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Agricultural landscapes are quite complex, especially in the Global South where fields are smaller, and agricultural practices are more varied. In this paper we report on our progress in digitizing the agricultural landscape (natural and man-made) in our study region of India. We use high resolution imagery and a UNet style segmentation model to generate the first of its kind national-scale multi-class panoptic segmentation output. Through this work we have been able to identify individual fields across 151.7M hectares, and delineating key features such as water resources and vegetation. We share how this output was validated by our team and externally by downstream users, including some sample use cases that can lead to targeted data driven decision making. We believe this dataset will contribute towards digitizing agriculture by generating the foundational baselayer., Comment: 34 pages, 7 tables, 15 figs

Determinantal point processes (DPPs) are random configurations of points with tunable negative dependence. Because sampling is tractable, DPPs are natural candidates for subsampling tasks, such as minibatch selection or coreset construction. A \emph{coreset} is a subset of a (large) training set, such that minimizing an empirical loss averaged over the coreset is a controlled replacement for the intractable minimization of the original empirical loss. Typically, the control takes the form of a guarantee that the average loss over the coreset approximates the total loss uniformly across the parameter space. Recent work has provided significant empirical support in favor of using DPPs to build randomized coresets, coupled with interesting theoretical results that are suggestive but leave some key questions unanswered. In particular, the central question of whether the cardinality of a DPP-based coreset is fundamentally smaller than one based on independent sampling remained open. In this paper, we answer this question in the affirmative, demonstrating that \emph{DPPs can provably outperform independently drawn coresets}. In this vein, we contribute a conceptual understanding of coreset loss as a \emph{linear statistic} of the (random) coreset. We leverage this structural observation to connect the coresets problem to a more general problem of concentration phenomena for linear statistics of DPPs, wherein we obtain \emph{effective concentration inequalities that extend well-beyond the state-of-the-art}, encompassing general non-projection, even non-symmetric kernels. The latter have been recently shown to be of interest in machine learning beyond coresets, but come with a limited theoretical toolbox, to the extension of which our result contributes. Finally, we are also able to address the coresets problem for vector-valued objective functions, a novelty in the coresets literature., Comment: Accepted at NeurIPS 2024 (Spotlight Paper). Authors are listed in alphabetical order

Designing neural network architectures that can handle data symmetry is crucial. This is especially important for geometric graphs whose properties are equivariance under Euclidean transformations. Current equivariant graph neural networks (EGNNs), particularly those using message passing, have a limitation in expressive power. Recent high-order graph neural networks can overcome this limitation, yet they lack equivariance properties, representing a notable drawback in certain applications in chemistry and physical sciences. In this paper, we introduce the Clifford Group Equivariant Graph Neural Networks (CG-EGNNs), a novel EGNN that enhances high-order message passing by integrating high-order local structures in the context of Clifford algebras. As a key benefit of using Clifford algebras, CG-EGNN can learn functions that capture equivariance from positional features. By adopting the high-order message passing mechanism, CG-EGNN gains richer information from neighbors, thus improving model performance. Furthermore, we establish the universality property of the $k$-hop message passing framework, showcasing greater expressive power of CG-EGNNs with additional $k$-hop message passing mechanism. We empirically validate that CG-EGNNs outperform previous methods on various benchmarks including n-body, CMU motion capture, and MD17, highlighting their effectiveness in geometric deep learning.

