Report Noisy Max and Above Threshold are two classical differentially private (DP) selection mechanisms. Their output is obtained by adding noise to a sequence of low-sensitivity queries and reporting the identity of the query whose (noisy) answer satisfies a certain condition. Pure DP guarantees for these mechanisms are easy to obtain when Laplace noise is added to the queries. On the other hand, when instantiated using Gaussian noise, standard analyses only yield approximate DP guarantees despite the fact that the outputs of these mechanisms lie in a discrete space. In this work, we revisit the analysis of Report Noisy Max and Above Threshold with Gaussian noise and show that, under the additional assumption that the underlying queries are bounded, it is possible to provide pure ex-ante DP bounds for Report Noisy Max and pure ex-post DP bounds for Above Threshold. The resulting bounds are tight and depend on closed-form expressions that can be numerically evaluated using standard methods. Empirically we find these lead to tighter privacy accounting in the high privacy, low data regime. Further, we propose a simple privacy filter for composing pure ex-post DP guarantees, and use it to derive a fully adaptive Gaussian Sparse Vector Technique mechanism. Finally, we provide experiments on mobility and energy consumption datasets demonstrating that our Sparse Vector Technique is practically competitive with previous approaches and requires less hyper-parameter tuning.

Recent developments in large language models have sparked interest in efficient pretraining methods. A recent effective paradigm is to perform stage-wise training, where the size of the model is gradually increased over the course of training (e.g. gradual stacking (Reddi et al., 2023)). While the resource and wall-time savings are appealing, it has limitations, particularly the inability to evaluate the full model during earlier stages, and degradation in model quality due to smaller model capacity in the initial stages. In this work, we propose an alternative framework, progressive subnetwork training, that maintains the full model throughout training, but only trains subnetworks within the model in each step. We focus on a simple instantiation of this framework, Random Path Training (RaPTr) that only trains a sub-path of layers in each step, progressively increasing the path lengths in stages. RaPTr achieves better pre-training loss for BERT and UL2 language models while requiring 20-33% fewer FLOPs compared to standard training, and is competitive or better than other efficient training methods. Furthermore, RaPTr shows better downstream performance on UL2, improving QA tasks and SuperGLUE by 1-5% compared to standard training and stacking. Finally, we provide a theoretical basis for RaPTr to justify (a) the increasing complexity of subnetworks in stages, and (b) the stability in loss across stage transitions due to residual connections and layer norm.

Time series analysis is vital for numerous applications, and transformers have become increasingly prominent in this domain. Leading methods customize the transformer architecture from NLP and CV, utilizing a patching technique to convert continuous signals into segments. Yet, time series data are uniquely challenging due to significant distribution shifts and intrinsic noise levels. To address these two challenges,we introduce the Sparse Vector Quantized FFN-Free Transformer (Sparse-VQ). Our methodology capitalizes on a sparse vector quantization technique coupled with Reverse Instance Normalization (RevIN) to reduce noise impact and capture sufficient statistics for forecasting, serving as an alternative to the Feed-Forward layer (FFN) in the transformer architecture. Our FFN-free approach trims the parameter count, enhancing computational efficiency and reducing overfitting. Through evaluations across ten benchmark datasets, including the newly introduced CAISO dataset, Sparse-VQ surpasses leading models with a 7.84% and 4.17% decrease in MAE for univariate and multivariate time series forecasting, respectively. Moreover, it can be seamlessly integrated with existing transformer-based models to elevate their performance.

Accurate solar power forecasting is crucial to integrate photovoltaic plants into the electric grid, schedule and secure the power grid safety. This problem becomes more demanding for those newly installed solar plants which lack sufficient data. Current research predominantly relies on historical solar power data or numerical weather prediction in a single-modality format, ignoring the complementary information provided in different modalities. In this paper, we propose a multi-modality fusion framework to integrate historical power data, numerical weather prediction, and satellite images, significantly improving forecast performance. We introduce a vector quantized framework that aligns modalities with varying information densities, striking a balance between integrating sufficient information and averting model overfitting. Our framework demonstrates strong zero-shot forecasting capability, which is especially useful for those newly installed plants. Moreover, we collect and release a multi-modal solar power (MMSP) dataset from real-world plants to further promote the research of multi-modal solar forecasting algorithms. Our extensive experiments show that our model not only operates with robustness but also boosts accuracy in both zero-shot forecasting and scenarios rich with training data, surpassing leading models. We have incorporated it into our eForecaster platform and deployed it for more than 300 solar plants with a capacity of over 15GW.

Mean-field reinforcement learning has become a popular theoretical framework for efficiently approximating large-scale multi-agent reinforcement learning (MARL) problems exhibiting symmetry. However, questions remain regarding the applicability of mean-field approximations: in particular, their approximation accuracy of real-world systems and conditions under which they become computationally tractable. We establish explicit finite-agent bounds for how well the MFG solution approximates the true $N$-player game for two popular mean-field solution concepts. Furthermore, for the first time, we establish explicit lower bounds indicating that MFGs are poor or uninformative at approximating $N$-player games assuming only Lipschitz dynamics and rewards. Finally, we analyze the computational complexity of solving MFGs with only Lipschitz properties and prove that they are in the class of \textsc{PPAD}-complete problems conjectured to be intractable, similar to general sum $N$ player games. Our theoretical results underscore the limitations of MFGs and complement and justify existing work by proving difficulty in the absence of common theoretical assumptions.

