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The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far less attention given to the effect of memory limitations on performance. Recently, this latter topic has drawn much interest in the engineering and computer science literature. In this survey paper, we attempt to review the state-of-the-art of statistical inference under memory constraints in several canonical problems, including hypothesis testing, parameter estimation, and distribution property testing/estimation. We discuss the main results in this developing field, and by identifying recurrent themes, we extract some fundamental building blocks for algorithmic construction, as well as useful techniques for lower bound derivations.

Kernel ridge regression, KRR, is a generalization of linear ridge regression that is non-linear in the data, but linear in the parameters. The solution can be obtained either as a closed-form solution, which includes solving a system of linear equations, or iteratively through gradient descent. Using the iterative approach opens up for changing the kernel during training, something that is investigated in this paper. We theoretically address the effects this has on model complexity and generalization. Based on our findings, we propose an update scheme for the bandwidth of translational-invariant kernels, where we let the bandwidth decrease to zero during training, thus circumventing the need for hyper-parameter selection. We demonstrate on real and synthetic data how decreasing the bandwidth during training outperforms using a constant bandwidth, selected by cross-validation and marginal likelihood maximization. We also show theoretically and empirically that using a decreasing bandwidth, we are able to achieve both zero training error in combination with good generalization, and a double descent behavior, phenomena that do not occur for KRR with constant bandwidth but are known to appear for neural networks.

We present Tachis, a higher-order separation logic to reason about the expected cost of probabilistic programs. Inspired by the uses of time credits for reasoning about the running time of deterministic programs, we introduce a novel notion of probabilistic cost credit. Probabilistic cost credits are a separation logic resource that can be used to pay for the cost of operations in programs, and that can be distributed across all possible branches of sampling instructions according to their weight, thus enabling us to reason about expected cost. The representation of cost credits as separation logic resources gives Tachis a great deal of flexibility and expressivity. In particular, it permits reasoning about amortized expected cost by storing excess credits as potential into data structures to pay for future operations. Tachis further supports a range of cost models, including running time and entropy usage. We showcase the versatility of this approach by applying our techniques to prove upper bounds on the expected cost of a variety of probabilistic algorithms and data structures, including randomized quicksort, hash tables, and meldable heaps. All of our results have been mechanized using Coq, Iris, and the Coquelicot real analysis library.

Reinforcement Learning (RL) is a continuously growing field that has the potential to revolutionize many areas of artificial intelligence. However, despite its promise, RL research is often hindered by the lack of standardization in environment and algorithm implementations. This makes it difficult for researchers to compare and build upon each other's work, slowing down progress in the field. Gymnasium is an open-source library that provides a standard API for RL environments, aiming to tackle this issue. Gymnasium's main feature is a set of abstractions that allow for wide interoperability between environments and training algorithms, making it easier for researchers to develop and test RL algorithms. In addition, Gymnasium provides a collection of easy-to-use environments, tools for easily customizing environments, and tools to ensure the reproducibility and robustness of RL research. Through this unified framework, Gymnasium significantly streamlines the process of developing and testing RL algorithms, enabling researchers to focus more on innovation and less on implementation details. By providing a standardized platform for RL research, Gymnasium helps to drive forward the field of reinforcement learning and unlock its full potential. Gymnasium is available online at //github.com/Farama-Foundation/Gymnasium

3D geometric shape completion hinges on representation learning and a deep understanding of geometric data. Without profound insights into the three-dimensional nature of the data, this task remains unattainable. Our work addresses this challenge of 3D shape completion given partial observations by proposing a transformer operating on the latent space representing Signed Distance Fields (SDFs). Instead of a monolithic volume, the SDF of an object is partitioned into smaller high-resolution patches leading to a sequence of latent codes. The approach relies on a smooth latent space encoding learned via a variational autoencoder (VAE), trained on millions of 3D patches. We employ an efficient masked autoencoder transformer to complete partial sequences into comprehensive shapes in latent space. Our approach is extensively evaluated on partial observations from ShapeNet and the ABC dataset where only fractions of the objects are given. The proposed POC-SLT architecture compares favorably with several baseline state-of-the-art methods, demonstrating a significant improvement in 3D shape completion, both qualitatively and quantitatively.