The differences in H2O2 production between conventional (CONV) and ultra-high dose rate (UHDR) irradiations in water radiolysis are still not fully understood. The lower levels of this radiolytic species, as a critical end product of water radiolysis, are particularly relevant for investigating the connection between the high-density energy deposition during short-duration physical events (ionizations or excitations) and biological responses of the FLASH effect. In this study, we developed a new Geant4-DNA chemistry model to simulate radiolysis considering the time structure of the irradiation pulse at different absorbed doses to liquid water of 0.01, 0.1, 1, and 2 Gy under 1 MeV electron irradiation. The model allows the description of the beam's temporal structure, including the pulse duration, the pulse repetition frequency, and the pulse amplitude for the different beam irradiation conditions through a wide dose rate range, from 0.01 Gy/s up to about 105 Gy/s, at various oxygen concentrations. The preliminary results indicate a correlation between the temporal structure of the pulses and a significant reduction in the production of reactive oxygen species (ROS) at different dose rates., Comment: 27 pages, 14 figures including 3 figures in appendix

Neural functional networks (NFNs) have recently gained significant attention due to their diverse applications, ranging from predicting network generalization and network editing to classifying implicit neural representation. Previous NFN designs often depend on permutation symmetries in neural networks' weights, which traditionally arise from the unordered arrangement of neurons in hidden layers. However, these designs do not take into account the weight scaling symmetries of $\ReLU$ networks, and the weight sign flipping symmetries of $\sin$ or $\Tanh$ networks. In this paper, we extend the study of the group action on the network weights from the group of permutation matrices to the group of monomial matrices by incorporating scaling/sign-flipping symmetries. Particularly, we encode these scaling/sign-flipping symmetries by designing our corresponding equivariant and invariant layers. We name our new family of NFNs the Monomial Matrix Group Equivariant Neural Functional Networks (Monomial-NFN). Because of the expansion of the symmetries, Monomial-NFN has much fewer independent trainable parameters compared to the baseline NFNs in the literature, thus enhancing the model's efficiency. Moreover, for fully connected and convolutional neural networks, we theoretically prove that all groups that leave these networks invariant while acting on their weight spaces are some subgroups of the monomial matrix group. We provide empirical evidence to demonstrate the advantages of our model over existing baselines, achieving competitive performance and efficiency., Comment: 10 pages in the main text. Published at NeurIPS 2024. The code is available at https://github.com/MathematicalAI-NUS/Monomial-NFN

Software is one of the most powerful tools that we humans have at our disposal; it allows a skilled programmer to interact with the world in complex and profound ways. At the same time, thanks to improvements in large language models (LLMs), there has also been a rapid development in AI agents that interact with and affect change in their surrounding environments. In this paper, we introduce OpenHands (f.k.a. OpenDevin), a platform for the development of powerful and flexible AI agents that interact with the world in similar ways to those of a human developer: by writing code, interacting with a command line, and browsing the web. We describe how the platform allows for the implementation of new agents, safe interaction with sandboxed environments for code execution, coordination between multiple agents, and incorporation of evaluation benchmarks. Based on our currently incorporated benchmarks, we perform an evaluation of agents over 15 challenging tasks, including software engineering (e.g., SWE-BENCH) and web browsing (e.g., WEBARENA), among others. Released under the permissive MIT license, OpenHands is a community project spanning academia and industry with more than 2.1K contributions from over 188 contributors., Comment: Code: https://github.com/All-Hands-AI/OpenHands

There is a significant gap between our theoretical understanding of optimization algorithms used in deep learning and their practical performance. Theoretical development usually focuses on proving convergence guarantees under a variety of different assumptions, which are themselves often chosen based on a rough combination of intuitive match to practice and analytical convenience. The theory/practice gap may then arise because of the failure to prove a theorem under such assumptions, or because the assumptions do not reflect reality. In this paper, we carefully measure the degree to which these assumptions are capable of explaining modern optimization algorithms by developing new empirical metrics that closely track the key quantities that must be controlled in theoretical analysis. All of our tested assumptions (including typical modern assumptions based on bounds on the Hessian) fail to reliably capture optimization performance. This highlights a need for new empirical verification of analytical assumptions used in theoretical analysis.

