NeurIPS 2024 论文列表

Conference on Neural Information Processing Systems

录用类型

4,562篇论文

按官方录用论文列表统计,可能与会议公布的数字略有出入。

  • Oral
    721.6%
  • Spotlight
    3828.4%
  • Poster
    4,06489.1%
  • 其他 / 未标注
    441.0%

浏览全部论文

Multi-Instance Partial-Label Learning with Margin Adjustment

Wei Tang, Yin-Fang Yang, Zhaofei Wang, Weijia Zhang, Min-Ling Zhang

展开摘要

Multi-instance partial-label learning (MIPL) is an emerging learning framework where each training sample is represented as a multi-instance bag associated with a candidate label set. Existing MIPL algorithms often overlook the margins for attention scores and predicted probabilities, leading to suboptimal generalization performance. A critical issue with these algorithms is that the highest prediction probability of the classifier may appear on a non-candidate label. In this paper, we propose an algorithm named MIPLMA, i.e., Multi-Instance Partial-Label learning with Margin Adjustment, which adjusts the margins for attention scores and predicted probabilities. We introduce a margin-aware attention mechanism to dynamically adjust the margins for attention scores and propose a margin distribution loss to constrain the margins between the predicted probabilities on candidate and non-candidate label sets. Experimental results demonstrate the superior performance of MIPLMA over existing MIPL algorithms, as well as other well-established multi-instance learning algorithms and partial-label learning algorithms.

Poster
Safe and Sparse Newton Method for Entropic-Regularized Optimal Transport

Zihao TANG, Yixuan Qiu

展开摘要

Computational optimal transport (OT) has received massive interests in the machine learning community, and great advances have been gained in the direction of entropic-regularized OT. The Sinkhorn algorithm, as well as its many improved versions, has become the *de facto* solution to large-scale OT problems. However, most of the existing methods behave like first-order methods, which typically require a large number of iterations to converge. More recently, Newton-type methods using sparsified Hessian matrices have demonstrated promising results on OT computation, but there still remain a lot of unresolved open questions. In this article, we make major new progresses towards this direction: first, we propose a novel Hessian sparsification scheme that promises a strict control of the approximation error; second, based on this sparsification scheme, we develop a *safe* Newton-type method that is guaranteed to avoid singularity in computing the search directions; third, the developed algorithm has a clear implementation for practical use, avoiding most hyperparameter tuning; and remarkably, we provide rigorous global and local convergence analysis of the proposed algorithm, which is lacking in the prior literature. Various numerical experiments are conducted to demonstrate the effectiveness of the proposed algorithm in solving large-scale OT problems.

Poster
When does perceptual alignment benefit vision representations?

Shobhita Sundaram, Stephanie Fu, Lukas Muttenthaler, Netanel Yakir Tamir, Lucy Chai, Simon Kornblith, Trevor Darrell, Phillip Isola

展开摘要

Humans judge perceptual similarity according to diverse visual attributes, including scene layout, subject location, and camera pose. Existing vision models understand a wide range of semantic abstractions but improperly weigh these attributes and thus make inferences misaligned with human perception. While vision representations have previously benefited from human preference alignment in contexts like image generation, the utility of perceptually aligned representations in more general-purpose settings remains unclear. Here, we investigate how aligning vision model representations to human perceptual judgments impacts their usability in standard computer vision tasks. We finetune state-of-the-art models on a dataset of human similarity judgments for synthetic image triplets and evaluate them across diverse computer vision tasks. We find that aligning models to perceptual judgments yields representations that improve upon the original backbones across many downstream tasks, including counting, semantic segmentation, depth estimation, instance retrieval, and retrieval-augmented generation. In addition, we find that performance is widely preserved on other tasks, including specialized out-of-distribution domains such as in medical imaging and 3D environment frames. Our results suggest that injecting an inductive bias about human perceptual knowledge into vision models can make them better representation learners.

