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Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the automated resolution of mathematical problems. However, the landscape of mathematical problem types is vast and varied, with LLM-oriented techniques undergoing evaluation across diverse datasets and settings. This diversity makes it challenging to discern the true advancements and obstacles within this burgeoning field. This survey endeavors to address four pivotal dimensions: i) a comprehensive exploration of the various mathematical problems and their corresponding datasets that have been investigated; ii) an examination of the spectrum of LLM-oriented techniques that have been proposed for mathematical problem-solving; iii) an overview of factors and concerns affecting LLMs in solving math; and iv) an elucidation of the persisting challenges within this domain. To the best of our knowledge, this survey stands as one of the first extensive examinations of the landscape of LLMs in the realm of mathematics, providing a holistic perspective on the current state, accomplishments, and future challenges in this rapidly evolving field.

相關內容

數學是關于(yu)數量、結(jie)構、變化等主題(ti)的探索。

Transformers have emerged as the backbone of large language models (LLMs). However, generation remains inefficient due to the need to store in memory a cache of key-value representations for past tokens, whose size scales linearly with the input sequence length and batch size. As a solution, we propose Dynamic Memory Compression (DMC), a method for on-line key-value cache compression at inference time. Most importantly, the model learns to apply different compression rates in different heads and layers. We retrofit pre-trained LLMs such as Llama 2 (7B, 13B and 70B) into DMC Transformers, achieving up to ~3.7x throughput increase in auto-regressive inference on a NVIDIA H100 GPU. DMC is applied via continued pre-training on a negligible percentage of the original data without adding any extra parameters. We find that DMC preserves the original downstream performance with up to 4x cache compression, outperforming up-trained grouped-query attention (GQA). GQA and DMC can be even combined to obtain compounded gains. As a result DMC fits longer contexts and larger batches within any given memory budget.

Audits are critical mechanisms for identifying the risks and limitations of deployed artificial intelligence (AI) systems. However, the effective execution of AI audits remains incredibly difficult. As a result, practitioners make use of various tools to support their efforts. Drawing on interviews with 35 AI audit practitioners and a landscape analysis of 390 tools, we map the current ecosystem of available AI audit tools. While there are many tools designed to assist practitioners with setting standards and evaluating AI systems, these tools often fell short of supporting the accountability goals of AI auditing in practice. We thus highlight areas for future tool development beyond evaluation -- from harms discovery to advocacy -- and outline challenges practitioners faced in their efforts to use AI audit tools. We conclude that resources are lacking to adequately support the full scope of needs for many AI audit practitioners and recommend that the field move beyond tools for just evaluation, towards more comprehensive infrastructure for AI accountability.

Endowing machines with abstract reasoning ability has been a long-term research topic in artificial intelligence. Raven's Progressive Matrix (RPM) is widely used to probe abstract visual reasoning in machine intelligence, where models will analyze the underlying rules and select one image from candidates to complete the image matrix. Participators of RPM tests can show powerful reasoning ability by inferring and combining attribute-changing rules and imagining the missing images at arbitrary positions of a matrix. However, existing solvers can hardly manifest such an ability in realistic RPM tests. In this paper, we propose a deep latent variable model for answer generation problems through Rule AbstractIon and SElection (RAISE). RAISE can encode image attributes into latent concepts and abstract atomic rules that act on the latent concepts. When generating answers, RAISE selects one atomic rule out of the global knowledge set for each latent concept to constitute the underlying rule of an RPM. In the experiments of bottom-right and arbitrary-position answer generation, RAISE outperforms the compared solvers in most configurations of realistic RPM datasets. In the odd-one-out task and two held-out configurations, RAISE can leverage acquired latent concepts and atomic rules to find the rule-breaking image in a matrix and handle problems with unseen combinations of rules and attributes.

We propose an objective intelligibility measure (OIM), called the Gammachirp Envelope Similarity Index (GESI), which can predict the speech intelligibility (SI) of simulated hearing loss (HL) sounds for normal hearing (NH) listeners. GESI is an intrusive method that computes the SI metric using the gammachirp filterbank (GCFB), the modulation filterbank, and the extended cosine similarity measure. The unique features of GESI are that i) it reflects the hearing impaired (HI) listener's HL that appears in the audiogram and is caused by active and passive cochlear dysfunction, ii) it provides a single goodness metric, as in the widely used STOI and ESTOI, that can be used immediately to evaluate SE algorithms, and iii) it provides a simple control parameter to accept the level asymmetry of the reference and test sounds and to deal with individual listening conditions and environments. We evaluated GESI and the conventional OIMs, STOI, ESTOI, MBSTOI, and HASPI versions 1 and 2 by using four SI experiments on words of male and female speech sounds in both laboratory and remote environments. GESI was shown to outperform the other OIMs in the evaluations. GESI could be used to improve SE algorithms in assistive listening devices for individual HI listeners.

