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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 conventional scores. 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. Finally, we explore the suitability of existing metrics for evaluating mathematical derivations and find evidence that, while they can 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 may improve their math capabilities beyond much larger LLMs, but current metrics are not appropriately assessing the quality of generated mathematical text.

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ACM/IEEE第23屆模型驅動工程語言和系統國際會議,是模型驅動軟件和系統工程的首要會議系列,由ACM-SIGSOFT和IEEE-TCSE支持組織。自1998年以來,模型涵蓋了建模的各個方面,從語言和方法到工具和應用程序。模特的參加者來自不同的背景,包括研究人員、學者、工程師和工業專業人士。MODELS 2019是一個論壇,參與者可以圍繞建模和模型驅動的軟件和系統交流前沿研究成果和創新實踐經驗。今年的版本將為建模社區提供進一步推進建模基礎的機會,并在網絡物理系統、嵌入式系統、社會技術系統、云計算、大數據、機器學習、安全、開源等新興領域提出建模的創新應用以及可持續性。 官網鏈接: · 哈希學習 · FAST · 泛函 · 可約的 ·
2023 年 9 月 27 日

Locality-sensitive hashing (LSH) is an effective randomized technique widely used in many machine learning tasks. The cost of hashing is proportional to data dimensions, and thus often the performance bottleneck when dimensionality is high and the number of hash functions involved is large. Surprisingly, however, little work has been done to improve the efficiency of LSH computation. In this paper, we design a simple yet efficient LSH scheme, named FastLSH, under l2 norm. By combining random sampling and random projection, FastLSH reduces the time complexity from O(n) to O(m) (m<n), where n is the data dimensionality and m is the number of sampled dimensions. Moreover, FastLSH has provable LSH property, which distinguishes it from the non-LSH fast sketches. We conduct comprehensive experiments over a collection of real and synthetic datasets for the nearest neighbor search task. Experimental results demonstrate that FastLSH is on par with the state-of-the-arts in terms of answer quality, space occupation and query efficiency, while enjoying up to 80x speedup in hash function evaluation. We believe that FastLSH is a promising alternative to the classic LSH scheme.

In computational neuroscience, there has been an increased interest in developing machine learning algorithms that leverage brain imaging data to provide estimates of "brain age" for an individual. Importantly, the discordance between brain age and chronological age (referred to as "brain age gap") can capture accelerated aging due to adverse health conditions and therefore, can reflect increased vulnerability towards neurological disease or cognitive impairments. However, widespread adoption of brain age for clinical decision support has been hindered due to lack of transparency and methodological justifications in most existing brain age prediction algorithms. In this paper, we leverage coVariance neural networks (VNN) to propose an anatomically interpretable framework for brain age prediction using cortical thickness features. Specifically, our brain age prediction framework extends beyond the coarse metric of brain age gap in Alzheimer's disease (AD) and we make two important observations: (i) VNNs can assign anatomical interpretability to elevated brain age gap in AD by identifying contributing brain regions, (ii) the interpretability offered by VNNs is contingent on their ability to exploit specific eigenvectors of the anatomical covariance matrix. Together, these observations facilitate an explainable perspective to the task of brain age prediction.

This paper studies the case of possibly high-dimensional covariates in the regression discontinuity design (RDD) analysis. In particular, we propose estimation and inference methods for the RDD models with covariate selection which perform stably regardless of the number of covariates. The proposed methods combine the local approach using kernel weights with $\ell_{1}$-penalization to handle high-dimensional covariates. We provide theoretical and numerical results which illustrate the usefulness of the proposed methods. Theoretically, we present risk and coverage properties for our point estimation and inference methods, respectively. Under certain special case, the proposed estimator becomes more efficient than the conventional covariate adjusted estimator at the cost of an additional sparsity condition. Numerically, our simulation experiments and empirical example show the robust behaviors of the proposed methods to the number of covariates in terms of bias and variance for point estimation and coverage probability and interval length for inference.

Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

Graph Neural Networks (GNNs), which generalize deep neural networks to graph-structured data, have drawn considerable attention and achieved state-of-the-art performance in numerous graph related tasks. However, existing GNN models mainly focus on designing graph convolution operations. The graph pooling (or downsampling) operations, that play an important role in learning hierarchical representations, are usually overlooked. In this paper, we propose a novel graph pooling operator, called Hierarchical Graph Pooling with Structure Learning (HGP-SL), which can be integrated into various graph neural network architectures. HGP-SL incorporates graph pooling and structure learning into a unified module to generate hierarchical representations of graphs. More specifically, the graph pooling operation adaptively selects a subset of nodes to form an induced subgraph for the subsequent layers. To preserve the integrity of graph's topological information, we further introduce a structure learning mechanism to learn a refined graph structure for the pooled graph at each layer. By combining HGP-SL operator with graph neural networks, we perform graph level representation learning with focus on graph classification task. Experimental results on six widely used benchmarks demonstrate the effectiveness of our proposed model.

It is important to detect anomalous inputs when deploying machine learning systems. The use of larger and more complex inputs in deep learning magnifies the difficulty of distinguishing between anomalous and in-distribution examples. At the same time, diverse image and text data are available in enormous quantities. We propose leveraging these data to improve deep anomaly detection by training anomaly detectors against an auxiliary dataset of outliers, an approach we call Outlier Exposure (OE). This enables anomaly detectors to generalize and detect unseen anomalies. In extensive experiments on natural language processing and small- and large-scale vision tasks, we find that Outlier Exposure significantly improves detection performance. We also observe that cutting-edge generative models trained on CIFAR-10 may assign higher likelihoods to SVHN images than to CIFAR-10 images; we use OE to mitigate this issue. We also analyze the flexibility and robustness of Outlier Exposure, and identify characteristics of the auxiliary dataset that improve performance.

Recently, graph neural networks (GNNs) have revolutionized the field of graph representation learning through effectively learned node embeddings, and achieved state-of-the-art results in tasks such as node classification and link prediction. However, current GNN methods are inherently flat and do not learn hierarchical representations of graphs---a limitation that is especially problematic for the task of graph classification, where the goal is to predict the label associated with an entire graph. Here we propose DiffPool, a differentiable graph pooling module that can generate hierarchical representations of graphs and can be combined with various graph neural network architectures in an end-to-end fashion. DiffPool learns a differentiable soft cluster assignment for nodes at each layer of a deep GNN, mapping nodes to a set of clusters, which then form the coarsened input for the next GNN layer. Our experimental results show that combining existing GNN methods with DiffPool yields an average improvement of 5-10% accuracy on graph classification benchmarks, compared to all existing pooling approaches, achieving a new state-of-the-art on four out of five benchmark data sets.

Aspect based sentiment analysis (ABSA) can provide more detailed information than general sentiment analysis, because it aims to predict the sentiment polarities of the given aspects or entities in text. We summarize previous approaches into two subtasks: aspect-category sentiment analysis (ACSA) and aspect-term sentiment analysis (ATSA). Most previous approaches employ long short-term memory and attention mechanisms to predict the sentiment polarity of the concerned targets, which are often complicated and need more training time. We propose a model based on convolutional neural networks and gating mechanisms, which is more accurate and efficient. First, the novel Gated Tanh-ReLU Units can selectively output the sentiment features according to the given aspect or entity. The architecture is much simpler than attention layer used in the existing models. Second, the computations of our model could be easily parallelized during training, because convolutional layers do not have time dependency as in LSTM layers, and gating units also work independently. The experiments on SemEval datasets demonstrate the efficiency and effectiveness of our models.

Deep neural networks (DNNs) have been found to be vulnerable to adversarial examples resulting from adding small-magnitude perturbations to inputs. Such adversarial examples can mislead DNNs to produce adversary-selected results. Different attack strategies have been proposed to generate adversarial examples, but how to produce them with high perceptual quality and more efficiently requires more research efforts. In this paper, we propose AdvGAN to generate adversarial examples with generative adversarial networks (GANs), which can learn and approximate the distribution of original instances. For AdvGAN, once the generator is trained, it can generate adversarial perturbations efficiently for any instance, so as to potentially accelerate adversarial training as defenses. We apply AdvGAN in both semi-whitebox and black-box attack settings. In semi-whitebox attacks, there is no need to access the original target model after the generator is trained, in contrast to traditional white-box attacks. In black-box attacks, we dynamically train a distilled model for the black-box model and optimize the generator accordingly. Adversarial examples generated by AdvGAN on different target models have high attack success rate under state-of-the-art defenses compared to other attacks. Our attack has placed the first with 92.76% accuracy on a public MNIST black-box attack challenge.

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