Poster
Just Add $100 More: Augmenting Pseudo-LiDAR Point Cloud for Resolving Class-imbalance Problem

Mincheol Chang, Siyeong Lee, Jinkyu Kim, Namil Kim

展开摘要

Typical LiDAR-based 3D object detection models are trained with real-world data collection, which is often imbalanced over classes. To deal with it, augmentation techniques are commonly used, such as copying ground truth LiDAR points and pasting them into scenes. However, existing methods struggle with the lack of sample diversity for minority classes and the limitation of suitable placement. In this work, we introduce a novel approach that utilizes pseudo LiDAR point clouds generated from low-cost miniatures or real-world videos, which is called Pseudo Ground Truth augmentation (PGT-Aug). PGT-Aug involves three key steps: (i) volumetric 3D instance reconstruction using a 2D-to-3D view synthesis model, (ii) object-level domain alignment with LiDAR intensity simulation, and (iii) a hybrid context-aware placement method from ground and map information. We demonstrate the superiority and generality of our method through performance improvements in extensive experiments conducted on popular benchmarks, i.e., nuScenes, KITTI, and Lyft, especially for the datasets with large domain gaps captured by different LiDAR configurations. The project webpage is https://just-add-100-more.github.io.

Poster
No Free Lunch Theorem and Black-Box Complexity Analysis for Adversarial Optimisation

Per Kristian Lehre, Shishen Lin

展开摘要

Black-box optimisation is one of the important areas in optimisation. The original No Free Lunch (NFL) theorems highlight the limitations of traditional black-box optimisation and learning algorithms, serving as a theoretical foundation for traditional optimisation. No Free Lunch Analysis in adversarial (also called maximin) optimisation is a long-standing problem [45 , 46]. This paper first rigorously proves a (NFL) Theorem for general black-box adversarial optimisation when considering Pure Strategy Nash Equilibrium (NE) as the solution concept. We emphasise the solution concept (i.e. define the optimality in adversarial optimisation) as the key in our NFL theorem. In particular, if Nash Equilibrium is considered as the solution concept and the cost of the algorithm is measured in terms of the number of columns and rows queried in the payoff matrix, then the average performance of all black-box adversarial optimisation algorithms is the same. Moreover, we first introduce black-box complexity to analyse the black-box adversarial optimisation algorithm. We employ Yao’s Principle and our new NFL Theorem to provide general lower bounds for the query complexity of finding a Nash Equilibrium in adversarial optimisation. Finally, we illustrate the practical ramifications of our results on simple two-player zero-sum games. More specifically, no black-box optimisation algorithm for finding the unique Nash equilibrium in two-player zero-sum games can exceed logarithmic complexity relative to search space size. Meanwhile, no black-box algorithm can solve any bimatrix game with unique NE with fewer than a linear number of queries in the size of the payoff matrix.

Poster
Test-Time Dynamic Image Fusion

Bing Cao, Yinan Xia, Yi Ding, Changqing Zhang, Qinghua Hu

展开摘要

The inherent challenge of image fusion lies in capturing the correlation of multi-source images and comprehensively integrating effective information from different sources. Most existing techniques fail to perform dynamic image fusion while notably lacking theoretical guarantees, leading to potential deployment risks in this field. Is it possible to conduct dynamic image fusion with a clear theoretical justification? In this paper, we give our solution from a generalization perspective. We proceed to reveal the generalized form of image fusion and derive a new test-time dynamic image fusion paradigm. It provably reduces the upper bound of generalization error. Specifically, we decompose the fused image into multiple components corresponding to its source data. The decomposed components represent the effective information from the source data, thus the gap between them reflects the \textit{Relative Dominability} (RD) of the uni-source data in constructing the fusion image. Theoretically, we prove that the key to reducing generalization error hinges on the negative correlation between the RD-based fusion weight and the uni-source reconstruction loss. Intuitively, RD dynamically highlights the dominant regions of each source and can be naturally converted to the corresponding fusion weight, achieving robust results. Extensive experiments and discussions with in-depth analysis on multiple benchmarks confirm our findings and superiority. Our code is available at https://github.com/Yinan-Xia/TTD.

Poster
Paralinguistics-Aware Speech-Empowered Large Language Models for Natural Conversation

Heeseung Kim, Soonshin Seo, Kyeongseok Jeong, Ohsung Kwon, Soyoon Kim, Jungwhan Kim, Jaehong Lee, Eunwoo Song, Myungwoo Oh, Jung-Woo Ha, Sungroh Yoon, Kang Min Yoo

