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This paper presents a theoretical analysis of the convergence rate of the Sinkhorn algorithm when the cost matrix is sparse. We derive bounds on the convergence rate that depend on the sparsity pattern and the degree of sparsity of the cost matrix. We also explore whether existing convergence results for dense cost matrices can be adapted or improved for the sparse case. Our analysis provides new insights into the behavior of the Sinkhorn algorithm in the presence of sparsity and highlights potential avenues for algorithmic improvements.

Large language models (LLMs) exhibit complementary strengths in various tasks, motivating the research of LLM ensembling. However, existing work focuses on training an extra reward model or fusion model to select or combine all candidate answers, posing a great challenge to the generalization on unseen data distributions. Besides, prior methods use textual responses as communication media, ignoring the valuable information in the internal representations. In this work, we propose a training-free ensemble framework DeePEn, fusing the informative probability distributions yielded by different LLMs at each decoding step. Unfortunately, the vocabulary discrepancy between heterogeneous LLMs directly makes averaging the distributions unfeasible due to the token misalignment. To address this challenge, DeePEn maps the probability distribution of each model from its own probability space to a universal relative space based on the relative representation theory, and performs aggregation. Next, we devise a search-based inverse transformation to transform the aggregated result back to the probability space of one of the ensembling LLMs (main model), in order to determine the next token. We conduct extensive experiments on ensembles of different number of LLMs, ensembles of LLMs with different architectures, and ensembles between the LLM and the specialist model. Experimental results show that (i) DeePEn achieves consistent improvements across six benchmarks covering subject examination, reasoning, and knowledge, (ii) a well-performing specialist model can benefit from a less effective LLM through distribution fusion, and (iii) DeePEn has complementary strengths with other ensemble methods such as voting.

This work investigates the computational expressivity of language models (LMs) based on recurrent neural networks (RNNs). Siegelmann and Sontag (1992) famously showed that RNNs with rational weights and hidden states and unbounded computation time are Turing complete. However, LMs define weightings over strings in addition to just (unweighted) language membership and the analysis of the computational power of RNN LMs (RLMs) should reflect this. We extend the Turing completeness result to the probabilistic case, showing how a rationally weighted RLM with unbounded computation time can simulate any deterministic probabilistic Turing machine (PTM) with rationally weighted transitions. Since, in practice, RLMs work in real-time, processing a symbol at every time step, we treat the above result as an upper bound on the expressivity of RLMs. We also provide a lower bound by showing that under the restriction to real-time computation, such models can simulate deterministic real-time rational PTMs.

Current methods to prevent crypto asset fraud are based on the analysis of transaction graphs within blockchain networks. While effective for identifying transaction patterns indicative of fraud, it does not capture the semantics of transactions and is constrained to blockchain data. Consequently, preventive methods based on transaction graphs are inherently limited. In response to these limitations, we propose the Kosmosis approach, which aims to incrementally construct a knowledge graph as new blockchain and social media data become available. During construction, it aims to extract the semantics of transactions and connect blockchain addresses to their real-world entities by fusing blockchain and social media data in a knowledge graph. This enables novel preventive methods against rug pulls as a form of crypto asset fraud. To demonstrate the effectiveness and practical applicability of the Kosmosis approach, we examine a series of real-world rug pulls from 2021. Through this case, we illustrate how Kosmosis can aid in identifying and preventing such fraudulent activities by leveraging the insights from the constructed knowledge graph.

Experimental materials science is experiencing significant growth due to automated experimentation and AI techniques. Integrated autonomous platforms are emerging, combining generative models, robotics, simulations, and automated systems for material synthesis. However, two major challenges remain: democratizing access to these technologies and creating accessible infrastructure for under-resourced scientists. This paper introduces the Quantum Data Hub (QDH), a community-accessible research infrastructure aimed at researchers working with quantum materials. QDH integrates with the National Data Platform, adhering to FAIR principles while proposing additional UNIT principles for usability, navigability, interpretability, and timeliness. The QDH facilitates collaboration and extensibility, allowing seamless integration of new researchers, instruments, and data into the system.

Algorithmic predictions are increasingly used to inform the allocations of goods and interventions in the public sphere. In these domains, predictions serve as a means to an end. They provide stakeholders with insights into likelihood of future events as a means to improve decision making quality, and enhance social welfare. However, if maximizing welfare is the ultimate goal, prediction is only a small piece of the puzzle. There are various other policy levers a social planner might pursue in order to improve bottom-line outcomes, such as expanding access to available goods, or increasing the effect sizes of interventions. Given this broad range of design decisions, a basic question to ask is: What is the relative value of prediction in algorithmic decision making? How do the improvements in welfare arising from better predictions compare to those of other policy levers? The goal of our work is to initiate the formal study of these questions. Our main results are theoretical in nature. We identify simple, sharp conditions determining the relative value of prediction vis-\`a-vis expanding access, within several statistical models that are popular amongst quantitative social scientists. Furthermore, we illustrate how these theoretical insights may be used to guide the design of algorithmic decision making systems in practice.

