We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few assumptions, rather than writing down long lists of chords/scales to memorize without an underlying principle. Our approach involves introducing constraints that limit the possible scales we can consider. For example, we may impose the constraint that two voices cannot be only a semitone apart as this is too dissonant. We can then study scales that do not contain notes that are a semitone apart. A more refined constraint avoids three voices colliding by studying scales that do not have three notes separated only by semitones. Additionally, we require that our scales are complete, which roughly means that they are the maximal sets of tones that satisfy these constraints. As it turns out, completeness as applied to these simple two/three voice constraints characterizes the types of scales that are commonly used in music composition. Surprisingly, there is a correspondence between scales subject to the two-voice constraint and those subject to the three-voice constraint. We formulate this correspondence as a duality statement that provides a way to understand scales subject to one type of constraint in terms of scales subject to the other. Finally, we combine these constraint ideas to provide a classification of chords.
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To augment language models with the ability to reason, researchers usually prompt or finetune them to produce chain of thought reasoning steps before producing the final answer. However, although people use natural language to reason effectively, it may be that LMs could reason more effectively with some intermediate computation that is not in natural language. In this work, we explore an alternative reasoning approach: instead of explicitly producing the chain of thought reasoning steps, we use the language model's internal hidden states to perform implicit reasoning. The implicit reasoning steps are distilled from a teacher model trained on explicit chain-of-thought reasoning, and instead of doing reasoning "horizontally" by producing intermediate words one-by-one, we distill it such that the reasoning happens "vertically" among the hidden states in different layers. We conduct experiments on a multi-digit multiplication task and a grade school math problem dataset and find that this approach enables solving tasks previously not solvable without explicit chain-of-thought, at a speed comparable to no chain-of-thought.
We present a unified probabilistic formulation for diffusion-based image editing, where a latent variable is edited in a task-specific manner and generally deviates from the corresponding marginal distribution induced by the original stochastic or ordinary differential equation (SDE or ODE). Instead, it defines a corresponding SDE or ODE for editing. In the formulation, we prove that the Kullback-Leibler divergence between the marginal distributions of the two SDEs gradually decreases while that for the ODEs remains as the time approaches zero, which shows the promise of SDE in image editing. Inspired by it, we provide the SDE counterparts for widely used ODE baselines in various tasks including inpainting and image-to-image translation, where SDE shows a consistent and substantial improvement. Moreover, we propose SDE-Drag -- a simple yet effective method built upon the SDE formulation for point-based content dragging. We build a challenging benchmark (termed DragBench) with open-set natural, art, and AI-generated images for evaluation. A user study on DragBench indicates that SDE-Drag significantly outperforms our ODE baseline, existing diffusion-based methods, and the renowned DragGAN. Our results demonstrate the superiority and versatility of SDE in image editing and push the boundary of diffusion-based editing methods.
Aspect-based sentiment classification (ASC) aims to judge the sentiment polarity conveyed by the given aspect term in a sentence. The sentiment polarity is not only determined by the local context but also related to the words far away from the given aspect term. Most recent efforts related to the attention-based models can not sufficiently distinguish which words they should pay more attention to in some cases. Meanwhile, graph-based models are coming into ASC to encode syntactic dependency tree information. But these models do not fully leverage syntactic dependency trees as they neglect to incorporate dependency relation tag information into representation learning effectively. In this paper, we address these problems by effectively modeling the local and global features. Firstly, we design a local encoder containing: a Gaussian mask layer and a covariance self-attention layer. The Gaussian mask layer tends to adjust the receptive field around aspect terms adaptively to deemphasize the effects of unrelated words and pay more attention to local information. The covariance self-attention layer can distinguish the attention weights of different words more obviously. Furthermore, we propose a dual-level graph attention network as a global encoder by fully employing dependency tag information to capture long-distance information effectively. Our model achieves state-of-the-art performance on both SemEval 2014 and Twitter datasets.
We demonstrate how conditional generation from diffusion models can be used to tackle a variety of realistic tasks in the production of music in 44.1kHz stereo audio with sampling-time guidance. The scenarios we consider include continuation, inpainting and regeneration of musical audio, the creation of smooth transitions between two different music tracks, and the transfer of desired stylistic characteristics to existing audio clips. We achieve this by applying guidance at sampling time in a simple framework that supports both reconstruction and classification losses, or any combination of the two. This approach ensures that generated audio can match its surrounding context, or conform to a class distribution or latent representation specified relative to any suitable pre-trained classifier or embedding model.
When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop a statistical method for nearest neighbor classification based on such imbalanced data sets. First, we construct a classifier for the binary classification problem and then extend it for classification problems involving more than two classes. Unlike the existing oversampling or undersampling methods, our proposed classifiers do not need to generate any pseudo observations or remove any existing observations, hence the results are exactly reproducible. We establish the Bayes risk consistency of these classifiers under appropriate regularity conditions. Their superior performance over the existing methods is amply demonstrated by analyzing several benchmark data sets.