We introduce a new zeroth-order algorithm for private stochastic optimization on nonconvex and nonsmooth objectives. Given a dataset of size $M$, our algorithm ensures $(\alpha,\alpha\rho^2/2)$-R\'enyi differential privacy and finds a $(\delta,\epsilon)$-stationary point so long as $M=\tilde\Omega\left(\frac{d}{\delta\epsilon^3} + \frac{d^{3/2}}{\rho\delta\epsilon^2}\right)$. This matches the optimal complexity of its non-private zeroth-order analog. Notably, although the objective is not smooth, we have privacy ``for free'' whenever $\rho \ge \sqrt{d}\epsilon$.

We introduce a S.O.S hierarchy of lower bounds for a polynomial optimization problem whose constraint is expressed as a matrix polynomial semidefinite condition. Our approach involves utilizing a penalty function framework to directly address the matrix-based constraint, making it applicable to both discrete and continuous polynomial optimization problems. We investigate the convergence rates of these bounds in both problem types. The proposed method yields a variation of Putinar's theorem tailored for positive polynomials within a compact semidefinite set, defined by a matrix polynomial semidefinite constraint. More specifically, we derive novel insights into the convergence rates and degree of additional terms in the representation within this modified version of Putinar's theorem, based on the Jackson's theorem and a version of {\L}ojasiewicz inequality.

This paper presents a distributed solution for the problem of collaborative collision avoidance for autonomous inland waterway ships. A two-layer collision avoidance framework that considers inland waterway traffic regulations is proposed to increase navigational safety for autonomous ships. Our approach allows for modifying traffic rules without changing the collision avoidance algorithm, and is based on a novel formulation of model predictive control (MPC) for collision avoidance of ships. This MPC formulation is designed for inland waterway traffic and can handle complex scenarios. The alternating direction method of multipliers is used as a scheme for exchanging and negotiating intentions among ships. Simulation results show that the proposed algorithm can comply with traffic rules. Furthermore, the proposed algorithm can safely deviate from traffic rules when necessary to increase efficiency in complex scenarios.

This paper proposes a transition system abstraction framework for neural network dynamical system models to enhance the model interpretability, with applications to complex dynamical systems such as human behavior learning and verification. To begin with, the localized working zone will be segmented into multiple localized partitions under the data-driven Maximum Entropy (ME) partitioning method. Then, the transition matrix will be obtained based on the set-valued reachability analysis of neural networks. Finally, applications to human handwriting dynamics learning and verification are given to validate our proposed abstraction framework, which demonstrates the advantages of enhancing the interpretability of the black-box model, i.e., our proposed framework is able to abstract a data-driven neural network model into a transition system, making the neural network model interpretable through verifying specifications described in Computational Tree Logic (CTL) languages., Comment: ACC 2024

We propose and analyze an efficient algorithm for solving the joint sparse recovery problem using a new regularization-based method, named orthogonally weighted $\ell_{2,1}$ ($\mathit{ow}\ell_{2,1}$), which is specifically designed to take into account the rank of the solution matrix. This method has applications in feature extraction, matrix column selection, and dictionary learning, and it is distinct from commonly used $\ell_{2,1}$ regularization and other existing regularization-based approaches because it can exploit the full rank of the row-sparse solution matrix, a key feature in many applications. We provide a proof of the method's rank-awareness, establish the existence of solutions to the proposed optimization problem, and develop an efficient algorithm for solving it, whose convergence is analyzed. We also present numerical experiments to illustrate the theory and demonstrate the effectiveness of our method on real-life problems.

We investigate the problem of estimating the structure of a weighted network from repeated measurements of a Gaussian Graphical Model (GGM) on the network. In this vein, we consider GGMs whose covariance structures align with the geometry of the weighted network on which they are based. Such GGMs have been of longstanding interest in statistical physics, and are referred to as the Gaussian Free Field (GFF). In recent years, they have attracted considerable interest in the machine learning and theoretical computer science. In this work, we propose a novel estimator for the weighted network (equivalently, its Laplacian) from repeated measurements of a GFF on the network, based on the Fourier analytic properties of the Gaussian distribution. In this pursuit, our approach exploits complex-valued statistics constructed from observed data, that are of interest on their own right. We demonstrate the effectiveness of our estimator with concrete recovery guarantees and bounds on the required sample complexity. In particular, we show that the proposed statistic achieves the parametric rate of estimation for fixed network size. In the setting of networks growing with sample size, our results show that for Erdos-Renyi random graphs $G(d,p)$ above the connectivity threshold, we demonstrate that network recovery takes place with high probability as soon as the sample size $n$ satisfies $n \gg d^4 \log d \cdot p^{-2}$.

