Computational-Statistical Tradeoffs at the Next-Token Prediction Barrier: Autoregressive and Imitation Learning under Misspecification

• URL: http://arxiv.org/abs/2502.12465v1
• Date: Tue, 18 Feb 2025 02:52:00 GMT
• Title: Computational-Statistical Tradeoffs at the Next-Token Prediction Barrier: Autoregressive and Imitation Learning under Misspecification
• Authors: Dhruv Rohatgi, Adam Block, Audrey Huang, Akshay Krishnamurthy, Dylan J. Foster,
• Abstract summary: Next-token prediction with the logarithmic loss is a cornerstone of autoregressive sequence modeling. Next-token prediction can be made robust so as to achieve $C=tilde O(H)$, representing moderate error amplification. No computationally efficient algorithm can achieve sub-polynomial approximation factor $C=e(log H)1-Omega(1)$.
• Score: 50.717692060500696
• License:
• Abstract: Next-token prediction with the logarithmic loss is a cornerstone of autoregressive sequence modeling, but, in practice, suffers from error amplification, where errors in the model compound and generation quality degrades as sequence length $H$ increases. From a theoretical perspective, this phenomenon should not appear in well-specified settings, and, indeed, a growing body of empirical work hypothesizes that misspecification, where the learner is not sufficiently expressive to represent the target distribution, may be the root cause. Under misspecification -- where the goal is to learn as well as the best-in-class model up to a multiplicative approximation factor $C\geq 1$ -- we confirm that $C$ indeed grows with $H$ for next-token prediction, lending theoretical support to this empirical hypothesis. We then ask whether this mode of error amplification is avoidable algorithmically, computationally, or information-theoretically, and uncover inherent computational-statistical tradeoffs. We show: (1) Information-theoretically, one can avoid error amplification and achieve $C=O(1)$. (2) Next-token prediction can be made robust so as to achieve $C=\tilde O(H)$, representing moderate error amplification, but this is an inherent barrier: any next-token prediction-style objective must suffer $C=\Omega(H)$. (3) For the natural testbed of autoregressive linear models, no computationally efficient algorithm can achieve sub-polynomial approximation factor $C=e^{(\log H)^{1-\Omega(1)}}$; however, at least for binary token spaces, one can smoothly trade compute for statistical power and improve on $C=\Omega(H)$ in sub-exponential time. Our results have consequences in the more general setting of imitation learning, where the widely-used behavior cloning algorithm generalizes next-token prediction.

Related papers

• Cross-validating causal discovery via Leave-One-Variable-Out [11.891940572224783]
  We use the "Leave-One-Variable-Out (LOVO)" prediction where $Y$ is inferred from $X$ without any joint observations of $X$ and $Y$. We demonstrate that causal models on the two subsets, in the form of Acyclic Directed Mixed Graphs (ADMGs), often entail conclusions on the dependencies between $X$ and $Y$. The prediction error can then be estimated since the joint distribution $P(X, Y)$ is assumed to be available, and $X$ and $Y$ have only been omitted for the purpose of fal
  arXiv  Detail & Related papers  (2024-11-08T15:15:34Z)
• Theoretical limits of descending $\ell_0$ sparse-regression ML algorithms [0.0]
  We develop a generic analytical program for studying performance of the emphmaximum-likelihood (ML) decoding. Key ML performance parameter, the residual emphroot mean square error ($textbfRMSE$) is uncovered to exhibit the so-called emphphase-transition (PT) phenomenon. Concrete implementation and practical relevance of the Fl RDT typically rely on the ability to conduct a sizeable set of the underlying numerical evaluations.
  arXiv  Detail & Related papers  (2024-10-10T06:33:41Z)
• Scaling Laws in Linear Regression: Compute, Parameters, and Data [86.48154162485712]
  We study the theory of scaling laws in an infinite dimensional linear regression setup. We show that the reducible part of the test error is $Theta(-(a-1) + N-(a-1)/a)$. Our theory is consistent with the empirical neural scaling laws and verified by numerical simulation.
  arXiv  Detail & Related papers  (2024-06-12T17:53:29Z)
• Mind the Gap: A Causal Perspective on Bias Amplification in Prediction & Decision-Making [58.06306331390586]
  We introduce the notion of a margin complement, which measures how much a prediction score $S$ changes due to a thresholding operation. We show that under suitable causal assumptions, the influences of $X$ on the prediction score $S$ are equal to the influences of $X$ on the true outcome $Y$.
  arXiv  Detail & Related papers  (2024-05-24T11:22:19Z)
• A Pseudo-Semantic Loss for Autoregressive Models with Logical Constraints [87.08677547257733]
  Neuro-symbolic AI bridges the gap between purely symbolic and neural approaches to learning. We show how to maximize the likelihood of a symbolic constraint w.r.t the neural network's output distribution. We also evaluate our approach on Sudoku and shortest-path prediction cast as autoregressive generation.
  arXiv  Detail & Related papers  (2023-12-06T20:58:07Z)
• Towards Faster Non-Asymptotic Convergence for Diffusion-Based Generative Models [49.81937966106691]
  We develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach.
  arXiv  Detail & Related papers  (2023-06-15T16:30:08Z)
• Stability and Risk Bounds of Iterative Hard Thresholding [41.082982732100696]
  We introduce a novel sparse generalization theory for IHT under the notion of algorithmic stability. We show that IHT with sparsity level $k$ enjoys an $mathcaltilde O(n-1/2sqrtlog(n)log(p))$ rate of convergence in sparse excess risk. Preliminary numerical evidence is provided to confirm our theoretical predictions.
  arXiv  Detail & Related papers  (2022-03-17T16:12:56Z)
• Exponential Error Suppression for Near-Term Quantum Devices [0.0]
  In NISQ era, complexity and scale required to adopt even the smallest QEC is prohibitive. We show that for the crucial case of estimating expectation values of observables one can indeed achieve an effective exponential suppression.
  arXiv  Detail & Related papers  (2020-11-11T18:00:38Z)
• Estimating Stochastic Linear Combination of Non-linear Regressions Efficiently and Scalably [23.372021234032363]
  We show that when the sub-sample sizes are large then the estimation errors will be sacrificed by too much. To the best of our knowledge, this is the first work that and guarantees for the lineartext+Stochasticity model.
  arXiv  Detail & Related papers  (2020-10-19T07:15:38Z)
• Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model [50.38446482252857]
  This paper is concerned with the sample efficiency of reinforcement learning, assuming access to a generative model (or simulator) We first consider $gamma$-discounted infinite-horizon Markov decision processes (MDPs) with state space $mathcalS$ and action space $mathcalA$. We prove that a plain model-based planning algorithm suffices to achieve minimax-optimal sample complexity given any target accuracy level.
  arXiv  Detail & Related papers  (2020-05-26T17:53:18Z)

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.