展开摘要

Recent work shows promising results in expanding the capabilities of large language models (LLM) to directly understand and synthesize speech. However, an LLM-based strategy for modeling spoken dialogs remains elusive, calling for further investigation. This paper introduces an extensive speech-text LLM framework, the Unified Spoken Dialog Model (USDM), designed to generate coherent spoken responses with naturally occurring prosodic features relevant to the given input speech without relying on explicit automatic speech recognition (ASR) or text-to-speech (TTS) systems. We have verified the inclusion of prosody in speech tokens that predominantly contain semantic information and have used this foundation to construct a prosody-infused speech-text model. Additionally, we propose a generalized speech-text pretraining scheme that enhances the capture of cross-modal semantics. To construct USDM, we fine-tune our speech-text model on spoken dialog data using a multi-step spoken dialog template that stimulates the chain-of-reasoning capabilities exhibited by the underlying LLM. Automatic and human evaluations on the DailyTalk dataset demonstrate that our approach effectively generates natural-sounding spoken responses, surpassing previous and cascaded baselines. Our code and checkpoints are available at https://github.com/naver-ai/usdm.

Poster
Provably Efficient Interactive-Grounded Learning with Personalized Reward

Mengxiao Zhang, Yuheng Zhang, Haipeng Luo, Paul Mineiro

展开摘要

Interactive-Grounded Learning (IGL) [Xie et al., 2021] is a powerful framework in which a learner aims at maximizing unobservable rewards through interacting with an environment and observing reward-dependent feedback on the taken actions. To deal with personalized rewards that are ubiquitous in applications such as recommendation systems, Maghakian et al. [2022] study a version of IGL with context-dependent feedback, but their algorithm does not come with theoretical guarantees. In this work, we consider the same problem and provide the first provably efficient algorithms with sublinear regret under realizability. Our analysis reveals that the step-function estimator of prior work can deviate uncontrollably due to finite-sample effects. Our solution is a novel Lipschitz reward estimator which underestimates the true reward and enjoys favorable generalization performances. Building on this estimator, we propose two algorithms, one based on explore-then-exploit and the other based on inverse-gap weighting. We apply IGL to learning from image feedback and learning from text feedback, which are reward-free settings that arise in practice. Experimental results showcase the importance of using our Lipschitz reward estimator and the overall effectiveness of our algorithms.

Poster
Nearest Neighbor Speculative Decoding for LLM Generation and Attribution

Minghan Li, Xilun Chen, Ari Holtzman, Beidi Chen, Jimmy Lin, Wen-tau Yih, Xi Victoria Lin

展开摘要

Large language models (LLMs) often hallucinate and lack the ability to provide attribution for their generations. Semi-parametric LMs, such as kNN-LM, approach these limitations by refining the output of an LM for a given prompt using its nearest neighbor matches in a non-parametric data store. However, these models often exhibit slow inference speeds and produce non-fluent texts. In this paper, we introduce Nearest Neighbor Speculative Decoding (NEST), a novel semi-parametric language modeling approach that is capable of incorporating real-world text spans of arbitrary length into the LM generations and providing attribution to their sources. NEST performs token-level retrieval at each inference step to compute a semi-parametric mixture distribution and identify promising span continuations in a corpus. It then uses an approximate speculative decoding procedure that accepts a prefix of the retrieved span or generates a new token. NEST significantly enhances the generation quality and attribution rate of the base LM across a variety of knowledge-intensive tasks, surpassing the conventional kNN-LM method and performing competitively with in-context retrieval augmentation. In addition, NEST substantially improves the generation speed, achieving a 1.8x speedup in inference time when applied to Llama-2-Chat 70B. Code will be released at https://github.com/facebookresearch/NEST/tree/main.

Poster
A Local Method for Satisfying Interventional Fairness with Partially Known Causal Graphs

Haoxuan Li, Yue Liu, Zhi Geng, Kun Zhang

展开摘要

Developing fair automated machine learning algorithms is critical in making safe and trustworthy decisions. Many causality-based fairness notions have been proposed to address the above issues by quantifying the causal connections between sensitive attributes and decisions, and when the true causal graph is fully known, certain algorithms that achieve interventional fairness have been proposed. However, when the true causal graph is unknown, it is still challenging to effectively and efficiently exploit partially directed acyclic graphs (PDAGs) to achieve interventional fairness. To exploit the PDAGs for achieving interventional fairness, previous methods have been built on variable selection or causal effect identification, but limited to reduced prediction accuracy or strong assumptions. In this paper, we propose a general min-max optimization framework that can achieve interventional fairness with promising prediction accuracy and can be extended to maximally oriented PDAGs (MPDAGs) with added background knowledge. Specifically, we first estimate all possible treatment effects of sensitive attributes on a given prediction model from all possible adjustment sets of sensitive attributes via an efficient local approach. Next, we propose to alternatively update the prediction model and possible estimated causal effects, where the prediction model is trained via a min-max loss to control the worst-case fairness violations. Extensive experiments on synthetic and real-world datasets verify the superiority of our methods. To benefit the research community, we have released our project at https://github.com/haoxuanli-pku/NeurIPS24-Interventional-Fairness-with-PDAGs.