Understanding emergent abilities, such as in-context learning (ICL) and chain-of-thought (CoT) prompting in large language models (LLMs), is of utmost importance. This importance stems not only from the better utilization of these capabilities across various tasks, but also from the proactive identification and mitigation of potential risks, including concerns of truthfulness, bias, and toxicity, that may arise alongside these capabilities. In this paper, we present a thorough survey on the interpretation and analysis of emergent abilities of LLMs. First, we provide a concise introduction to the background and definition of emergent abilities. Then, we give an overview of advancements from two perspectives: 1) a macro perspective, emphasizing studies on the mechanistic interpretability and delving into the mathematical foundations behind emergent abilities; and 2) a micro-perspective, concerning studies that focus on empirical interpretability by examining factors associated with these abilities. We conclude by highlighting the challenges encountered and suggesting potential avenues for future research. We believe that our work establishes the basis for further exploration into the interpretation of emergent abilities.
Lately, propelled by the phenomenal advances around the transformer architecture, the legal NLP field has enjoyed spectacular growth. To measure progress, well curated and challenging benchmarks are crucial. However, most benchmarks are English only and in legal NLP specifically there is no multilingual benchmark available yet. Additionally, many benchmarks are saturated, with the best models clearly outperforming the best humans and achieving near perfect scores. We survey the legal NLP literature and select 11 datasets covering 24 languages, creating LEXTREME. To provide a fair comparison, we propose two aggregate scores, one based on the datasets and one on the languages. The best baseline (XLM-R large) achieves both a dataset aggregate score a language aggregate score of 61.3. This indicates that LEXTREME is still very challenging and leaves ample room for improvement. To make it easy for researchers and practitioners to use, we release LEXTREME on huggingface together with all the code required to evaluate models and a public Weights and Biases project with all the runs.
Bases have become an integral part of modern deep learning-based models for time series forecasting due to their ability to act as feature extractors or future references. To be effective, a basis must be tailored to the specific set of time series data and exhibit distinct correlation with each time series within the set. However, current state-of-the-art methods are limited in their ability to satisfy both of these requirements simultaneously. To address this challenge, we propose BasisFormer, an end-to-end time series forecasting architecture that leverages learnable and interpretable bases. This architecture comprises three components: First, we acquire bases through adaptive self-supervised learning, which treats the historical and future sections of the time series as two distinct views and employs contrastive learning. Next, we design a Coef module that calculates the similarity coefficients between the time series and bases in the historical view via bidirectional cross-attention. Finally, we present a Forecast module that selects and consolidates the bases in the future view based on the similarity coefficients, resulting in accurate future predictions. Through extensive experiments on six datasets, we demonstrate that BasisFormer outperforms previous state-of-the-art methods by 11.04\% and 15.78\% respectively for univariate and multivariate forecasting tasks. Code is available at: \url{//github.com/nzl5116190/Basisformer}
The rapid development of deep learning has made a great progress in segmentation, one of the fundamental tasks of computer vision. However, the current segmentation algorithms mostly rely on the availability of pixel-level annotations, which are often expensive, tedious, and laborious. To alleviate this burden, the past years have witnessed an increasing attention in building label-efficient, deep-learning-based segmentation algorithms. This paper offers a comprehensive review on label-efficient segmentation methods. To this end, we first develop a taxonomy to organize these methods according to the supervision provided by different types of weak labels (including no supervision, coarse supervision, incomplete supervision and noisy supervision) and supplemented by the types of segmentation problems (including semantic segmentation, instance segmentation and panoptic segmentation). Next, we summarize the existing label-efficient segmentation methods from a unified perspective that discusses an important question: how to bridge the gap between weak supervision and dense prediction -- the current methods are mostly based on heuristic priors, such as cross-pixel similarity, cross-label constraint, cross-view consistency, cross-image relation, etc. Finally, we share our opinions about the future research directions for label-efficient deep segmentation.
Due to their inherent capability in semantic alignment of aspects and their context words, attention mechanism and Convolutional Neural Networks (CNNs) are widely applied for aspect-based sentiment classification. However, these models lack a mechanism to account for relevant syntactical constraints and long-range word dependencies, and hence may mistakenly recognize syntactically irrelevant contextual words as clues for judging aspect sentiment. To tackle this problem, we propose to build a Graph Convolutional Network (GCN) over the dependency tree of a sentence to exploit syntactical information and word dependencies. Based on it, a novel aspect-specific sentiment classification framework is raised. Experiments on three benchmarking collections illustrate that our proposed model has comparable effectiveness to a range of state-of-the-art models, and further demonstrate that both syntactical information and long-range word dependencies are properly captured by the graph convolution structure.
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