We propose several new lower bounds on the bandwidth cost of MDS convertible codes using a linear-algebraic framework. The derived bounds improve previous results in certain parameter regimes and match the bandwidth cost of the construction proposed by Maturana and Rashmi (2022 IEEE International Symposium on Information Theory) for rF≤rI≤kF, implying that our bounds are tight in this case.

Generative models aim to simulate realistic effects of various actions across different contexts, from text generation to visual effects. Despite significant efforts to build real-world simulators, the application of generative models to virtual worlds, like financial markets, remains under-explored. In financial markets, generative models can simulate complex market effects of participants with various behaviors, enabling interaction under different market conditions, and training strategies without financial risk. This simulation relies on the finest structured data in financial market like orders thus building the finest realistic simulation. We propose Large Market Model (LMM), an order-level generative foundation model, for financial market simulation, akin to language modeling in the digital world. Our financial Market Simulation engine (MarS), powered by LMM, addresses the domain-specific need for realistic, interactive and controllable order generation. Key observations include LMM's strong scalability across data size and model complexity, and MarS's robust and practicable realism in controlled generation with market impact. We showcase MarS as a forecast tool, detection system, analysis platform, and agent training environment, thus demonstrating MarS's ``paradigm shift'' potential for a variety of financial applications. We release the code of MarS at https://github.com/microsoft/MarS/.

Data-driven decision-making processes increasingly utilize end-to-end learnable deep neural networks to render final decisions. Sometimes, the output of the forward functions in certain layers is determined by the solutions to mathematical optimization problems, leading to the emergence of differentiable optimization layers that permit gradient back-propagation. However, real-world scenarios often involve large-scale datasets and numerous constraints, presenting significant challenges. Current methods for differentiating optimization problems typically rely on implicit differentiation, which necessitates costly computations on the Jacobian matrices, resulting in low efficiency. In this paper, we introduce BPQP, a differentiable convex optimization framework designed for efficient end-to-end learning. To enhance efficiency, we reformulate the backward pass as a simplified and decoupled quadratic programming problem by leveraging the structural properties of the Karush–Kuhn–Tucker (KKT) matrix. This reformulation enables the use of first-order optimization algorithms in calculating the backward pass gradients, allowing our framework to potentially utilize any state-of-the-art solver. As solver technologies evolve, BPQP can continuously adapt and improve its efficiency. Extensive experiments on both simulated and real-world datasets demonstrate that BPQP achieves a significant improvement in efficiency—typically an order of magnitude faster in overall execution time compared to other differentiable optimization layers. Our results not only highlight the efficiency gains of BPQP but also underscore its superiority over differential optimization layer baselines.

As one of the major threats to the healthy development of various online platforms, fraud has become increasingly committed in the form of gangs since collusive fraudulent activities are much easier to obtain illicit benefits with lower exposure risk. To detect fraudsters in a gang, spatio-temporal graph neural network models have been widely applied to detect both temporal and spatial collusive patterns. However, a closer peek into real-world records of fraudsters can reveal that fraud gangs usually conduct community-level camouflage, specified by two types, i.e., temporal and spatial camouflage. Such camouflage can disguise gangs as benign communities by concealing collusive patterns and thus deceiving many existing graph neural network models. In the meantime, many existing graph neural network models suffer from the challenge of extreme sample imbalance caused by rare fraudsters hidden among massive users. To handle all these challenges, in this paper, we propose a generative adversarial network framework, named Adversarial Camouflage Detector, to detect fraudsters. Concretely, this ACD framework consists of four modules, in charge of community division, camouflage identification, fraudster detection, and camouflage generation, respectively. The first three modules form up a discriminator that uses spatio-temporal graph neural networks as the foundation model and enhance fraudster detection by amplifying the gangs' collusive patterns through automatically identifying and removing camouflage. Meanwhile, the camouflage generation module plays as the generator role that generates fraudsters samples by competing against the discriminator to alleviate the challenge of sample imbalance and increase the model robustness. The experimental result shows that our proposed method outperforms other methods on real-world datasets.

Sequence learning has attracted much research attention from the machine learning community in recent years. In many applications, a sequence learning task is usually associated with multiple temporally correlated auxiliary tasks, which are different in terms of how much input information to use or which future step to predict. For example, (i) in simultaneous machine translation, one can conduct translation under different latency (i.e., how many input words to read/wait before translation); (ii) in stock trend forecasting, one can predict the price of a stock in different future days (e.g., tomorrow, the day after tomorrow). While it is clear that those temporally correlated tasks can help each other, there is a very limited exploration on how to better leverage multiple auxiliary tasks to boost the performance of the main task. In this work, we introduce a learnable scheduler to sequence learning, which can adaptively select auxiliary tasks for training depending on the model status and the current training data. The scheduler and the model for the main task are jointly trained through bi-level optimization. Experiments show that our method significantly improves the performance of simultaneous machine translation and stock trend forecasting.