Poster
Deep Learning Through A Telescoping Lens: A Simple Model Provides Empirical Insights On Grokking, Gradient Boosting & Beyond

Alan Jeffares, Alicia Curth, Mihaela van der Schaar

展开摘要

Deep learning sometimes appears to work in unexpected ways. In pursuit of a deeper understanding of its surprising behaviors, we investigate the utility of a simple yet accurate model of a trained neural network consisting of a sequence of first-order approximations telescoping out into a single empirically operational tool for practical analysis. Across three case studies, we illustrate how it can be applied to derive new empirical insights on a diverse range of prominent phenomena in the literature -- including double descent, grokking, linear mode connectivity, and the challenges of applying deep learning on tabular data -- highlighting that this model allows us to construct and extract metrics that help predict and understand the a priori unexpected performance of neural networks. We also demonstrate that this model presents a pedagogical formalism allowing us to isolate components of the training process even in complex contemporary settings, providing a lens to reason about the effects of design choices such as architecture & optimization strategy, and reveals surprising parallels between neural network learning and gradient boosting.

Poster
Single-Loop Stochastic Algorithms for Difference of Max-Structured Weakly Convex Functions

Quanqi Hu, Qi Qi, Zhaosong Lu, Tianbao Yang

展开摘要

In this paper, we study a class of non-smooth non-convex problems in the form of $\min_{x}[\max_{y\in\mathcal Y}\phi(x, y) - \max_{z\in\mathcal Z}\psi(x, z)]$, where both $\Phi(x) = \max_{y\in\mathcal Y}\phi(x, y)$ and $\Psi(x)=\max_{z\in\mathcal Z}\psi(x, z)$ are weakly convex functions, and $\phi(x, y), \psi(x, z)$ are strongly concave functions in terms of $y$ and $z$, respectively. It covers two families of problems that have been studied but are missing single-loop stochastic algorithms, i.e., difference of weakly convex functions and weakly convex strongly-concave min-max problems. We propose a stochastic Moreau envelope approximate gradient method dubbed SMAG, the first single-loop algorithm for solving these problems, and provide a state-of-the-art non-asymptotic convergence rate. The key idea of the design is to compute an approximate gradient of the Moreau envelopes of $\Phi, \Psi$ using only one step of stochastic gradient update of the primal and dual variables. Empirically, we conduct experiments on positive-unlabeled (PU) learning and partial area under ROC curve (pAUC) optimization with an adversarial fairness regularizer to validate the effectiveness of our proposed algorithms.

Poster
Understanding Visual Feature Reliance through the Lens of Complexity

Thomas FEL, Louis Béthune, Andrew Kyle Lampinen, Thomas Serre, Katherine Hermann

展开摘要

Recent studies suggest that deep learning models' inductive bias towards favoring simpler features may be an origin of shortcut learning. Yet, there has been limited focus on understanding the complexities of the myriad features that models learn. In this work, we introduce a new metric for quantifying feature complexity, based on V-information and capturing whether a feature requires complex computational transformations to be extracted. Using this V-information metric, we analyze the complexities of 10,000 features—represented as directions in the penultimate layer—that were extracted from a standard ImageNet-trained vision model. Our study addresses four key questions: First, we ask what features look like as a function of complexity, and find a spectrum of simple-to-complex features present within the model. Second, we ask when features are learned during training. We find that simpler features dominate early in training, and more complex features emerge gradually. Third, we investigate where within the network simple and complex features "flow," and find that simpler features tend to bypass the visual hierarchy via residual connections. Fourth, we explore the connection between features' complexity and their importance for driving the network's decision. We find that complex features tend to be less important. Surprisingly, important features become accessible at earlier layers during training, like a "sedimentation process," allowing the model to build upon these foundational elements.

