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In this paper, we introduce an algorithm for data quantization based on the principles of Kashin representation. This approach hinges on decomposing any given vector, matrix, or tensor into two factors. The first factor maintains a small infinity norm, while the second exhibits a similarly constrained norm when multiplied by an orthogonal matrix. Surprisingly, the entries of factors after decomposition are well-concentrated around several peaks, which allows us to efficiently replace them with corresponding centroids for quantization purposes. We study the theoretical properties of the proposed approach and rigorously evaluate our compression algorithm in the context of next-word prediction tasks and on a set of downstream tasks for text classification. Our findings demonstrate that Kashin Quantization achieves competitive or superior quality in model performance while ensuring data compression, marking a significant advancement in the field of data quantization.

In this study, we identify the need for an interpretable, quantitative score of the repeatability, or consistency, of image generation in diffusion models. We propose a semantic approach, using a pairwise mean CLIP (Contrastive Language-Image Pretraining) score as our semantic consistency score. We applied this metric to compare two state-of-the-art open-source image generation diffusion models, Stable Diffusion XL and PixArt-{\alpha}, and we found statistically significant differences between the semantic consistency scores for the models. Agreement between the Semantic Consistency Score selected model and aggregated human annotations was 94%. We also explored the consistency of SDXL and a LoRA-fine-tuned version of SDXL and found that the fine-tuned model had significantly higher semantic consistency in generated images. The Semantic Consistency Score proposed here offers a measure of image generation alignment, facilitating the evaluation of model architectures for specific tasks and aiding in informed decision-making regarding model selection.

We identify the nonlinear normal modes spawning from the stable equilibrium of a double pendulum under gravity, and we establish their connection to homoclinic orbits through the unstable upright position as energy increases. This result is exploited to devise an efficient swing-up strategy for a double pendulum with weak, saturating actuators. Our approach involves stabilizing the system onto periodic orbits associated with the nonlinear modes while gradually injecting energy. Since these modes are autonomous system evolutions, the required control effort for stabilization is minimal. Even with actuator limitations of less than 1% of the maximum gravitational torque, the proposed method accomplishes the swing-up of the double pendulum by allowing sufficient time.

We continue the study of doubly-efficient proof systems for verifying agnostic PAC learning, for which we obtain the following results. - We construct an interactive protocol for learning the $t$ largest Fourier characters of a given function $f \colon \{0,1\}^n \to \{0,1\}$ up to an arbitrarily small error, wherein the verifier uses $\mathsf{poly}(t)$ random examples. This improves upon the Interactive Goldreich-Levin protocol of Goldwasser, Rothblum, Shafer, and Yehudayoff (ITCS 2021) whose sample complexity is $\mathsf{poly}(t,n)$. - For agnostically learning the class $\mathsf{AC}^0[2]$ under the uniform distribution, we build on the work of Carmosino, Impagliazzo, Kabanets, and Kolokolova (APPROX/RANDOM 2017) and design an interactive protocol, where given a function $f \colon \{0,1\}^n \to \{0,1\}$, the verifier learns the closest hypothesis up to $\mathsf{polylog}(n)$ multiplicative factor, using quasi-polynomially many random examples. In contrast, this class has been notoriously resistant even for constructing realisable learners (without a prover) using random examples. - For agnostically learning $k$-juntas under the uniform distribution, we obtain an interactive protocol, where the verifier uses $O(2^k)$ random examples to a given function $f \colon \{0,1\}^n \to \{0,1\}$. Crucially, the sample complexity of the verifier is independent of $n$. We also show that if we do not insist on doubly-efficient proof systems, then the model becomes trivial. Specifically, we show a protocol for an arbitrary class $\mathcal{C}$ of Boolean functions in the distribution-free setting, where the verifier uses $O(1)$ labeled examples to learn $f$.

Active learning (AL) techniques aim to maximally utilize a labeling budget by iteratively selecting instances that are most likely to improve prediction accuracy. However, their benefit compared to random sampling has not been consistent across various setups, e.g., different datasets, classifiers. In this empirical study, we examine how a combination of different factors might obscure any gains from an AL technique. Focusing on text classification, we rigorously evaluate AL techniques over around 1000 experiments that vary wrt the dataset, batch size, text representation and the classifier. We show that AL is only effective in a narrow set of circumstances. We also address the problem of using metrics that are better aligned with real world expectations. The impact of this study is in its insights for a practitioner: (a) the choice of text representation and classifier is as important as that of an AL technique, (b) choice of the right metric is critical in assessment of the latter, and, finally, (c) reported AL results must be holistically interpreted, accounting for variables other than just the query strategy.

