A computational phase transition for learning-to-sample from Ising models

• URL: http://arxiv.org/abs/2605.24752v1
• Date: Sat, 23 May 2026 22:04:30 GMT
• Title: A computational phase transition for learning-to-sample from Ising models
• Abstract summary: We study emphlearning-to-sample -- a basic algorithmic task underlying generative modeling.<n>We construct a family of Ising models of constantly bounded-width which lie just beyond the spectral threshold.<n>Results show that learning-to-sample can be more difficult than parameter learning.
• Score: 26.34581413505931
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study \emph{learning-to-sample} -- a basic algorithmic task underlying generative modeling -- for Ising models, a standard testbed for algorithmic ideas in both theoretical computer science and machine learning. Given i.i.d. samples of an unknown target distribution, the goal of learning-to-sample is to learn a computationally efficient generation procedure that produces new samples following approximately the same distribution. We construct a family of Ising models of constantly bounded-width which lie just beyond the spectral threshold $λ_{\max}(J)-λ_{\min}(J)=1$, and show that learning-to-sample for this family is computationally hard under standard cryptographic assumptions, even when the learner is given both polynomially many i.i.d. samples from the model and explicit access to its parameters. Combined with results of [AJKPV24,KLV25] showing tractability of learning-to-sample below the spectral threshold, this establishes a sharp computational phase transition at the spectral threshold. Moreover, combined with prior results on parameter learning for bounded-width Ising models [KM17,WSD19,VML20], this shows that learning-to-sample can be more difficult than parameter learning. Finally, we show that any efficient learner for these hard instances exhibits a natural memorization-hallucination dichotomy: the learner must either output configurations that, after a simple transformation, match the (transformed) training data or place substantial mass on configurations of negligible probability under the target distribution.

Related papers

• A Neuro-inspired Interpretation of Unlearning in Large Language Models through Sample-level Unlearning Difficulty [12.382999548648726]
  Existing studies assume a uniform unlearning difficulty across samples.<n>We propose a Memory Removal Difficulty ($mathrmMRD$) metric to quantify sample-level unlearning difficulty.<n>We also propose an $mathrmMRD$-based weighted sampling method to optimize existing unlearning algorithms.
  arXiv  Detail & Related papers  (2025-04-09T07:48:10Z)
• Dimension-free Score Matching and Time Bootstrapping for Diffusion Models [19.62665684173391]
  Diffusion models generate samples by estimating the score function of the target distribution at various noise levels.<n>We introduce a martingale-based error decomposition and sharp variance bounds, enabling efficient learning from dependent data.<n>Building on these insights, we propose Bootstrapped Score Matching (BSM), a variance reduction technique that leverages previously learned scores to improve accuracy at higher noise levels.
  arXiv  Detail & Related papers  (2025-02-14T18:32:22Z)
• Learning to sample fibers for goodness-of-fit testing [0.0]
  We consider the problem of constructing exact goodness-of-fit tests for discrete exponential family models.<n>We translate the problem into a Markov decision process and demonstrate a reinforcement learning approach for learning good moves' for sampling.<n>Our algorithm is based on an actor-critic sampling scheme, with provable convergence.
  arXiv  Detail & Related papers  (2024-05-22T19:33:58Z)
• Limits of Transformer Language Models on Learning to Compose Algorithms [77.2443883991608]
  We evaluate training LLaMA models and prompting GPT-4 and Gemini on four tasks demanding to learn a composition of several discrete sub-tasks. Our results indicate that compositional learning in state-of-the-art Transformer language models is highly sample inefficient.
  arXiv  Detail & Related papers  (2024-02-08T16:23:29Z)
• The Languini Kitchen: Enabling Language Modelling Research at Different Scales of Compute [66.84421705029624]
  We introduce an experimental protocol that enables model comparisons based on equivalent compute, measured in accelerator hours. We pre-process an existing large, diverse, and high-quality dataset of books that surpasses existing academic benchmarks in quality, diversity, and document length. This work also provides two baseline models: a feed-forward model derived from the GPT-2 architecture and a recurrent model in the form of a novel LSTM with ten-fold throughput.
  arXiv  Detail & Related papers  (2023-09-20T10:31:17Z)
• Towards Automated Imbalanced Learning with Deep Hierarchical Reinforcement Learning [57.163525407022966]
  Imbalanced learning is a fundamental challenge in data mining, where there is a disproportionate ratio of training samples in each class. Over-sampling is an effective technique to tackle imbalanced learning through generating synthetic samples for the minority class. We propose AutoSMOTE, an automated over-sampling algorithm that can jointly optimize different levels of decisions.
  arXiv  Detail & Related papers  (2022-08-26T04:28:01Z)
• Pairwise Learning via Stagewise Training in Proximal Setting [0.0]
  We combine adaptive sample size and importance sampling techniques for pairwise learning, with convergence guarantees for nonsmooth convex pairwise loss functions. We demonstrate that sampling opposite instances at each reduces the variance of the gradient, hence accelerating convergence.
  arXiv  Detail & Related papers  (2022-08-08T11:51:01Z)
• Exploring Complementary Strengths of Invariant and Equivariant Representations for Few-Shot Learning [96.75889543560497]
  In many real-world problems, collecting a large number of labeled samples is infeasible. Few-shot learning is the dominant approach to address this issue, where the objective is to quickly adapt to novel categories in presence of a limited number of samples. We propose a novel training mechanism that simultaneously enforces equivariance and invariance to a general set of geometric transformations.
  arXiv  Detail & Related papers  (2021-03-01T21:14:33Z)
• Goal-directed Generation of Discrete Structures with Conditional Generative Models [85.51463588099556]
  We introduce a novel approach to directly optimize a reinforcement learning objective, maximizing an expected reward. We test our methodology on two tasks: generating molecules with user-defined properties and identifying short python expressions which evaluate to a given target value.
  arXiv  Detail & Related papers  (2020-10-05T20:03:13Z)
• PAC Bounds for Imitation and Model-based Batch Learning of Contextual Markov Decision Processes [31.83144400718369]
  We consider the problem of batch multi-task reinforcement learning with observed context descriptors, motivated by its application to personalized medical treatment. We study two general classes of learning algorithms: direct policy learning (DPL), an imitation-learning based approach which learns from expert trajectories, and model-based learning.
  arXiv  Detail & Related papers  (2020-06-11T11:57:08Z)
• Learning Gaussian Graphical Models via Multiplicative Weights [54.252053139374205]
  We adapt an algorithm of Klivans and Meka based on the method of multiplicative weight updates. The algorithm enjoys a sample complexity bound that is qualitatively similar to others in the literature. It has a low runtime $O(mp2)$ in the case of $m$ samples and $p$ nodes, and can trivially be implemented in an online manner.
  arXiv  Detail & Related papers  (2020-02-20T10:50:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.