While classical scaling, just like principal component analysis, is parameter-free, other methods for embedding multivariate data require the selection of one or several tuning parameters. This tuning can be difficult due to the unsupervised nature of the situation. We propose a simple, almost obvious, approach to supervise the choice of tuning parameter(s): minimize a notion of stress. We apply this approach to the selection of the patch size in a prototypical patch-stitching embedding method, both in the multidimensional scaling (aka network localization) setting and in the dimensionality reduction (aka manifold learning) setting. In our study, we uncover a new bias--variance tradeoff phenomenon.
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Quantum programs are notoriously difficult to code and verify due to unintuitive quantum knowledge associated with quantum programming. Automated tools relieving the tedium and errors associated with low-level quantum details would hence be highly desirable. In this paper, we initiate the study of program synthesis for quantum unitary programs that recursively define a family of unitary circuits for different input sizes, which are widely used in existing quantum programming languages. Specifically, we present QSynth, the first quantum program synthesis framework, including a new inductive quantum programming language, its specification, a sound logic for reasoning, and an encoding of the reasoning procedure into SMT instances. By leveraging existing SMT solvers, QSynth successfully synthesizes ten quantum unitary programs including quantum adder circuits, quantum eigenvalue inversion circuits and Quantum Fourier Transformation, which can be readily transpiled to executable programs on major quantum platforms, e.g., Q#, IBM Qiskit, and AWS Braket.
We propose a method to control material attributes of objects like roughness, metallic, albedo, and transparency in real images. Our method capitalizes on the generative prior of text-to-image models known for photorealism, employing a scalar value and instructions to alter low-level material properties. Addressing the lack of datasets with controlled material attributes, we generated an object-centric synthetic dataset with physically-based materials. Fine-tuning a modified pre-trained text-to-image model on this synthetic dataset enables us to edit material properties in real-world images while preserving all other attributes. We show the potential application of our model to material edited NeRFs.
One of the most common problem-solving heuristics is by analogy. For a given problem, a solver can be viewed as a strategic walk on its fitness landscape. Thus if a solver works for one problem instance, we expect it will also be effective for other instances whose fitness landscapes essentially share structural similarities with each other. However, due to the black-box nature of combinatorial optimization, it is far from trivial to infer such similarity in real-world scenarios. To bridge this gap, by using local optima network as a proxy of fitness landscapes, this paper proposed to leverage graph data mining techniques to conduct qualitative and quantitative analyses to explore the latent topological structural information embedded in those landscapes. By conducting large-scale empirical experiments on three classic combinatorial optimization problems, we gain concrete evidence to support the existence of structural similarity between landscapes of the same classes within neighboring dimensions. We also interrogated the relationship between landscapes of different problem classes.
Distributional reinforcement learning algorithms have attempted to utilize estimated uncertainty for exploration, such as optimism in the face of uncertainty. However, using the estimated variance for optimistic exploration may cause biased data collection and hinder convergence or performance. In this paper, we present a novel distributional reinforcement learning algorithm that selects actions by randomizing risk criterion to avoid one-sided tendency on risk. We provide a perturbed distributional Bellman optimality operator by distorting the risk measure and prove the convergence and optimality of the proposed method with the weaker contraction property. Our theoretical results support that the proposed method does not fall into biased exploration and is guaranteed to converge to an optimal return. Finally, we empirically show that our method outperforms other existing distribution-based algorithms in various environments including Atari 55 games.
Language models are increasingly being deployed for general problem solving across a wide range of tasks, but are still confined to token-level, left-to-right decision-making processes during inference. This means they can fall short in tasks that require exploration, strategic lookahead, or where initial decisions play a pivotal role. To surmount these challenges, we introduce a new framework for language model inference, Tree of Thoughts (ToT), which generalizes over the popular Chain of Thought approach to prompting language models, and enables exploration over coherent units of text (thoughts) that serve as intermediate steps toward problem solving. ToT allows LMs to perform deliberate decision making by considering multiple different reasoning paths and self-evaluating choices to decide the next course of action, as well as looking ahead or backtracking when necessary to make global choices. Our experiments show that ToT significantly enhances language models' problem-solving abilities on three novel tasks requiring non-trivial planning or search: Game of 24, Creative Writing, and Mini Crosswords. For instance, in Game of 24, while GPT-4 with chain-of-thought prompting only solved 4% of tasks, our method achieved a success rate of 74%. Code repo with all prompts: //github.com/princeton-nlp/tree-of-thought-llm.
