Transformers Provably Solve Parity Efficiently with Chain of Thought

• URL: http://arxiv.org/abs/2410.08633v2
• Date: Mon, 25 Nov 2024 03:39:51 GMT
• Title: Transformers Provably Solve Parity Efficiently with Chain of Thought
• Authors: Juno Kim, Taiji Suzuki,
• Abstract summary: This work provides the first theoretical analysis of training transformers to solve complex problems. We consider training a one-layer transformer to solve the fundamental $k$-parity problem.
• Score: 40.78854925996
• License:
• Abstract: This work provides the first theoretical analysis of training transformers to solve complex problems by recursively generating intermediate states, analogous to fine-tuning for chain-of-thought (CoT) reasoning. We consider training a one-layer transformer to solve the fundamental $k$-parity problem, extending the work on RNNs by Wies et al. (2023). We establish three key results: (1) any finite-precision gradient-based algorithm, without intermediate supervision, requires substantial iterations to solve parity with finite samples. (2) In contrast, when intermediate parities are incorporated into the loss function, our model can learn parity in one gradient update when aided by \emph{teacher forcing}, where ground-truth labels of the reasoning chain are provided at each generation step. (3) Even without teacher forcing, where the model must generate CoT chains end-to-end, parity can be learned efficiently if augmented data is employed to internally verify the soundness of intermediate steps. Our findings, supported by numerical experiments, show that task decomposition and stepwise reasoning naturally arise from optimizing transformers with CoT; moreover, self-consistency checking can improve multi-step reasoning ability, aligning with empirical studies of CoT.

Related papers

• A Theoretical Understanding of Chain-of-Thought: Coherent Reasoning and Error-Aware Demonstration [41.88275731297211]
  We show that, compared to Stepwise ICL, the transformer gains better error correction ability and more accurate predictions if the reasoning from earlier steps is integrated. We propose an improvement on CoT by incorporating both correct and incorrect reasoning paths in the demonstration.
  arXiv  Detail & Related papers  (2024-10-21T22:07:20Z)
• Can Looped Transformers Learn to Implement Multi-step Gradient Descent for In-context Learning? [69.4145579827826]
  We show a fast flow on the regression loss despite the gradient non-ity algorithms for our convergence landscape. This is the first theoretical analysis for multi-layer Transformer in this setting.
  arXiv  Detail & Related papers  (2024-10-10T18:29:05Z)
• From Sparse Dependence to Sparse Attention: Unveiling How Chain-of-Thought Enhances Transformer Sample Efficiency [17.612497960364916]
  Chain-of-thought (CoT) significantly enhances the reasoning performance of large language models (LLM) We demonstrate that CoT can substantially improve sample efficiency even when representation power is sufficient. We show that CoT simplifies the learning process by introducing sparse dependencies among input tokens, and leads to a sparse and interpretable attention.
  arXiv  Detail & Related papers  (2024-10-07T19:45:09Z)
• Training Nonlinear Transformers for Chain-of-Thought Inference: A Theoretical Generalization Analysis [82.51626700527837]
  Chain-of-shift (CoT) is an efficient method that enables the reasoning ability of large language models by augmenting the query using examples with multiple intermediate steps. We show that despite the theoretical success of CoT, it fails to provide an accurate generalization when CoT does.
  arXiv  Detail & Related papers  (2024-10-03T03:12:51Z)
• Unveiling the Statistical Foundations of Chain-of-Thought Prompting Methods [59.779795063072655]
  Chain-of-Thought (CoT) prompting and its variants have gained popularity as effective methods for solving multi-step reasoning problems. We analyze CoT prompting from a statistical estimation perspective, providing a comprehensive characterization of its sample complexity.
  arXiv  Detail & Related papers  (2024-08-25T04:07:18Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• Transformer Meets Boundary Value Inverse Problems [4.165221477234755]
  Transformer-based deep direct sampling method is proposed for solving a class of boundary value inverse problem. A real-time reconstruction is achieved by evaluating the learned inverse operator between carefully designed data and reconstructed images.
  arXiv  Detail & Related papers  (2022-09-29T17:45:25Z)
• Learning Iterative Robust Transformation Synchronization [71.73273007900717]
  We propose to use graph neural networks (GNNs) to learn transformation synchronization. In this work, we avoid handcrafting robust loss functions, and propose to use graph neural networks (GNNs) to learn transformation synchronization.
  arXiv  Detail & Related papers  (2021-11-01T07:03:14Z)

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.