Various perception-aware planning approaches have attempted to enhance the state estimation accuracy during maneuvers, while the feature matchability among frames, a crucial factor influencing estimation accuracy, has often been overlooked. In this paper, we present APACE, an Agile and Perception-Aware trajeCtory gEneration framework for quadrotors aggressive flight, that takes into account feature matchability during trajectory planning. We seek to generate a perception-aware trajectory that reduces the error of visual-based estimator while satisfying the constraints on smoothness, safety, agility and the quadrotor dynamics. The perception objective is achieved by maximizing the number of covisible features while ensuring small enough parallax angles. Additionally, we propose a differentiable and accurate visibility model that allows decomposition of the trajectory planning problem for efficient optimization resolution. Through validations conducted in both a photorealistic simulator and real-world experiments, we demonstrate that the trajectories generated by our method significantly improve state estimation accuracy, with root mean square error (RMSE) reduced by up to an order of magnitude. The source code will be released to benefit the community.

Answering questions within business and finance requires reasoning, precision, and a wide-breadth of technical knowledge. Together, these requirements make this domain difficult for large language models (LLMs). We introduce BizBench, a benchmark for evaluating models' ability to reason about realistic financial problems. BizBench comprises eight quantitative reasoning tasks, focusing on question-answering (QA) over financial data via program synthesis. We include three financially-themed code-generation tasks from newly collected and augmented QA data. Additionally, we isolate the reasoning capabilities required for financial QA: reading comprehension of financial text and tables for extracting intermediate values, and understanding financial concepts and formulas needed to calculate complex solutions. Collectively, these tasks evaluate a model's financial background knowledge, ability to parse financial documents, and capacity to solve problems with code. We conduct an in-depth evaluation of open-source and commercial LLMs, comparing and contrasting the behavior of code-focused and language-focused models. We demonstrate that the current bottleneck in performance is due to LLMs' limited business and financial understanding, highlighting the value of a challenging benchmark for quantitative reasoning within this domain.

In reaction to growing concerns about the potential harms of artificial intelligence (AI), societies have begun to demand more transparency about how AI models and systems are created and used. To address these concerns, several efforts have proposed documentation templates containing questions to be answered by model developers. These templates provide a useful starting point, but no single template can cover the needs of diverse documentation consumers. It is possible in principle, however, to create a repeatable methodology to generate truly useful documentation. Richards et al. [25] proposed such a methodology for identifying specific documentation needs and creating templates to address those needs. Although this is a promising proposal, it has not been evaluated. This paper presents the first evaluation of this user-centered methodology in practice, reporting on the experiences of a team in the domain of AI for healthcare that adopted it to increase transparency for several AI models. The methodology was found to be usable by developers not trained in user-centered techniques, guiding them to creating a documentation template that addressed the specific needs of their consumers while still being reusable across different models and use cases. Analysis of the benefits and costs of this methodology are reviewed and suggestions for further improvement in both the methodology and supporting tools are summarized.

Recent advances in instruction-tuned Large Vision-Language Models (LVLMs) have imbued the models with the ability to generate high-level, image-grounded explanations with ease. While such capability is largely attributed to the rich world knowledge contained within the Large Language Models (LLMs), our work reveals their shortcomings in fine-grained visual categorization (FGVC) across six different benchmark settings. Most recent state-of-the-art LVLMs like LLaVa-1.5, InstructBLIP and GPT-4V not only severely deteriorate in terms of classification performance, e.g., average drop of 65.58 in EM for Stanford Dogs for LLaVA-1.5, but also struggle to generate an accurate explanation with detailed attributes based on the concept that appears within an input image despite their capability to generate holistic image-level descriptions. In-depth analyses show that instruction-tuned LVLMs exhibit modality gap, showing discrepancy when given textual and visual inputs that correspond to the same concept, preventing the image modality from leveraging the rich parametric knowledge within the LLMs. In an effort to further the community's endeavor in this direction, we propose a multiple granularity attribute-centric evaluation benchmark, Finer, which aims to establish a ground to evaluate LVLMs' fine-grained visual comprehension ability and provide significantly improved explainability.

Knowledge graphs are important resources for many artificial intelligence tasks but often suffer from incompleteness. In this work, we propose to use pre-trained language models for knowledge graph completion. We treat triples in knowledge graphs as textual sequences and propose a novel framework named Knowledge Graph Bidirectional Encoder Representations from Transformer (KG-BERT) to model these triples. Our method takes entity and relation descriptions of a triple as input and computes scoring function of the triple with the KG-BERT language model. Experimental results on multiple benchmark knowledge graphs show that our method can achieve state-of-the-art performance in triple classification, link prediction and relation prediction tasks.

Distant supervision can effectively label data for relation extraction, but suffers from the noise labeling problem. Recent works mainly perform soft bag-level noise reduction strategies to find the relatively better samples in a sentence bag, which is suboptimal compared with making a hard decision of false positive samples in sentence level. In this paper, we introduce an adversarial learning framework, which we named DSGAN, to learn a sentence-level true-positive generator. Inspired by Generative Adversarial Networks, we regard the positive samples generated by the generator as the negative samples to train the discriminator. The optimal generator is obtained until the discrimination ability of the discriminator has the greatest decline. We adopt the generator to filter distant supervision training dataset and redistribute the false positive instances into the negative set, in which way to provide a cleaned dataset for relation classification. The experimental results show that the proposed strategy significantly improves the performance of distant supervision relation extraction comparing to state-of-the-art systems.

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