Large Language Models (LLMs) represent formidable tools for sequence modeling, boasting an innate capacity for general pattern recognition. Nevertheless, their broader spatial reasoning capabilities, especially applied to numerical trajectory data, remain insufficiently explored. In this paper, we investigate the out-of-the-box performance of ChatGPT-3.5, ChatGPT-4 and Llama 2 7B models when confronted with 3D robotic trajectory data from the CALVIN baseline and associated tasks, including 2D directional and shape labeling. Additionally, we introduce a novel prefix-based prompting mechanism, which yields a 33% improvement on the 3D trajectory data and an increase of up to 10% on SpartQA tasks over zero-shot prompting (with gains for other prompting types as well). The experimentation with 3D trajectory data offers an intriguing glimpse into the manner in which LLMs engage with numerical and spatial information, thus laying a solid foundation for the identification of target areas for future enhancements.
Testing complex simulation models can be expensive and time consuming. Current state-of-the-art methods that explore this problem are fully-supervised; i.e. they require that all examples are labeled. On the other hand, the GenClu system (introduced in this paper) takes a semi-supervised approach; i.e. (a) only a small subset of information is actually labeled (via simulation) and (b) those labels are then spread across the rest of the data. When applied to five open-source simulation models of cyber-physical systems, GenClu's test generation can be multiple orders of magnitude faster than the prior state of the art. Further, when assessed via mutation testing, tests generated by GenClu were as good or better than anything else tested here. Hence, we recommend semi-supervised methods over prior methods (evolutionary search and fully-supervised learning).
Modeling the ratio of two dependent components as a function of covariates is a frequently pursued objective in observational research. Despite the high relevance of this topic in medical studies, where biomarker ratios are often used as surrogate endpoints for specific diseases, existing models are based on oversimplified assumptions, assuming e.g.\@ independence or strictly positive associations between the components. In this paper, we close this gap in the literature and propose a regression model where the marginal distributions of the two components are linked by Frank copula. A key feature of our model is that it allows for both positive and negative correlations between the components, with one of the model parameters being directly interpretable in terms of Kendall's rank correlation coefficient. We study our method theoretically, evaluate finite sample properties in a simulation study and demonstrate its efficacy in an application to diagnosis of Alzheimer's disease via ratios of amyloid-beta and total tau protein biomarkers.
The fusion of causal models with deep learning introducing increasingly intricate data sets, such as the causal associations within images or between textual components, has surfaced as a focal research area. Nonetheless, the broadening of original causal concepts and theories to such complex, non-statistical data has been met with serious challenges. In response, our study proposes redefinitions of causal data into three distinct categories from the standpoint of causal structure and representation: definite data, semi-definite data, and indefinite data. Definite data chiefly pertains to statistical data used in conventional causal scenarios, while semi-definite data refers to a spectrum of data formats germane to deep learning, including time-series, images, text, and others. Indefinite data is an emergent research sphere inferred from the progression of data forms by us. To comprehensively present these three data paradigms, we elaborate on their formal definitions, differences manifested in datasets, resolution pathways, and development of research. We summarize key tasks and achievements pertaining to definite and semi-definite data from myriad research undertakings, present a roadmap for indefinite data, beginning with its current research conundrums. Lastly, we classify and scrutinize the key datasets presently utilized within these three paradigms.
As artificial intelligence (AI) models continue to scale up, they are becoming more capable and integrated into various forms of decision-making systems. For models involved in moral decision-making, also known as artificial moral agents (AMA), interpretability provides a way to trust and understand the agent's internal reasoning mechanisms for effective use and error correction. In this paper, we provide an overview of this rapidly-evolving sub-field of AI interpretability, introduce the concept of the Minimum Level of Interpretability (MLI) and recommend an MLI for various types of agents, to aid their safe deployment in real-world settings.
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