World Models for Math Story Problems

Solving math story problems is a complex task for students and NLP models alike, requiring them to understand the world as described in the story and reason over it to compute an answer. Recent years have seen impressive performance on automatically solving these problems with large pre-trained language models and innovative techniques to prompt them. However, it remains unclear if these models possess accurate representations of mathematical concepts. This leads to lack of interpretability and trustworthiness which impedes their usefulness in various applications. In this paper, we consolidate previous work on categorizing and representing math story problems and develop MathWorld, which is a graph-based semantic formalism specific for the domain of math story problems. With MathWorld, we can assign world models to math story problems which represent the situations and actions introduced in the text and their mathematical relationships. We combine math story problems from several existing datasets and annotate a corpus of 1,019 problems and 3,204 logical forms with MathWorld. Using this data, we demonstrate the following use cases of MathWorld: (1) prompting language models with synthetically generated question-answer pairs to probe their reasoning and world modeling abilities, and (2) generating new problems by using the world models as a design space.

Infusing Lattice Symmetry Priors in Attention Mechanisms for Sample-Efficient Abstract Geometric Reasoning

The Abstraction and Reasoning Corpus (ARC) (Chollet, 2019) and its most recent language-complete instantiation (LARC) has been postulated as an important step towards general AI. Yet, even state-of-the-art machine learning models struggle to achieve meaningful performance on these problems, falling behind non-learning based approaches. We argue that solving these tasks requires extreme generalization that can only be achieved by proper accounting for core knowledge priors. As a step towards this goal, we focus on geometry priors and introduce LatFormer, a model that incorporates lattice symmetry priors in attention masks. We show that, for any transformation of the hypercubic lattice, there exists a binary attention mask that implements that group action. Hence, our study motivates a modification to the standard attention mechanism, where attention weights are scaled using soft masks generated by a convolutional network. Experiments on synthetic geometric reasoning show that LatFormer requires 2 orders of magnitude fewer data than standard attention and transformers. Moreover, our results on ARC and LARC tasks that incorporate geometric priors provide preliminary evidence that these complex datasets do not lie out of the reach of deep learning models.

Adaptive and Personalized Exercise Generation for Online Language Learning

Adaptive learning aims to provide customized educational activities (e.g., exercises) to address individual learning needs. However, manual construction and delivery of such activities is a laborious process. Thus, in this paper, we study a novel task of adaptive and personalized exercise generation for online language learning. To this end, we combine a knowledge tracing model that estimates each student's evolving knowledge states from their learning history and a controlled text generation model that generates exercise sentences based on the student's current estimated knowledge state and instructor requirements of desired properties (e.g., domain knowledge and difficulty). We train and evaluate our model on real-world learner interaction data from Duolingo and demonstrate that LMs guided by student states can generate superior exercises. Then, we discuss the potential use of our model in educational applications using various simulations. These simulations show that our model can adapt to students' individual abilities and can facilitate their learning efficiency by personalizing learning sequences.

Membership Inference Attacks against Language Models via Neighbourhood Comparison

Membership Inference attacks (MIAs) aim to predict whether a data sample was present in the training data of a machine learning model or not, and are widely used for assessing the privacy risks of language models. Most existing attacks rely on the observation that models tend to assign higher probabilities to their training samples than non-training points. However, simple thresholding of the model score in isolation tends to lead to high false-positive rates as it does not account for the intrinsic complexity of a sample. Recent work has demonstrated that reference-based attacks which compare model scores to those obtained from a reference model trained on similar data can substantially improve the performance of MIAs. However, in order to train reference models, attacks of this kind make the strong and arguably unrealistic assumption that an adversary has access to samples closely resembling the original training data. Therefore, we investigate their performance in more realistic scenarios and find that they are highly fragile in relation to the data distribution used to train reference models. To investigate whether this fragility provides a layer of safety, we propose and evaluate neighbourhood attacks, which compare model scores for a given sample to scores of synthetically generated neighbour texts and therefore eliminate the need for access to the training data distribution. We show that, in addition to being competitive with reference-based attacks that have perfect knowledge about the training data distribution, our attack clearly outperforms existing reference-free attacks as well as reference-based attacks with imperfect knowledge, which demonstrates the need for a reevaluation of the threat model of adversarial attacks.

Learning the String Partial Order

We show that most structured prediction problems can be solved in linear time and space by considering them as partial orderings of the tokens in the input string. Our method computes real numbers for each token in an input string and sorts the tokens accordingly, resulting in as few as 2 total orders of the tokens in the string. Each total order possesses a set of edges oriented from smaller to greater tokens. The intersection of total orders results in a partial order over the set of input tokens, which is then decoded into a directed graph representing the desired structure. Experiments show that our method achieves 95.4 LAS and 96.9 UAS by using an intersection of 2 total orders, 95.7 LAS and 97.1 UAS with 4 on the English Penn Treebank dependency parsing benchmark. Our method is also the first linear-complexity coreference resolution model and achieves 79.2 F1 on the English OntoNotes benchmark, which is comparable with state of the art.