Existing medical text datasets usually take the form of question and answer pairs that support the task of natural language generation, but lacking the composite annotations of the medical terms. In this study, we publish a Vietnamese dataset of medical questions from patients with sentence-level and entity-level annotations for the Intent Classification and Named Entity Recognition tasks. The tag sets for two tasks are in medical domain and can facilitate the development of task-oriented healthcare chatbots with better comprehension of queries from patients. We train baseline models for the two tasks and propose a simple self-supervised training strategy with span-noise modelling that substantially improves the performance. Dataset and code will be published at https://github.com/tadeephuy/ViMQ, Comment: accepted at ICONIP 2021

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [42], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by a oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. We also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justify the advantage of using moderate or large smoothing radius with the method. Furthermore, if the noise level decays to zero when approaching global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based method in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

This work takes a look at data models often used in digital twins and presents preliminary results specifically from surface reconstruction and semantic segmentation models trained using simulated data. This work is expected to serve as a ground work for future endeavours in data contextualisation inside a digital twin., Comment: Extended abstract, Northern Lights Deep Learning Conference, 2023

We develop a new reduction that converts any online convex optimization algorithm suffering $O(\sqrt{T})$ regret into an $\epsilon$-differentially private stochastic convex optimization algorithm with the optimal convergence rate $\tilde O(1/\sqrt{T} + \sqrt{d}/\epsilon T)$ on smooth losses in linear time, forming a direct analogy to the classical non-private "online-to-batch" conversion. By applying our techniques to more advanced adaptive online algorithms, we produce adaptive differentially private counterparts whose convergence rates depend on apriori unknown variances or parameter norms.

We introduce new algorithms and convergence guarantees for privacy-preserving non-convex Empirical Risk Minimization (ERM) on smooth $d$-dimensional objectives. We develop an improved sensitivity analysis of stochastic gradient descent on smooth objectives that exploits the recurrence of examples in different epochs. By combining this new approach with recent analysis of momentum with private aggregation techniques, we provide an $(\epsilon,\delta)$-differential private algorithm that finds a gradient of norm $\tilde O\left(\frac{d^{1/3}}{(\epsilon N)^{2/3}}\right)$ in $O\left(\frac{N^{7/3}\epsilon^{4/3}}{d^{2/3}}\right)$ gradient evaluations, improving the previous best gradient bound of $\tilde O\left(\frac{d^{1/4}}{\sqrt{\epsilon N}}\right)$.

The identification of governing equations for dynamical systems is everlasting challenges for the fundamental research in science and engineering. Machine learning has exhibited great success to learn and predict dynamical systems from data. However, the fundamental challenges still exist: discovering the exact governing equations from highly noisy data. In present work, we propose a compressive sensing-assisted mixed integer optimization (CS-MIO) method to make a step forward from a modern discrete optimization lens. In particular, we first formulate the problem into a mixed integer optimization model. The discrete optimization nature of the model leads to exact variable selection by means of cardinality constraint, and hereby powerful capability of exact discovery of governing equations from noisy data. Such capability is further enhanced by incorporating compressive sensing and regularization techniques for highly noisy data and high-dimensional problems. The case studies on classical dynamical systems have shown that CS-MIO can discover the exact governing equations from large-noise data, with up to two orders of magnitude larger noise comparing with state-of-the-art method. We also show its effectiveness for high-dimensional dynamical system identification through the chaotic Lorenz 96 system.