Scientific discovery and engineering design are currently limited by the time and cost of physical experiments, selected mostly through trial-and-error and intuition that require deep domain expertise. Numerical simulations present an alternative to physical experiments but are usually infeasible for complex real-world domains due to the computational requirements of existing numerical methods. Artificial intelligence (AI) presents a potential paradigm shift by developing fast data-driven surrogate models. In particular, an AI framework, known as Neural Operators, presents a principled framework for learning mappings between functions defined on continuous domains, e.g., spatiotemporal processes and partial differential equations (PDE). They can extrapolate and predict solutions at new locations unseen during training, i.e., perform zero-shot super-resolution. Neural Operators can augment or even replace existing simulators in many applications, such as computational fluid dynamics, weather forecasting, and material modeling, while being 4-5 orders of magnitude faster. Further, Neural Operators can be integrated with physics and other domain constraints enforced at finer resolutions to obtain high-fidelity solutions and good generalization. Since Neural Operators are differentiable, they can directly optimize parameters for inverse design and other inverse problems. We believe that Neural Operators present a transformative approach to simulation and design, enabling rapid research and development.

Predicting the solubility of given molecules remains crucial in the pharmaceutical industry. In this study, we revisited this extensively studied topic, leveraging the capabilities of contemporary computing resources. We employed two machine learning models: a linear regression model and a graph convolutional neural network (GCNN) model, using various experimental datasets. Both methods yielded reasonable predictions, with the GCNN model exhibiting the highest level of performance. However, the present GCNN model has limited interpretability while the linear regression model allows scientists for a greater in-depth analysis of the underlying factors through feature importance analysis, although more human inputs and evaluations on the overall dataset is required. From the perspective of chemistry, using the linear regression model, we elucidated the impact of individual atom species and functional groups on overall solubility, highlighting the significance of comprehending how chemical structure influences chemical properties in the drug development process. It is learned that introducing oxygen atoms can increase the solubility of organic molecules, while almost all other hetero atoms except oxygen and nitrogen tend to decrease solubility.

Learning representations on large-sized graphs is a long-standing challenge due to the inter-dependence nature involved in massive data points. Transformers, as an emerging class of foundation encoders for graph-structured data, have shown promising performance on small graphs due to its global attention capable of capturing all-pair influence beyond neighboring nodes. Even so, existing approaches tend to inherit the spirit of Transformers in language and vision tasks, and embrace complicated models by stacking deep multi-head attentions. In this paper, we critically demonstrate that even using a one-layer attention can bring up surprisingly competitive performance across node property prediction benchmarks where node numbers range from thousand-level to billion-level. This encourages us to rethink the design philosophy for Transformers on large graphs, where the global attention is a computation overhead hindering the scalability. We frame the proposed scheme as Simplified Graph Transformers (SGFormer), which is empowered by a simple attention model that can efficiently propagate information among arbitrary nodes in one layer. SGFormer requires none of positional encodings, feature/graph pre-processing or augmented loss. Empirically, SGFormer successfully scales to the web-scale graph ogbn-papers100M and yields up to 141x inference acceleration over SOTA Transformers on medium-sized graphs. Beyond current results, we believe the proposed methodology alone enlightens a new technical path of independent interest for building Transformers on large graphs.

Current state-of-the-art analyses on the convergence of gradient descent for training neural networks focus on characterizing properties of the loss landscape, such as the Polyak-Lojaciewicz (PL) condition and the restricted strong convexity. While gradient descent converges linearly under such conditions, it remains an open question whether Nesterov's momentum enjoys accelerated convergence under similar settings and assumptions. In this work, we consider a new class of objective functions, where only a subset of the parameters satisfies strong convexity, and show Nesterov's momentum achieves acceleration in theory for this objective class. We provide two realizations of the problem class, one of which is deep ReLU networks, which --to the best of our knowledge--constitutes this work the first that proves accelerated convergence rate for non-trivial neural network architectures.

Adversarial machine learning (AML) studies the adversarial phenomenon of machine learning, which may make inconsistent or unexpected predictions with humans. Some paradigms have been recently developed to explore this adversarial phenomenon occurring at different stages of a machine learning system, such as backdoor attack occurring at the pre-training, in-training and inference stage; weight attack occurring at the post-training, deployment and inference stage; adversarial attack occurring at the inference stage. However, although these adversarial paradigms share a common goal, their developments are almost independent, and there is still no big picture of AML. In this work, we aim to provide a unified perspective to the AML community to systematically review the overall progress of this field. We firstly provide a general definition about AML, and then propose a unified mathematical framework to covering existing attack paradigms. According to the proposed unified framework, we build a full taxonomy to systematically categorize and review existing representative methods for each paradigm. Besides, using this unified framework, it is easy to figure out the connections and differences among different attack paradigms, which may inspire future researchers to develop more advanced attack paradigms. Finally, to facilitate the viewing of the built taxonomy and the related literature in adversarial machine learning, we further provide a website, \ie, \url{http://adversarial-ml.com}, where the taxonomies and literature will be continuously updated.

