We revisit the question of characterizing the convergence rate of plug-in estimators of optimal transport costs. It is well known that an empirical measure comprising independent samples from an absolutely continuous distribution on $\mathbb{R}^d$ converges to that distribution at the rate $n^{-1/d}$ in Wasserstein distance, which can be used to prove that plug-in estimators of many optimal transport costs converge at this same rate. However, we show that when the cost is smooth, this analysis is loose: plug-in estimators based on empirical measures converge quadratically faster, at the rate $n^{-2/d}$. As a corollary, we show that the Wasserstein distance between two distributions is significantly easier to estimate when the measures are well-separated. We also prove lower bounds, showing not only that our analysis of the plug-in estimator is tight, but also that no other estimator can enjoy significantly faster rates of convergence uniformly over all pairs of measures. Our proofs rely on empirical process theory arguments based on tight control of $L^2$ covering numbers for locally Lipschitz and semi-concave functions. As a byproduct of our proofs, we derive $L^\infty$ estimates on the displacement induced by the optimal coupling between any two measures satisfying suitable concentration and anticoncentration conditions, for a wide range of cost functions.
Recent work by Bravyi, Gosset, and Koenig showed that there exists a search problem that a constant-depth quantum circuit can solve, but that any constant-depth classical circuit with bounded fan-in cannot. They also pose the question: Can we achieve a similar proof of separation for an input-independent sampling task? In this paper, we show that the answer to this question is yes when the number of random input bits given to the classical circuit is bounded. We introduce a distribution $D_{n}$ over $\{0,1\}^n$ and construct a constant-depth uniform quantum circuit family $\{C_n\}_n$ such that $C_n$ samples from a distribution close to $D_{n}$ in total variation distance. For any $\delta < 1$ we also prove, unconditionally, that any classical circuit with bounded fan-in gates that takes as input $kn + n^\delta$ i.i.d. Bernouli random variables with entropy $1/k$ and produces output close to $D_{n}$ in total variation distance has depth $\Omega(\log \log n)$. This gives an unconditional proof that constant-depth quantum circuits can sample from distributions that can't be reproduced by constant-depth bounded fan-in classical circuits, even up to additive error. We also show a similar separation between constant-depth quantum circuits with advice and classical circuits with bounded fan-in and fan-out, but access to an unbounded number of i.i.d random inputs. The distribution $D_n$ and classical circuit lower bounds are inspired by work of Viola, in which he shows a different (but related) distribution cannot be sampled from approximately by constant-depth bounded fan-in classical circuits.
Foundation models, such as Large language Models (LLMs), have attracted significant amount of interest due to their large number of applications. Existing works show that appropriate prompt design, such as Chain-of-Thoughts, can unlock LLM's powerful capacity in diverse areas. However, when handling tasks involving repetitive sub-tasks and/or deceptive contents, such as arithmetic calculation and article-level fake news detection, existing prompting strategies either suffers from insufficient expressive power or intermediate errors triggered by hallucination. To make LLM more discerning to such intermediate errors, we propose to guide LLM with a Divide-and-Conquer program that simultaneously ensures superior expressive power and disentangles task decomposition, sub-task resolution, and resolution assembly process. Theoretic analysis reveals that our strategy can guide LLM to extend the expressive power of fixed-depth Transformer. Experiments indicate that our proposed method can achieve better performance than typical prompting strategies in tasks bothered by intermediate errors and deceptive contents, such as large integer multiplication, hallucination detection and misinformation detection.
Dairy farming consumes a significant amount of energy, making it an energy-intensive sector within agriculture. Integrating renewable energy generation into dairy farming could help address this challenge. Effective battery management is important for integrating renewable energy generation. Managing battery charging and discharging poses significant challenges because of fluctuations in electrical consumption, the intermittent nature of renewable energy generation, and fluctuations in energy prices. Artificial Intelligence (AI) has the potential to significantly improve the use of renewable energy in dairy farming, however, there is limited research conducted in this particular domain. This research considers Ireland as a case study as it works towards attaining its 2030 energy strategy centered on the utilization of renewable sources. This study proposes a Q-learning-based algorithm for scheduling battery charging and discharging in a dairy farm setting. This research also explores the effect of the proposed algorithm by adding wind generation data and considering additional case studies. The proposed algorithm reduces the cost of imported electricity from the grid by 13.41\%, peak demand by 2\%, and 24.49\% when utilizing wind generation. These results underline how reinforcement learning is highly effective in managing batteries in the dairy farming sector.
Diffusion Probabilistic Models (DPM) have shown remarkable efficacy in the synthesis of high-quality images. However, their inference process characteristically requires numerous, potentially hundreds, of iterative steps, which could exaggerate the problem of exposure bias due to the training and inference discrepancy. Previous work has attempted to mitigate this issue by perturbing inputs during training, which consequently mandates the retraining of the DPM. In this work, we conduct a systematic study of exposure bias in DPM and, intriguingly, we find that the exposure bias could be alleviated with a novel sampling method that we propose, without retraining the model. We empirically and theoretically show that, during inference, for each backward time step $t$ and corresponding state $\hat{x}_t$, there might exist another time step $t_s$ which exhibits superior coupling with $\hat{x}_t$. Based on this finding, we introduce a sampling method named Time-Shift Sampler. Our framework can be seamlessly integrated to existing sampling algorithms, such as DDPM, DDIM and other high-order solvers, inducing merely minimal additional computations. Experimental results show our method brings significant and consistent improvements in FID scores on different datasets and sampling methods. For example, integrating Time-Shift Sampler to F-PNDM yields a FID=3.88, achieving 44.49\% improvements as compared to F-PNDM, on CIFAR-10 with 10 sampling steps, which is more performant than the vanilla DDIM with 100 sampling steps. Our code is available at //github.com/Mingxiao-Li/TS-DPM.