Understanding Arithmetic Reasoning in Language Models using Causal Mediation Analysis

Mathematical reasoning in large language models (LLMs) has garnered attention in recent research, but there is limited understanding of how these models process and store information related to arithmetic tasks. In this paper, we present a mechanistic interpretation of LLMs for arithmetic-based questions using a causal mediation analysis framework. By intervening on the activations of specific model components and measuring the resulting changes in predicted probabilities, we identify the subset of parameters responsible for specific predictions. We analyze two pre-trained language models with different sizes (2.8B and 6B parameters). Experimental results reveal that a small set of mid-late layers significantly affect predictions for arithmetic-based questions, with distinct activation patterns for correct and wrong predictions. We also investigate the role of the attention mechanism and compare the model's activation patterns for arithmetic queries with the prediction of factual knowledge. Our findings provide insights into the mechanistic interpretation of LLMs for arithmetic tasks and highlight the specific components involved in arithmetic reasoning.

All Roads Lead to Rome? Exploring the Invariance of Transformers' Representations

Transformer models bring propelling advances in various NLP tasks, thus inducing lots of interpretability research on the learned representations of the models. However, we raise a fundamental question regarding the reliability of the representations. Specifically, we investigate whether transformers learn essentially isomorphic representation spaces, or those that are sensitive to the random seeds in their pretraining process. In this work, we formulate the Bijection Hypothesis, which suggests the use of bijective methods to align different models' representation spaces. We propose a model based on invertible neural networks, BERT-INN, to learn the bijection more effectively than other existing bijective methods such as the canonical correlation analysis (CCA). We show the advantage of BERT-INN both theoretically and through extensive experiments, and apply it to align the reproduced BERT embeddings to draw insights that are meaningful to the interpretability research. Our code is at https://github.com/twinkle0331/BERT-similarity.

MathDial: A Dialogue Tutoring Dataset with Rich Pedagogical Properties Grounded in Math Reasoning Problems

Although automatic dialogue tutors hold great potential in making education personalized and more accessible, research on such systems has been hampered by a lack of sufficiently large and high-quality datasets. However, collecting such datasets remains challenging, as recording tutoring sessions raises privacy concerns and crowdsourcing leads to insufficient data quality. To address this problem, we propose a framework to semi-synthetically generate such dialogues by pairing real teachers with a large language model (LLM) scaffolded to represent common student errors. In this paper, we describe our ongoing efforts to use this framework to collect MathDial, a dataset of currently ca. 1.5k tutoring dialogues grounded in multi-step math word problems. We show that our dataset exhibits rich pedagogical properties, focusing on guiding students using sense-making questions to let them explore problems. Moreover, we outline that MathDial and its grounding annotations can be used to finetune language models to be more effective tutors (and not just solvers) and highlight remaining challenges that need to be addressed by the research community. We will release our dataset publicly to foster research in this socially important area of NLP.

When Does Aggregating Multiple Skills with Multi-Task Learning Work? A Case Study in Financial NLP

Multi-task learning (MTL) aims at achieving a better model by leveraging data and knowledge from multiple tasks. However, MTL does not always work -- sometimes negative transfer occurs between tasks, especially when aggregating loosely related skills, leaving it an open question when MTL works. Previous studies show that MTL performance can be improved by algorithmic tricks. However, what tasks and skills should be included is less well explored. In this work, we conduct a case study in Financial NLP where multiple datasets exist for skills relevant to the domain, such as numeric reasoning and sentiment analysis. Due to the task difficulty and data scarcity in the Financial NLP domain, we explore when aggregating such diverse skills from multiple datasets with MTL can work. Our findings suggest that the key to MTL success lies in skill diversity, relatedness between tasks, and choice of aggregation size and shared capacity. Specifically, MTL works well when tasks are diverse but related, and when the size of the task aggregation and the shared capacity of the model are balanced to avoid overwhelming certain tasks.

RecurrentGPT: Interactive Generation of (Arbitrarily) Long Text

The fixed-size context of Transformer makes GPT models incapable of generating arbitrarily long text. In this paper, we introduce RecurrentGPT, a language-based simulacrum of the recurrence mechanism in RNNs. RecurrentGPT is built upon a large language model (LLM) such as ChatGPT and uses natural language to simulate the Long Short-Term Memory mechanism in an LSTM. At each timestep, RecurrentGPT generates a paragraph of text and updates its language-based long-short term memory stored on the hard drive and the prompt, respectively. This recurrence mechanism enables RecurrentGPT to generate texts of arbitrary length without forgetting. Since human users can easily observe and edit the natural language memories, RecurrentGPT is interpretable and enables interactive generation of long text. RecurrentGPT is an initial step towards next-generation computer-assisted writing systems beyond local editing suggestions. In addition to producing AI-generated content (AIGC), we also demonstrate the possibility of using RecurrentGPT as an interactive fiction that directly interacts with consumers. We call this usage of generative models by ``AI As Contents'' (AIAC), which we believe is the next form of conventional AIGC. We further demonstrate the possibility of using RecurrentGPT to create personalized interactive fiction that directly interacts with readers instead of interacting with writers. More broadly, RecurrentGPT demonstrates the utility of borrowing ideas from popular model designs in cognitive science and deep learning for prompting LLMs. Our code is available at https://github.com/aiwaves-cn/RecurrentGPT and an online demo is available at https://www.aiwaves.org/recurrentgpt.