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Mar 12

Generating Mathematical Derivations with Large Language Models

The derivation of mathematical results in specialised fields using Large Language Models (LLMs) is an emerging research direction that can help identify models' limitations, and potentially support mathematical discovery. In this paper, we leverage a symbolic engine to generate derivations of equations at scale, and investigate the capabilities of LLMs when deriving goal equations from premises. Specifically, we employ in-context learning for GPT and fine-tune a range of T5 models to compare the robustness and generalisation of pre-training strategies to specialised models. Empirical results show that fine-tuned FLAN-T5-large (MathT5) outperforms GPT models on all static and out-of-distribution test sets in terms of absolute performance. However, an in-depth analysis reveals that the fine-tuned models are more sensitive to perturbations involving unseen symbols and (to a lesser extent) changes to equation structure. In addition, we analyse 1.7K equations and over 200 derivations to highlight common reasoning errors such as the inclusion of incorrect, irrelevant, and redundant equations, along with the tendency to skip derivation steps. Finally, we explore the suitability of existing metrics for evaluating mathematical derivations finding evidence that, while they capture general properties such as sensitivity to perturbations, they fail to highlight fine-grained reasoning errors and essential differences between models. Overall, this work demonstrates that training models on synthetic data can improve their mathematical capabilities beyond larger architectures.

Evaluating Correctness and Faithfulness of Instruction-Following Models for Question Answering

Retriever-augmented instruction-following models are attractive alternatives to fine-tuned approaches for information-seeking tasks such as question answering (QA). By simply prepending retrieved documents in its input along with an instruction, these models can be adapted to various information domains and tasks without additional fine-tuning. While the model responses tend to be natural and fluent, the additional verbosity makes traditional QA evaluation metrics such as exact match (EM) and F1 unreliable for accurately quantifying model performance. In this work, we investigate the performance of instruction-following models across three information-seeking QA tasks. We use both automatic and human evaluation to evaluate these models along two dimensions: 1) how well they satisfy the user's information need (correctness), and 2) whether they produce a response based on the provided knowledge (faithfulness). Guided by human evaluation and analysis, we highlight the shortcomings of traditional metrics for both correctness and faithfulness. We then propose simple token-overlap based and model-based metrics that reflect the true performance of these models. Our analysis reveals that instruction-following models are competitive, and sometimes even outperform fine-tuned models for correctness. However, these models struggle to stick to the provided knowledge and often hallucinate in their responses. We hope our work encourages a more holistic evaluation of instruction-following models for QA. Our code and data is available at https://github.com/McGill-NLP/instruct-qa

Image Labels Are All You Need for Coarse Seagrass Segmentation

Seagrass meadows serve as critical carbon sinks, but accurately estimating the amount of carbon they store requires knowledge of the seagrass species present. Using underwater and surface vehicles equipped with machine learning algorithms can help to accurately estimate the composition and extent of seagrass meadows at scale. However, previous approaches for seagrass detection and classification have required full supervision from patch-level labels. In this paper, we reframe seagrass classification as a weakly supervised coarse segmentation problem where image-level labels are used during training (25 times fewer labels compared to patch-level labeling) and patch-level outputs are obtained at inference time. To this end, we introduce SeaFeats, an architecture that uses unsupervised contrastive pretraining and feature similarity to separate background and seagrass patches, and SeaCLIP, a model that showcases the effectiveness of large language models as a supervisory signal in domain-specific applications. We demonstrate that an ensemble of SeaFeats and SeaCLIP leads to highly robust performance, with SeaCLIP conservatively predicting the background class to avoid false seagrass misclassifications in blurry or dark patches. Our method outperforms previous approaches that require patch-level labels on the multi-species 'DeepSeagrass' dataset by 6.8% (absolute) for the class-weighted F1 score, and by 12.1% (absolute) F1 score for seagrass presence/absence on the 'Global Wetlands' dataset. We also present two case studies for real-world deployment: outlier detection on the Global Wetlands dataset, and application of our method on imagery collected by FloatyBoat, an autonomous surface vehicle.