A Symbolic Framework for Evaluating Mathematical Reasoning and Generalisation with Transformers

• URL: http://arxiv.org/abs/2305.12563v2
• Date: Mon, 8 Apr 2024 14:29:06 GMT
• Title: A Symbolic Framework for Evaluating Mathematical Reasoning and Generalisation with Transformers
• Authors: Jordan Meadows, Marco Valentino, Damien Teney, Andre Freitas,
• Abstract summary: We evaluate the generalisability of Transformers to out-of-distribution mathematical reasoning problems. We compare the capabilities of GPT-4, GPT-3.5, and a canon of fine-tuned BERT models. Surprisingly, our evaluation reveals that the average in-distribution performance of fine-tuned models surpasses GPT-3.5, and rivals GPT-4.
• Score: 17.075558137261986
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper proposes a methodology for generating and perturbing detailed derivations of equations at scale, aided by a symbolic engine, to evaluate the generalisability of Transformers to out-of-distribution mathematical reasoning problems. Instantiating the framework in the context of sequence classification tasks, we compare the capabilities of GPT-4, GPT-3.5, and a canon of fine-tuned BERT models, exploring the relationship between specific operators and generalisation failure via the perturbation of reasoning aspects such as symmetry and variable surface forms. Surprisingly, our empirical evaluation reveals that the average in-distribution performance of fine-tuned models surpasses GPT-3.5, and rivals GPT-4. However, perturbations to input reasoning can reduce their performance by up to 80 F1 points. Overall, the results suggest that the in-distribution performance of smaller open-source models may potentially rival GPT by incorporating appropriately structured derivation dependencies during training, and highlight a shared weakness between BERT and GPT involving a relative inability to decode indirect references to mathematical entities. We release the full codebase, constructed datasets, and fine-tuned models to encourage future progress in the field.

Related papers

• Harmonic Loss Trains Interpretable AI Models [13.745919535064429]
  We introduce harmonic loss as an alternative to the standard cross-entropy loss for training neural networks and large language models. We first validate the performance of harmonic models across algorithmic, vision, and language datasets. We demonstrate that models trained with harmonic loss outperform standard models by: (a) enhancing interpretability, (b) requiring less data for generalization, and (c) reducing grokking.
  arXiv  Detail & Related papers  (2025-02-03T18:57:17Z)
• Rethinking Relation Extraction: Beyond Shortcuts to Generalization with a Debiased Benchmark [53.876493664396506]
  Benchmarks are crucial for evaluating machine learning algorithm performance, facilitating comparison and identifying superior solutions. This paper addresses the issue of entity bias in relation extraction tasks, where models tend to rely on entity mentions rather than context. We propose a debiased relation extraction benchmark DREB that breaks the pseudo-correlation between entity mentions and relation types through entity replacement. To establish a new baseline on DREB, we introduce MixDebias, a debiasing method combining data-level and model training-level techniques.
  arXiv  Detail & Related papers  (2025-01-02T17:01:06Z)
• HG-Adapter: Improving Pre-Trained Heterogeneous Graph Neural Networks with Dual Adapters [53.97380482341493]
  "pre-train, prompt-tuning" has demonstrated impressive performance for tuning pre-trained heterogeneous graph neural networks (HGNNs) We propose a unified framework that combines two new adapters with potential labeled data extension to improve the generalization of pre-trained HGNN models.
  arXiv  Detail & Related papers  (2024-11-02T06:43:54Z)
• Fairness-Aware Estimation of Graphical Models [13.39268712338485]
  This paper examines the issue of fairness in the estimation of graphical models (GMs) Standard GMs can result in biased outcomes, especially when the underlying data involves sensitive characteristics or protected groups. We introduce a comprehensive framework designed to reduce bias in the estimation of GMs related to protected attributes.
  arXiv  Detail & Related papers  (2024-08-30T16:30:00Z)
• GenBench: A Benchmarking Suite for Systematic Evaluation of Genomic Foundation Models [56.63218531256961]
  We introduce GenBench, a benchmarking suite specifically tailored for evaluating the efficacy of Genomic Foundation Models. GenBench offers a modular and expandable framework that encapsulates a variety of state-of-the-art methodologies. We provide a nuanced analysis of the interplay between model architecture and dataset characteristics on task-specific performance.
  arXiv  Detail & Related papers  (2024-06-01T08:01:05Z)
• A PAC-Bayesian Perspective on the Interpolating Information Criterion [54.548058449535155]
  We show how a PAC-Bayes bound is obtained for a general class of models, characterizing factors which influence performance in the interpolating regime. We quantify how the test error for overparameterized models achieving effectively zero training error depends on the quality of the implicit regularization imposed by e.g. the combination of model, parameter-initialization scheme.
  arXiv  Detail & Related papers  (2023-11-13T01:48:08Z)
• Aggregation Weighting of Federated Learning via Generalization Bound Estimation [65.8630966842025]
  Federated Learning (FL) typically aggregates client model parameters using a weighting approach determined by sample proportions. We replace the aforementioned weighting method with a new strategy that considers the generalization bounds of each local model.
  arXiv  Detail & Related papers  (2023-11-10T08:50:28Z)
• Boosted Control Functions: Distribution generalization and invariance in confounded models [10.503777692702952]
  We introduce a strong notion of invariance that allows for distribution generalization even in the presence of nonlinear, non-identifiable structural functions. We propose the ControlTwicing algorithm to estimate the Boosted Control Function (BCF) using flexible machine-learning techniques.
  arXiv  Detail & Related papers  (2023-10-09T15:43:46Z)
• Controlling Equational Reasoning in Large Language Models with Prompt Interventions [3.9735602856280132]
  This paper investigates how hallucination rates in Large Language Models (LLMs) may be controlled via a symbolic data generation framework. We generate data for a derivation generation task using a symbolic engine, applying targeted interventions to prompts to perturb features of mathematical derivations. We then evaluate the effect of prompt interventions across a range of LLMs including fine-tuned T5 models, GPT, and LLaMa-based models.
  arXiv  Detail & Related papers  (2023-07-19T14:13:02Z)
• Towards Principled Disentanglement for Domain Generalization [90.9891372499545]
  A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data. We first formalize the OOD generalization problem as constrained optimization, called Disentanglement-constrained Domain Generalization (DDG) Based on the transformation, we propose a primal-dual algorithm for joint representation disentanglement and domain generalization.
  arXiv  Detail & Related papers  (2021-11-27T07:36:32Z)

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.