Dynamic programming (DP) is an algorithmic design paradigm for the efficient, exact solution of otherwise intractable, combinatorial problems. However, DP algorithm design is often presented in an ad-hoc manner. It is sometimes difficult to justify algorithm correctness. To address this issue, this paper presents a rigorous algebraic formalism for systematically deriving DP algorithms, based on semiring polymorphism. We start with a specification, construct an algorithm to compute the required solution which is self-evidently correct because it exhaustively generates and evaluates all possible solutions meeting the specification. We then derive, through the use of shortcut fusion, an implementation of this algorithm which is both efficient and correct. We also demonstrate how, with the use of semiring lifting, the specification can be augmented with combinatorial constraints, showing how these constraints can be fused with the algorithm. We furthermore demonstrate how existing DP algorithms for a given combinatorial problem can be abstracted from their original context and re-purposed. This approach can be applied to the full scope of combinatorial problems expressible in terms of semirings. This includes, for example: optimal probability and Viterbi decoding, probabilistic marginalization, logical inference, fuzzy sets, differentiable softmax, relational and provenance queries. The approach, building on ideas from the existing literature on constructive algorithmics, exploits generic properties of polymorphic functions, tupling and formal sums and algebraic simplifications arising from constraint algebras. We demonstrate the effectiveness of this formalism for some example applications arising in signal processing, bioinformatics and reliability engineering. Python software implementing these algorithms can be downloaded from: http://www.maxlittle.net/software/dppolyalg.zip.

Sinhala is the native language of the Sinhalese people who make up the largest ethnic group of Sri Lanka. The language belongs to the globe-spanning language tree, Indo-European. However, due to poverty in both linguistic and economic capital, Sinhala, in the perspective of Natural Language Processing tools and research, remains a resource-poor language which has neither the economic drive its cousin English has nor the sheer push of the law of numbers a language such as Chinese has. A number of research groups from Sri Lanka have noticed this dearth and the resultant dire need for proper tools and research for Sinhala natural language processing. However, due to various reasons, these attempts seem to lack coordination and awareness of each other. The objective of this paper is to fill that gap of a comprehensive literature survey of the publicly available Sinhala natural language tools and research so that the researchers working in this field can better utilize contributions of their peers. As such, we shall be uploading this paper to arXiv and perpetually update it periodically to reflect the advances made in the field.

In this paper, we provide the first convergence guarantee for the factorization approach. Specifically, to avoid the scaling ambiguity and to facilitate theoretical analysis, we optimize over the so-called left-orthogonal TT format which enforces orthonormality among most of the factors. To ensure the orthonormal structure, we utilize the Riemannian gradient descent (RGD) for optimizing those factors over the Stiefel manifold. We first delve into the TT factorization problem and establish the local linear convergence of RGD. Notably, the rate of convergence only experiences a linear decline as the tensor order increases. We then study the sensing problem that aims to recover a TT format tensor from linear measurements. Assuming the sensing operator satisfies the restricted isometry property (RIP), we show that with a proper initialization, which could be obtained through spectral initialization, RGD also converges to the ground-truth tensor at a linear rate. Furthermore, we expand our analysis to encompass scenarios involving Gaussian noise in the measurements. We prove that RGD can reliably recover the ground truth at a linear rate, with the recovery error exhibiting only polynomial growth in relation to the tensor order. We conduct various experiments to validate our theoretical findings.

The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any joint distribution with arbitrary dependence across entries. We propose an incoherent-constrained least-square estimator and prove its tightness both in the sense of deterministic lower bound and matching minimax risks under various noise distributions. To attain this, we establish a novel result asserting that the difference between two arbitrary low-rank incoherent matrices must spread energy out across its entries, in other words cannot be too sparse, which sheds light on the structure of incoherent low-rank matrices and may be of independent interest. We then showcase the applications of our framework to several important statistical machine learning problems. In the problem of estimating a structured Markov transition kernel, the proposed method achieves the minimax optimality and the result can be extended to estimating the conditional mean operator, a crucial component in reinforcement learning. The applications to multitask regression and structured covariance estimation are also presented. We propose an alternating minimization algorithm to approximately solve the potentially hard optimization problem. Numerical results corroborate the effectiveness of our method which typically converges in a few steps.

We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) method based on conditional quantile regression. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension, conditioned on the data and previous posterior dimensions. Posterior samples are obtained by interpolating the predicted quantiles using monotonic cubic Hermite spline, with specific treatment for the tail behavior and multi-modal distributions. We introduce an alternative definition for the Bayesian credible region using the local Cumulative Density Function (CDF), offering substantially faster evaluation than the traditional Highest Posterior Density Region (HPDR). In case of limited simulation budget and/or known model misspecification, a post-processing broadening step can be integrated into NQE to ensure the unbiasedness of the posterior estimation with negligible additional computational cost. We demonstrate that the proposed NQE method achieves state-of-the-art performance on a variety of benchmark problems.