith review arXiv
[46]

arXiv preprint arXiv:1712.00679 , year=

GANGs: Generative adversarial network games , author=. arXiv preprint arXiv:1712.00679 , year=

work page arXiv
[47]

AAAI Conference on Artificial Intelligence , year=

GMAN: A generative multi-adversarial network , author=. AAAI Conference on Artificial Intelligence , year=

work page
[48]

2019 IEEE international parallel and distributed processing symposium (IPDPS) , pages=

Md-gan: Multi-discriminator generative adversarial networks for distributed datasets , author=. 2019 IEEE international parallel and distributed processing symposium (IPDPS) , pages=. 2019 , organization=

work page 2019
[49]

Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) , year =

Hu Xu and Saining Xie and Po-Yao Huang and Licheng Yu and Russell Howes and Gargi Ghosh and Luke Zettlemoyer and Christoph Feichtenhofer , title =. Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) , year =

work page
[50]

Benelux Conference on Artificial Intelligence , pages=

Beyond local nash equilibria for adversarial networks , author=. Benelux Conference on Artificial Intelligence , pages=. 2018 , organization=

work page 2018
[51]

Advances in Neural Information Processing Systems , volume=

Diffusion Models Beat GANs on Image Synthesis , author=. Advances in Neural Information Processing Systems , volume=

work page
[52]

Proceedings of the 38th International Conference on Machine Learning , pages=

Improved Denoising Diffusion Probabilistic Models , author=. Proceedings of the 38th International Conference on Machine Learning , pages=. 2021 , publisher=

work page 2021
[53]

Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision , pages=

Agree to Disagree: When Deep Learning Models with Identical Architectures Learn Dissimilar Features , author=. Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision , pages=

work page
[54]

Advances in Neural Information Processing Systems , volume=

Score-based Generative Modeling in Latent Space , author=. Advances in Neural Information Processing Systems , volume=

work page
[55]

International Conference on Learning Representations , year=

Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality , author=. International Conference on Learning Representations , year=

work page
[56]

Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback

Open problems and fundamental limitations of reinforcement learning from human feedback , author=. arXiv preprint arXiv:2307.15217 , year=

work page internal anchor Pith review arXiv
[57]

arXiv preprint arXiv:2402.05070 , year =

A roadmap to pluralistic alignment , author=. arXiv preprint arXiv:2402.05070 , year=

work page arXiv
[58]

Constitutional AI: Harmlessness from AI Feedback

Constitutional AI: Harmlessness from AI feedback , author=. arXiv preprint arXiv:2212.08073 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[59]

European Review , volume=

Improving ratings: audit in the British University system , author=. European Review , volume=. 1997 , publisher=

work page 1997
[60]

Minds and Machines , volume=

Artificial intelligence, values, and alignment , author=. Minds and Machines , volume=. 2020 , publisher=

work page 2020
[61]

Supervising strong learners by amplifying weak experts

Supervising strong learners by amplifying weak experts , author=. arXiv preprint arXiv:1810.08575 , year=

work page Pith review arXiv
[62]

Advances in neural information processing systems , volume=

Gans trained by a two time-scale update rule converge to a local nash equilibrium , author=. Advances in neural information processing systems , volume=

work page
[64]

International Conference on Machine Learning , pages=

On kinetic optimal probability paths for generative models , author=. International Conference on Machine Learning , pages=. 2023 , organization=

work page 2023
[66]

Proceedings of the AAAI Conference on Artificial Intelligence , volume=

The Alignment Game: A Theory of Long-Horizon Alignment Through Recursive Curation , author=. Proceedings of the AAAI Conference on Artificial Intelligence , volume=

work page
[67]

arXiv preprint arXiv:2305.15785 , year=

Talking About Large Language Models , author=. arXiv preprint arXiv:2305.15785 , year=

work page arXiv
[68]