Object counting typically uses 2D point annotations. The complexity of object shapes and the subjectivity of annotators may lead to annotation inconsistency, potentially confusing counting model training. Some sophisticated noise-resistance counting methods have been proposed to alleviate this issue. Differently, we aim to directly refine the initial point annotations before training counting models. For that, we propose the Shifted Autoencoders (SAE), which enhances annotation consistency. Specifically, SAE applies random shifts to initial point annotations and employs a UNet to restore them to their original positions. Similar to MAE reconstruction, the trained SAE captures general position knowledge and ignores specific manual offset noise. This allows to restore the initial point annotations to more general and thus consistent positions. Extensive experiments show that using such refined consistent annotations to train some advanced (including noise-resistance) object counting models steadily/significantly boosts their performances. Remarkably, the proposed SAE helps to set new records on nine datasets. We will make codes and refined point annotations available.
Migrations of systems from on-site premises to the cloud has been a fundamental endeavor by many industrial institutions. A crucial component of such cloud migrations is the transition of databases to be hosted online. In this work, we consider the difficulties of this migration for SQL databases. While SQL is one of the prominent methods for storing database procedures, there are a plethora of different SQL dialects (e.g., MySQL, Postgres, etc.) which can complicate migrations when the on-premise SQL dialect differs to the dialect hosted on the cloud. Tools exist by common cloud provides such as AWS and Azure to aid in translating between dialects in order to mitigate the majority of the difficulties. However, these tools do not successfully translate $100\%$ of the code. Consequently, software engineers must manually convert the remainder of the untranslated database. For large organizations, this task quickly becomes intractable and so more innovative solutions are required. We consider this challenge a novel yet vital industrial research problem for any large corporation that is considering cloud migrations. Furthermore, we introduce potential avenues of research to tackle this challenge that have yielded promising preliminary results.
With the rapid increase of observational, experimental and simulated data for stochastic systems, tremendous efforts have been devoted to identifying governing laws underlying the evolution of these systems. Despite the broad applications of non-Gaussian fluctuations in numerous physical phenomena, the data-driven approaches to extracting stochastic dynamics with L\'{e}vy noise are relatively few. In this work, we propose a Weak Collocation Regression (WCR) to explicitly reveal unknown stochastic dynamical systems, i.e., the Stochastic Differential Equation (SDE) with both $\alpha$-stable L\'{e}vy noise and Gaussian noise, from discrete aggregate data. This method utilizes the evolution equation of the probability distribution function, i.e., the Fokker-Planck (FP) equation. With the weak form of the FP equation, the WCR constructs a linear system of unknown parameters where all integrals are evaluated by Monte Carlo method with the observations. Then, the unknown parameters are obtained by a sparse linear regression. For a SDE with L\'{e}vy noise, the corresponding FP equation is a partial integro-differential equation (PIDE), which contains nonlocal terms, and is difficult to deal with. The weak form can avoid complicated multiple integrals. Our approach can simultaneously distinguish mixed noise types, even in multi-dimensional problems. Numerical experiments demonstrate that our method is accurate and computationally efficient.
To enable large-scale and efficient deployment of artificial intelligence (AI), the combination of AI and edge computing has spawned Edge Intelligence, which leverages the computing and communication capabilities of end devices and edge servers to process data closer to where it is generated. A key technology for edge intelligence is the privacy-protecting machine learning paradigm known as Federated Learning (FL), which enables data owners to train models without having to transfer raw data to third-party servers. However, FL networks are expected to involve thousands of heterogeneous distributed devices. As a result, communication efficiency remains a key bottleneck. To reduce node failures and device exits, a Hierarchical Federated Learning (HFL) framework is proposed, where a designated cluster leader supports the data owner through intermediate model aggregation. Therefore, based on the improvement of edge server resource utilization, this paper can effectively make up for the limitation of cache capacity. In order to mitigate the impact of soft clicks on the quality of user experience (QoE), the authors model the user QoE as a comprehensive system cost. To solve the formulaic problem, the authors propose a decentralized caching algorithm with federated deep reinforcement learning (DRL) and federated learning (FL), where multiple agents learn and make decisions independently
For the purpose of efficient and cost-effective large-scale data labeling, crowdsourcing is increasingly being utilized. To guarantee the quality of data labeling, multiple annotations need to be collected for each data sample, and truth inference algorithms have been developed to accurately infer the true labels. Despite previous studies having released public datasets to evaluate the efficacy of truth inference algorithms, these have typically focused on a single type of crowdsourcing task and neglected the temporal information associated with workers' annotation activities. These limitations significantly restrict the practical applicability of these algorithms, particularly in the context of long-term and online truth inference. In this paper, we introduce a substantial crowdsourcing annotation dataset collected from a real-world crowdsourcing platform. This dataset comprises approximately two thousand workers, one million tasks, and six million annotations. The data was gathered over a period of approximately six months from various types of tasks, and the timestamps of each annotation were preserved. We analyze the characteristics of the dataset from multiple perspectives and evaluate the effectiveness of several representative truth inference algorithms on this dataset. We anticipate that this dataset will stimulate future research on tracking workers' abilities over time in relation to different types of tasks, as well as enhancing online truth inference.
Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.