This paper studies the computational complexity of a robust variant of a two-stage submodular minimization problem that we call Robust Submodular Minimizer. In this problem, we are given $k$ submodular functions $f_1,\dots,f_k$ over a set family $2^V$, which represent $k$ possible scenarios in the future when we will need to find an optimal solution for one of these scenarios, i.e., a minimizer for one of the functions. The present task is to find a set $X \subseteq V$ that is close to some optimal solution for each $f_i$ in the sense that some minimizer of $f_i$ can be obtained from $X$ by adding/removing at most $d$ elements for a given integer $d$. The main contribution of this paper is to provide a complete computational map of this problem with respect to parameters $k$ and $d$, which reveals a tight complexity threshold for both parameters: (1) Robust Submodular Minimizer can be solved in polynomial time when $k \leq 2$, but is NP-hard if $k$ is a constant with $k \geq 3$. (2) Robust Submodular Minimizer can be solved in polynomial time when $d=0$, but is NP-hard if $d$ is a constant with $d \geq 1$. (3) Robust Submodular Minimizer is fixed-parameter tractable when parameterized by $(k,d)$. We also show that if some submodular function $f_i$ has a polynomial number of minimizers, then the problem becomes fixed-parameter tractable when parameterized by $d$. We remark that all our hardness results hold even if each submodular function is given by a cut function of a directed graph.

Quadrotors have gained popularity over the last decade, aiding humans in complex tasks such as search and rescue, mapping and exploration. Despite their mechanical simplicity and versatility compared to other types of aerial vehicles, they remain vulnerable to rotor failures. In this paper, we propose an algorithmic and mechanical approach to addressing the quadrotor fault-tolerant problem in case of rotor failures. First, we present a fault-tolerant detection and control scheme that includes various attitude error metrics. The scheme transitions to a fault-tolerant control mode by surrendering the yaw control. Subsequently, to ensure compatibility with platform sensing constraints, we investigate the relationship between variations in robot rotational drag, achieved through a modular mechanical design appendage, resulting in yaw rates within sensor limits. This analysis offers a platform-agnostic framework for designing more reliable and robust quadrotors in the event of rotor failures. Extensive experimental results validate the proposed approach providing insights into successfully designing a cost-effective quadrotor capable of fault-tolerant control. The overall design enhances safety in scenarios of faulty rotors, without the need for additional sensors or computational resources.

The convergence of materials science and artificial intelligence has unlocked new opportunities for gathering, analyzing, and generating novel materials sourced from extensive scientific literature. Despite the potential benefits, persistent challenges such as manual annotation, precise extraction, and traceability issues remain. Large language models have emerged as promising solutions to address these obstacles. This paper introduces Functional Materials Knowledge Graph (FMKG), a multidisciplinary materials science knowledge graph. Through the utilization of advanced natural language processing techniques, extracting millions of entities to form triples from a corpus comprising all high-quality research papers published in the last decade. It organizes unstructured information into nine distinct labels, covering Name, Formula, Acronym, Structure/Phase, Properties, Descriptor, Synthesis, Characterization Method, Application, and Domain, seamlessly integrating papers' Digital Object Identifiers. As the latest structured database for functional materials, FMKG acts as a powerful catalyst for expediting the development of functional materials and a fundation for building a more comprehensive material knowledge graph using full paper text. Furthermore, our research lays the groundwork for practical text-mining-based knowledge management systems, not only in intricate materials systems but also applicable to other specialized domains.

In the past decade, we have witnessed the rise of deep learning to dominate the field of artificial intelligence. Advances in artificial neural networks alongside corresponding advances in hardware accelerators with large memory capacity, together with the availability of large datasets enabled researchers and practitioners alike to train and deploy sophisticated neural network models that achieve state-of-the-art performance on tasks across several fields spanning computer vision, natural language processing, and reinforcement learning. However, as these neural networks become bigger, more complex, and more widely used, fundamental problems with current deep learning models become more apparent. State-of-the-art deep learning models are known to suffer from issues that range from poor robustness, inability to adapt to novel task settings, to requiring rigid and inflexible configuration assumptions. Ideas from collective intelligence, in particular concepts from complex systems such as self-organization, emergent behavior, swarm optimization, and cellular systems tend to produce solutions that are robust, adaptable, and have less rigid assumptions about the environment configuration. It is therefore natural to see these ideas incorporated into newer deep learning methods. In this review, we will provide a historical context of neural network research's involvement with complex systems, and highlight several active areas in modern deep learning research that incorporate the principles of collective intelligence to advance its current capabilities. To facilitate a bi-directional flow of ideas, we also discuss work that utilize modern deep learning models to help advance complex systems research. We hope this review can serve as a bridge between complex systems and deep learning communities to facilitate the cross pollination of ideas and foster new collaborations across disciplines.

As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.