We study the sample complexity of reinforcement learning (RL) in Mean-Field Games (MFGs) with model-based function approximation that requires strategic exploration to find a Nash Equilibrium policy. We introduce the Partial Model-Based Eluder Dimension (P-MBED), a more effective notion to characterize the model class complexity. Notably, P-MBED measures the complexity of the single-agent model class converted from the given mean-field model class, and potentially, can be exponentially lower than the MBED proposed by \citet{huang2023statistical}. We contribute a model elimination algorithm featuring a novel exploration strategy and establish sample complexity results polynomial w.r.t.~P-MBED. Crucially, our results reveal that, under the basic realizability and Lipschitz continuity assumptions, \emph{learning Nash Equilibrium in MFGs is no more statistically challenging than solving a logarithmic number of single-agent RL problems}. We further extend our results to Multi-Type MFGs, generalizing from conventional MFGs and involving multiple types of agents. This extension implies statistical tractability of a broader class of Markov Games through the efficacy of mean-field approximation. Finally, inspired by our theoretical algorithm, we present a heuristic approach with improved computational efficiency and empirically demonstrate its effectiveness.

Information theoretic quantities play a central role in machine learning. The recent surge in the complexity of data and models has increased the demand for accurate estimation of these quantities. However, as the dimension grows the estimation presents significant challenges, with existing methods struggling already in relatively low dimensions. To address this issue, in this work, we introduce $\texttt{REMEDI}$ for efficient and accurate estimation of differential entropy, a fundamental information theoretic quantity. The approach combines the minimization of the cross-entropy for simple, adaptive base models and the estimation of their deviation, in terms of the relative entropy, from the data density. Our approach demonstrates improvement across a broad spectrum of estimation tasks, encompassing entropy estimation on both synthetic and natural data. Further, we extend important theoretical consistency results to a more generalized setting required by our approach. We illustrate how the framework can be naturally extended to information theoretic supervised learning models, with a specific focus on the Information Bottleneck approach. It is demonstrated that the method delivers better accuracy compared to the existing methods in Information Bottleneck. In addition, we explore a natural connection between $\texttt{REMEDI}$ and generative modeling using rejection sampling and Langevin dynamics.

Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving MILPs, and many commercial and academic software packages exist. Nevertheless, the availability of data, both from problem instances and from solvers, and the desire to solve new problems and larger (real-life) instances, trigger the need for continuing algorithmic development. MILP solvers use branch and bound as their main component. In recent years, there has been an explosive development in the use of machine learning algorithms for enhancing all main tasks involved in the branch-and-bound algorithm, such as primal heuristics, branching, cutting planes, node selection and solver configuration decisions. This paper presents a survey of such approaches, addressing the vision of integration of machine learning and mathematical optimization as complementary technologies, and how this integration can benefit MILP solving. In particular, we give detailed attention to machine learning algorithms that automatically optimize some metric of branch-and-bound efficiency. We also address how to represent MILPs in the context of applying learning algorithms, MILP benchmarks and software.

Urban area-of-interest (AOI) refers to an integrated urban functional zone with defined polygonal boundaries. The rapid development of urban commerce has led to increasing demands for highly accurate and timely AOI data. However, existing research primarily focuses on coarse-grained functional zones for urban planning or regional economic analysis, and often neglects the expiration of AOI in the real world. They fail to fulfill the precision demands of Mobile Internet Online-to-Offline (O2O) businesses. These businesses require accuracy down to a specific community, school, or hospital. In this paper, we propose a comprehensive end-to-end multimodal deep learning framework designed for simultaneously detecting accurate AOI boundaries and validating the reliability of AOI by leveraging remote sensing imagery coupled with geographical prior, titled AOITR. Unlike conventional AOI generation methods, such as the Road-cut method that segments road networks at various levels, our approach diverges from semantic segmentation algorithms that depend on pixel-level classification. Instead, our AOITR begins by selecting a point-of-interest (POI) of specific category, and uses it to retrieve corresponding remote sensing imagery and geographical prior such as entrance POIs and road nodes. This information helps to build a multimodal detection model based on transformer encoder-decoder architecture to regress the AOI polygon. Additionally, we utilize the dynamic features from human mobility, nearby POIs, and logistics addresses for AOI reliability evaluation via a cascaded network module. The experimental results reveal that our algorithm achieves a significant improvement on Intersection over Union (IoU) metric, surpassing previous methods by a large margin.

This paper will examine what makes a being intelligent, whether that be a biological being or an artificial silicon being on a computer. Special attention will be paid to the being having the ability to characterize and control a collective system of many identical conservative sub-systems conservatively interacting. The essence of intelligence will be found to be the golden rule -- "the collective acts as one" or "knowing the global consequences of local actions". The flow of the collective is a small set of twinkling textures, that are governed by a puppeteer who is pulling a small number of strings according to a geodesic motion of least action, determined by the symmetries. Controlling collective conservative systems is difficult and has historically been done by adding significant viscosity to the system to stabilize the desirable meta stable equilibriums of maximum performance, but it degrades or destroys them in the process. There is an alternative. Once the optimum twinkling textures of the meta stable equilibriums are identified, the collective system can be moved to the optimum twinkling textures, then quickly vibrated according to the textures so that the collective system remains at the meta stable equilibrium. Well educated intelligence knows the global consequences of its local actions so that it will not take short term actions that will lead to poor long term outcomes. In contrast, trained intelligence or trained stupidity will optimize its short term actions, leading to poor long term outcomes. Well educated intelligence is inherently good, but trained stupidity is inherently evil and should be feared. Particular attention is paid to the control and optimization of economic and social collectives. These new results are also applicable to physical collectives such as fields, fluids and plasmas.