Poster
Matrix Denoising with Doubly Heteroscedastic Noise: Fundamental Limits and Optimal Spectral Methods

Yihan Zhang, Marco Mondelli

展开摘要

We study the matrix denoising problem of estimating the singular vectors of a rank-$1$ signal corrupted by noise with both column and row correlations. Existing works are either unable to pinpoint the exact asymptotic estimation error or, when they do so, the resulting approaches (e.g., based on whitening or singular value shrinkage) remain vastly suboptimal. On top of this, most of the literature has focused on the special case of estimating the left singular vector of the signal when the noise only possesses row correlation (one-sided heteroscedasticity). In contrast, our work establishes the information-theoretic and algorithmic limits of matrix denoising with doubly heteroscedastic noise. We characterize the exact asymptotic minimum mean square error, and design a novel spectral estimator with rigorous optimality guarantees: under a technical condition, it attains positive correlation with the signals whenever information-theoretically possible and, for one-sided heteroscedasticity, it also achieves the Bayes-optimal error. Numerical experiments demonstrate the significant advantage of our theoretically principled method with the state of the art. The proofs draw connections with statistical physics and approximate message passing, departing drastically from standard random matrix theory techniques.

Poster
Non-asymptotic Convergence of Training Transformers for Next-token Prediction

Ruiquan Huang, Yingbin Liang, Jing Yang

展开摘要

Transformers have achieved extraordinary success in modern machine learning due to their excellent ability to handle sequential data, especially in next-token prediction (NTP) tasks. However, the theoretical understanding of their performance in NTP is limited, with existing studies focusing mainly on asymptotic performance. This paper provides a fine-grained non-asymptotic analysis of the training dynamics of a one-layer transformer consisting of a self-attention module followed by a feed-forward layer. We first characterize the essential structural properties of training datasets for NTP using a mathematical framework based on partial orders. Then, we design a two-stage training algorithm, where the pre-processing stage for training the feed-forward layer and the main stage for training the attention layer exhibit fast convergence performance. Specifically, both layers converge sub-linearly to the direction of their corresponding max-margin solutions. We also show that the cross-entropy loss enjoys a linear convergence rate. Furthermore, we show that the trained transformer presents non-trivial prediction ability with dataset shift, which sheds light on the remarkable generalization performance of transformers. Our analysis technique involves the development of novel properties on the attention gradient and further in-depth analysis of how these properties contribute to the convergence of the training process. Our experiments further validate our theoretical findings.

Poster
Watch Out for Your Agents! Investigating Backdoor Threats to LLM-Based Agents

Wenkai Yang, Xiaohan Bi, Yankai Lin, Sishuo Chen, Jie Zhou, Xu Sun

展开摘要

Driven by the rapid development of Large Language Models (LLMs), LLM-based agents have been developed to handle various real-world applications, including finance, healthcare, and shopping, etc. It is crucial to ensure the reliability and security of LLM-based agents during applications. However, the safety issues of LLM-based agents are currently under-explored. In this work, we take the first step to investigate one of the typical safety threats, backdoor attack, to LLM-based agents. We first formulate a general framework of agent backdoor attacks, then we present a thorough analysis of different forms of agent backdoor attacks. Specifically, compared with traditional backdoor attacks on LLMs that are only able to manipulate the user inputs and model outputs, agent backdoor attacks exhibit more diverse and covert forms: (1) From the perspective of the final attacking outcomes, the agent backdoor attacker can not only choose to manipulate the final output distribution, but also introduce the malicious behavior in an intermediate reasoning step only, while keeping the final output correct. (2) Furthermore, the former category can be divided into two subcategories based on trigger locations, in which the backdoor trigger can either be hidden in the user query or appear in an intermediate observation returned by the external environment. We implement the above variations of agent backdoor attacks on two typical agent tasks including web shopping and tool utilization. Extensive experiments show that LLM-based agents suffer severely from backdoor attacks and such backdoor vulnerability cannot be easily mitigated by current textual backdoor defense algorithms. This indicates an urgent need for further research on the development of targeted defenses against backdoor attacks on LLM-based agents. Warning: This paper may contain biased content.