Advances in neural information processing systems , volume=

Training language models to follow instructions with human feedback , author=. Advances in neural information processing systems , volume=

work page
[69]

Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback

Training a helpful and harmless assistant with reinforcement learning from human feedback , author=. arXiv preprint arXiv:2204.05862 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[70]

Improving alignment of dialogue agents via targeted human judgements

Improving alignment of dialogue agents via targeted human judgements , author=. arXiv preprint arXiv:2209.14375 , year=

work page internal anchor Pith review arXiv
[71]

2023 , publisher=

Sparks of artificial general intelligence: Early experiments with gpt-4 , author=. 2023 , publisher=

work page 2023
[72]

The method of paired comparisons , author=

Rank analysis of incomplete block designs: I. The method of paired comparisons , author=. Biometrika , volume=. 1952 , publisher=

work page 1952
[73]

Social Choice and Individual Values , author=

work page
[74]

Penguin , year=

Human Compatible: Artificial Intelligence and the Problem of Control , author=. Penguin , year=

work page
[76]

The Twelfth International Conference on Learning Representations , year=

Self-consuming generative models go mad , author=. The Twelfth International Conference on Learning Representations , year=

work page
[77]

OpenAI , year=

Language Models are Unsupervised Multitask Learners , author=. OpenAI , year=

work page
[78]

Is model collapse inevitable? Breaking the curse of recursion by accumulating real and synthetic data,

Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Data , author=. arXiv preprint arXiv:2404.01413 , year=

work page arXiv
[80]

arXiv preprint arXiv:2310.16048 , year=

AI Alignment and Social Choice: Fundamental Limitations and Policy Implications , author=. arXiv preprint arXiv:2310.16048 , year=

work page arXiv
[81]

arXiv preprint arXiv:2411.04991 , year=

Rethinking bradley-terry models in preference-based reward modeling: Foundations, theory, and alternatives , author=. arXiv preprint arXiv:2411.04991 , year=

work page arXiv
[82]

arXiv preprint arXiv:2410.02197 , year=

Beyond Bradley-Terry Models: A General Preference Model for Language Model Alignment , author=. arXiv preprint arXiv:2410.02197 , year=

work page arXiv
[83]

arXiv preprint arXiv:2506.09401 , year=

A theoretical basis for model collapse in recursive training , author=. arXiv preprint arXiv:2506.09401 , year=

work page arXiv
[84]

arXiv preprint arXiv:2402.07712 , year=

Model Collapse Demystified: The Case of Regression , author=. arXiv preprint arXiv:2402.07712 , year=

work page arXiv
[85]

Journal of the Royal Statistical Society: Series A (Statistics in Society) , volume=

A diagnostic framework for the Bradley--Terry model , author=. Journal of the Royal Statistical Society: Series A (Statistics in Society) , volume=. 2022 , publisher=

work page 2022
[86]

Impossibility and uncertainty theorems in AI value alignment,

Impossibility and Uncertainty Theorems in AI Value Alignment (or why your AGI should not have a utility function) , author=. arXiv preprint arXiv:1901.00064 , year=

work page arXiv 1901
[87]

Representative social choice: From learning theory to ai alignment.arXiv preprint arXiv:2410.23953,

Representative Social Choice: From Learning Theory to AI Alignment , author=. arXiv preprint arXiv:2410.23953 , year=

work page arXiv
[88]

arXiv preprint arXiv:2309.01291 , year=

Generative Social Choice , author=. arXiv preprint arXiv:2309.01291 , year=

work page arXiv
[89]

Nature Human Behaviour , volume=

Human-centred mechanism design with Democratic AI , author=. Nature Human Behaviour , volume=. 2022 , publisher=

work page 2022
[90]

arXiv preprint arXiv:2406.07515 , year=

Beyond Model Collapse: Scaling Up with Synthesized Data Requires Reinforcement , author=. arXiv preprint arXiv:2406.07515 , year=

work page arXiv

Showing first 80 references.