Quantum error-correcting codes (QECCs) are necessary for fault-tolerant quantum computation. Surface codes are a class of topological QECCs that have attracted significant attention due to their exceptional error-correcting capabilities and easy implementation. In the decoding process of surface codes, the syndromes are crucial for error correction, however, they are not always correctly measured. Most of the existing decoding algorithms for surface codes need extra measurements to correct syndromes with errors, which implies a potential increase in inference complexity and decoding latency. In this paper, we propose a high-performance list decoding algorithm for surface codes with erroneous syndromes, where syndrome soft information is incorporated in the decoding, allowing qubits and syndrome to be recovered without needing extra measurements. Precisely, we first use belief propagation (BP) decoding for pre-processing with syndrome soft information, followed by ordered statistics decoding (OSD) for post-processing to list and recover both qubits and syndromes. Numerical results demonstrate that our proposed algorithm efficiently recovers erroneous syndromes and significantly improves the decoding performance of surface codes with erroneous syndromes compared to minimum-weight perfect matching (MWPM), BP and original BP-OSD algorithms.

Recent advances in foundation models, particularly Large Language Models (LLMs) and Multimodal Large Language Models (MLLMs), facilitate intelligent agents being capable of performing complex tasks. By leveraging the ability of (M)LLMs to process and interpret Graphical User Interfaces (GUIs), these agents can autonomously execute user instructions by simulating human-like interactions such as clicking and typing. This survey consolidates recent research on (M)LLM-based GUI agents, highlighting key innovations in data, frameworks, and applications. We begin by discussing representative datasets and benchmarks. Next, we summarize a unified framework that captures the essential components used in prior research, accompanied by a taxonomy. Additionally, we explore commercial applications of (M)LLM-based GUI agents. Drawing from existing work, we identify several key challenges and propose future research directions. We hope this paper will inspire further developments in the field of (M)LLM-based GUI agents.

Mixture-of-Experts (MoE) has emerged as a practical approach to scale up parameters for the Transformer model to achieve better generalization while maintaining a sub-linear increase in computation overhead. Current MoE models are mainly built with expert parallelism on distributed devices. However, it usually depends on homogeneous devices to deploy and suffers from heavy communication overhead and computation redundancy. In this paper, we explore developing a \texttt{H}eterogeneous-aware \texttt{EX}pert \texttt{A}llocation framework, \textbf{\texttt{HEXA-MoE}}, with significantly enhanced computing efficiency. It contains two components: ($1$) \textit{Expert-Specific Operators}. We replace the typical general matrix multiplication or grouped matrix multiplication interfaces with our operators, which allows the computing to be performed in an in-place manner with \textbf{ZERO} redundancy. ($2$) \textit{Adaptive Data- and Model-Centric Configurations} for different workload scales. Specifically, we introduce a pipeline-shared cache on each device to tackle the heavy memory consumption in the existing data-centric MoE library. Comprehensive experiments on the Swin-MoE benchmark consistently reveal the effectiveness of our \texttt{HEXA-MoE} framework, i.e., reducing $10\%\sim48\%$ memory consumption and achieving $0.5\sim4.3\times$ speed up compared to current state-of-the-art MoE libraries. Furthermore, we examine our \texttt{HEXA-MoE} with heterogeneous devices for both data- and model-centric settings. Promising results show that employing optimal parallel configuration with \texttt{HEXA-MoE} on heterogeneous devices can substantially minimize overall latency. Codes are available at //github.com/UNITES-Lab/HEXA-MoE.

Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids (in Lagrangian descriptions). Existing approaches, however, require the supervision of consecutive particle properties, including positions and velocities. In this paper, we consider a partially observable scenario known as fluid dynamics grounding, that is, inferring the state transitions and interactions within the fluid particle systems from sequential visual observations of the fluid surface. We propose a differentiable two-stage network named NeuroFluid. Our approach consists of (i) a particle-driven neural renderer, which involves fluid physical properties into the volume rendering function, and (ii) a particle transition model optimized to reduce the differences between the rendered and the observed images. NeuroFluid provides the first solution to unsupervised learning of particle-based fluid dynamics by training these two models jointly. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities. It is a potential alternative approach to understanding complex fluid mechanics, such as turbulence, that are difficult to model using traditional methods of mathematical physics.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.