Poster
Taming Generative Diffusion Prior for Universal Blind Image Restoration

Siwei Tu, Weidong Yang, Ben Fei

展开摘要

Diffusion models have been widely utilized for image restoration. However, previous blind image restoration methods still need to assume the type of degradation model while leaving the parameters to be optimized, limiting their real-world applications. Therefore, we aim to tame generative diffusion prior for universal blind image restoration dubbed BIR-D, which utilizes an optimizable convolutional kernel to simulate the degradation model and dynamically update the parameters of the kernel in the diffusion steps, enabling it to achieve blind image restoration results even in various complex situations. Besides, based on mathematical reasoning, we have provided an empirical formula for the chosen of adaptive guidance scale, eliminating the need for a grid search for the optimal parameter. Experimentally, Our BIR-D has demonstrated superior practicality and versatility than off-the-shelf unsupervised methods across various tasks both on real-world and synthetic datasets, qualitatively and quantitatively. BIR-D is able to fulfill multi-guidance blind image restoration. Moreover, BIR-D can also restore images that undergo multiple and complicated degradations, demonstrating the practical applications. The code is available at https://github.com/Tusiwei/BIR-D.

Poster
AID: Attention Interpolation of Text-to-Image Diffusion

Qiyuan He, Jinghao Wang, Ziwei Liu, Angela Yao

展开摘要

Conditional diffusion models can create unseen images in various settings, aiding image interpolation. Interpolation in latent spaces is well-studied, but interpolation with specific conditions like text or image is less understood. Common approaches interpolate linearly in the conditioning space but tend to result in inconsistent images with poor fidelity. This work introduces a novel training-free technique named \textbf{Attention Interpolation via Diffusion (AID)}. AID has two key contributions: \textbf{1)} a fused inner/outer interpolated attention layer to boost image consistency and fidelity; and \textbf{2)} selection of interpolation coefficients via a beta distribution to increase smoothness. Additionally, we present an AID variant called \textbf{Prompt-guided Attention Interpolation via Diffusion (PAID)}, which \textbf{3)} treats interpolation as a condition-dependent generative process. Experiments demonstrate that our method achieves greater consistency, smoothness, and efficiency in condition-based interpolation, aligning closely with human preferences. Furthermore, PAID offers substantial benefits for compositional generation, controlled image editing, image morphing and image-controlled generation, all while remaining training-free.

Poster
Diffusion for World Modeling: Visual Details Matter in Atari

Eloi Alonso, Adam Jelley, Vincent Micheli, Anssi Kanervisto, Amos Storkey, Tim Pearce, François Fleuret

展开摘要

World models constitute a promising approach for training reinforcement learning agents in a safe and sample-efficient manner. Recent world models predominantly operate on sequences of discrete latent variables to model environment dynamics. However, this compression into a compact discrete representation may ignore visual details that are important for reinforcement learning. Concurrently, diffusion models have become a dominant approach for image generation, challenging well-established methods modeling discrete latents. Motivated by this paradigm shift, we introduce DIAMOND (DIffusion As a Model Of eNvironment Dreams), a reinforcement learning agent trained in a diffusion world model. We analyze the key design choices that are required to make diffusion suitable for world modeling, and demonstrate how improved visual details can lead to improved agent performance. DIAMOND achieves a mean human normalized score of 1.46 on the competitive Atari 100k benchmark; a new best for agents trained entirely within a world model. We further demonstrate that DIAMOND's diffusion world model can stand alone as an interactive neural game engine by training on static *Counter-Strike: Global Offensive* gameplay. To foster future research on diffusion for world modeling, we release our code, agents, videos and playable world models at https://diamond-wm.github.io.

Spotlight
Towards a theory of how the structure of language is acquired by deep neural networks

Francesco Cagnetta, Matthieu Wyart

展开摘要

How much data is required to learn the structure of a language via next-token prediction? We study this question for synthetic datasets generated via a Probabilistic Context-Free Grammar (PCFG)---a hierarchical generative model that captures the tree-like structure of natural languages. We determine token-token correlations analytically in our model and show that they can be used to build a representation of the grammar's hidden variables, the longer the range the deeper the variable. In addition, a finite training set limits the resolution of correlations to an effective range, whose size grows with that of the training set. As a result, a Language Model trained with increasingly many examples can build a deeper representation of the grammar's structure, thus reaching good performance despite the high dimensionality of the problem. We conjecture that the relationship between training set size and effective range of correlations holds beyond our synthetic datasets, and we test it in a collection of lines from Shakespeare's plays. In particular, we show that reducing the input size leads to saturation of the test loss decay at a characteristic training set size that can be predicted in our framework.

Poster