Sampling invariant distributions from an Ito diffusion process presents a significant challenge in stochastic simulation. Traditional numerical solvers for stochastic differential equations require both a fine step size and a lengthy simulation period, resulting in both biased and correlated samples. Current deep learning-based method solves the stationary Fokker--Planck equation to determine the invariant probability density function in form of deep neural networks, but they generally do not directly address the problem of sampling from the computed density function. In this work, we introduce a framework that employs a weak generative sampler (WGS) to directly generate independent and identically distributed (iid) samples induced by a transformation map derived from the stationary Fokker--Planck equation. Our proposed loss function is based on the weak form of the Fokker--Planck equation, integrating normalizing flows to characterize the invariant distribution and facilitate sample generation from the base distribution. Our randomized test function circumvents the need for mini-max optimization in the traditional weak formulation. Distinct from conventional generative models, our method neither necessitates the computationally intensive calculation of the Jacobian determinant nor the invertibility of the transformation map. A crucial component of our framework is the adaptively chosen family of test functions in the form of Gaussian kernel functions with centres selected from the generated data samples. Experimental results on several benchmark examples demonstrate the effectiveness of our method, which offers both low computational costs and excellent capability in exploring multiple metastable states.

Blockchains revolutionized centralized sectors like banking and finance by promoting decentralization and transparency. In a blockchain, information is transmitted through transactions issued by participants or applications. Miners crucially select, order, and validate pending transactions for block inclusion, prioritizing those with higher incentives or fees. The order in which transactions are included can impact the blockchain final state. Moreover, applications running on top of a blockchain often rely on governance protocols to decentralize the decision-making power to make changes to their core functionality. These changes can affect how participants interact with these applications. Since one token equals one vote, participants holding multiple tokens have a higher voting power to support or reject the proposed changes. The extent to which this voting power is distributed is questionable and if highly concentrated among a few holders can lead to governance attacks. In this thesis, we audit the Bitcoin and Ethereum blockchains to investigate the norms followed by miners in determining the transaction prioritization. We also audit decentralized governance protocols such as Compound to evaluate whether the voting power is fairly distributed among the participants. Our findings have significant implications for future developments of blockchains and decentralized applications.

As image recognition models become more prevalent, scalable coding methods for machines and humans gain more importance. Applications of image recognition models include traffic monitoring and farm management. In these use cases, the scalable coding method proves effective because the tasks require occasional image checking by humans. Existing image compression methods for humans and machines meet these requirements to some extent. However, these compression methods are effective solely for specific image recognition models. We propose a learning-based scalable image coding method for humans and machines that is compatible with numerous image recognition models. We combine an image compression model for machines with a compression model, providing additional information to facilitate image decoding for humans. The features in these compression models are fused using a feature fusion network to achieve efficient image compression. Our method's additional information compression model is adjusted to reduce the number of parameters by enabling combinations of features of different sizes in the feature fusion network. Our approach confirms that the feature fusion network efficiently combines image compression models while reducing the number of parameters. Furthermore, we demonstrate the effectiveness of the proposed scalable coding method by evaluating the image compression performance in terms of decoded image quality and bitrate.

Deep neural networks have achieved remarkable success in computer vision tasks. Existing neural networks mainly operate in the spatial domain with fixed input sizes. For practical applications, images are usually large and have to be downsampled to the predetermined input size of neural networks. Even though the downsampling operations reduce computation and the required communication bandwidth, it removes both redundant and salient information obliviously, which results in accuracy degradation. Inspired by digital signal processing theories, we analyze the spectral bias from the frequency perspective and propose a learning-based frequency selection method to identify the trivial frequency components which can be removed without accuracy loss. The proposed method of learning in the frequency domain leverages identical structures of the well-known neural networks, such as ResNet-50, MobileNetV2, and Mask R-CNN, while accepting the frequency-domain information as the input. Experiment results show that learning in the frequency domain with static channel selection can achieve higher accuracy than the conventional spatial downsampling approach and meanwhile further reduce the input data size. Specifically for ImageNet classification with the same input size, the proposed method achieves 1.41% and 0.66% top-1 accuracy improvements on ResNet-50 and MobileNetV2, respectively. Even with half input size, the proposed method still improves the top-1 accuracy on ResNet-50 by 1%. In addition, we observe a 0.8% average precision improvement on Mask R-CNN for instance segmentation on the COCO dataset.