Dissecting Multiplication in Transformers: Insights into LLMs

• URL: http://arxiv.org/abs/2407.15360v1
• Date: Mon, 22 Jul 2024 04:07:26 GMT
• Title: Dissecting Multiplication in Transformers: Insights into LLMs
• Authors: Luyu Qiu, Jianing Li, Chi Su, Chen Jason Zhang, Lei Chen,
• Abstract summary: We focus on a typical arithmetic task, integer multiplication, to explore and explain the imperfection of transformers in this domain. We provide comprehensive analysis of a vanilla transformer trained to perform n-digit integer multiplication. We propose improvements to enhance transformers performance on multiplication tasks.
• Score: 23.109124772063574
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Transformer-based large language models have achieved remarkable performance across various natural language processing tasks. However, they often struggle with seemingly easy tasks like arithmetic despite their vast capabilities. This stark disparity raise human's concerns about their safe and ethical use, hinder their widespread adoption.In this paper, we focus on a typical arithmetic task, integer multiplication, to explore and explain the imperfection of transformers in this domain. We provide comprehensive analysis of a vanilla transformer trained to perform n-digit integer multiplication. Our observations indicate that the model decomposes multiplication task into multiple parallel subtasks, sequentially optimizing each subtask for each digit to complete the final multiplication. Based on observation and analysis, we infer the reasons of transformers deficiencies in multiplication tasks lies in their difficulty in calculating successive carryovers and caching intermediate results, and confirmed this inference through experiments. Guided by these findings, we propose improvements to enhance transformers performance on multiplication tasks. These enhancements are validated through rigorous testing and mathematical modeling, not only enhance transformer's interpretability, but also improve its performance, e.g., we achieve over 99.9% accuracy on 5-digit integer multiplication with a tiny transformer, outperform LLMs GPT-4. Our method contributes to the broader fields of model understanding and interpretability, paving the way for analyzing more complex tasks and Transformer models. This work underscores the importance of explainable AI, helping to build trust in large language models and promoting their adoption in critical applications.

Related papers

• Interpreting Affine Recurrence Learning in GPT-style Transformers [54.01174470722201]
  In-context learning allows GPT-style transformers to generalize during inference without modifying their weights. This paper focuses specifically on their ability to learn and predict affine recurrences as an ICL task. We analyze the model's internal operations using both empirical and theoretical approaches.
  arXiv  Detail & Related papers  (2024-10-22T21:30:01Z)
• How Numerical Precision Affects Mathematical Reasoning Capabilities of LLMs [69.55103380185612]
  We identify numerical precision as a key factor that influences Transformer-based Large Language Models' effectiveness in mathematical tasks. Our results show that Transformers operating with low numerical precision fail to address arithmetic tasks, such as iterated addition and integer multiplication. In contrast, Transformers with standard numerical precision can efficiently handle these tasks with significantly smaller model sizes.
  arXiv  Detail & Related papers  (2024-10-17T17:59:35Z)
• Unveil Benign Overfitting for Transformer in Vision: Training Dynamics, Convergence, and Generalization [88.5582111768376]
  We study the optimization of a Transformer composed of a self-attention layer with softmax followed by a fully connected layer under gradient descent on a certain data distribution model. Our results establish a sharp condition that can distinguish between the small test error phase and the large test error regime, based on the signal-to-noise ratio in the data model.
  arXiv  Detail & Related papers  (2024-09-28T13:24:11Z)
• Does learning the right latent variables necessarily improve in-context learning? [13.828665019247444]
  Large autoregressive models like Transformers can solve tasks through in-context learning (ICL) without learning new weights. In this paper, we investigate the effect of explicitly inferring task latents. We find little discernible difference between the two; biasing towards task-relevant latent variables does not lead to better out-of-distribution performance.
  arXiv  Detail & Related papers  (2024-05-29T15:06:10Z)
• Understanding Addition in Transformers [2.07180164747172]
  This paper provides a comprehensive analysis of a one-layer Transformer model trained to perform n-digit integer addition. Our findings suggest that the model dissects the task into parallel streams dedicated to individual digits, employing varied algorithms tailored to different positions within the digits.
  arXiv  Detail & Related papers  (2023-10-19T19:34:42Z)
• Eureka-Moments in Transformers: Multi-Step Tasks Reveal Softmax Induced Optimization Problems [27.681141346132286]
  We study rapid improvements of the training loss in transformers when being confronted with multi-step decision tasks. We use synthetic tasks to study the problem in detail, but the leaps in performance can be observed also for language modeling and in-context learning. We find connections and show that ways to improve on the synthetic multi-step tasks can be used to improve the training of language modeling and ICL.
  arXiv  Detail & Related papers  (2023-10-19T17:55:06Z)
• Faith and Fate: Limits of Transformers on Compositionality [109.79516190693415]
  We investigate the limits of transformer large language models across three representative compositional tasks. These tasks require breaking problems down into sub-steps and synthesizing these steps into a precise answer. Our empirical findings suggest that transformer LLMs solve compositional tasks by reducing multi-step compositional reasoning into linearized subgraph matching.
  arXiv  Detail & Related papers  (2023-05-29T23:24:14Z)
• Optimizing Non-Autoregressive Transformers with Contrastive Learning [74.46714706658517]
  Non-autoregressive Transformers (NATs) reduce the inference latency of Autoregressive Transformers (ATs) by predicting words all at once rather than in sequential order. In this paper, we propose to ease the difficulty of modality learning via sampling from the model distribution instead of the data distribution.
  arXiv  Detail & Related papers  (2023-05-23T04:20:13Z)
• Pretrained Transformers as Universal Computation Engines [105.00539596788127]
  We investigate the capability of a transformer pretrained on natural language to generalize to other modalities with minimal finetuning. We study finetuning it on a variety of sequence classification tasks spanning numerical computation, vision, and protein fold prediction. We find that such pretraining enables FPT to generalize in zero-shot to these modalities, matching the performance of a transformer fully trained on these tasks.
  arXiv  Detail & Related papers  (2021-03-09T06:39:56Z)
• Translational Equivariance in Kernelizable Attention [3.236198583140341]
  We show how translational equivariance can be implemented in efficient Transformers based on kernelizable attention. Our experiments highlight that the devised approach significantly improves robustness of Performers to shifts of input images.
  arXiv  Detail & Related papers  (2021-02-15T17:14:15Z)

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.