In this paper, we initiate the computational problem of jointly designing information and contracts. We consider three possible classes of contracts with decreasing flexibility and increasing simplicity: ambiguous contracts, menus of explicit contracts and explicit single contract. Ambiguous contracts allow the principal to conceal the applied payment schemes through a contract that depends on the unknown state of nature, while explicit contracts reveal the contract prior to the agent's decision. Our results show a trade-off between the simplicity of the contracts and the computational complexity of the joint design. Indeed, we show that an approximately-optimal mechanism with ambiguous contracts can be computed in polynomial time. However, they are convoluted mechanisms and not well-suited for some real-world scenarios. Conversely, explicit menus of contracts and single contracts are simpler mechanisms, but they cannot be computed efficiently. In particular, we show that computing the optimal mechanism with explicit menus of contracts and single contracts is APX-Hard. We also characterize the structure of optimal mechanisms. Interestingly, direct mechanisms are optimal for both the most flexible ambiguous contracts and the least flexible explicit single contract, but they are suboptimal for that with menus of contracts. Finally, motivated by our hardness results, we turn our attention to menus of linear contracts and single linear contracts. We show that both the problem of computing the optimal mechanism with an explicit menu of linear contracts and an explicit single linear contract admits an FPTAS.
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This paper derives a complete set of quadratic constraints (QCs) for the repeated ReLU. The complete set of QCs is described by a collection of matrix copositivity conditions. We also show that only two functions satisfy all QCs in our complete set: the repeated ReLU and flipped ReLU. Thus our complete set of QCs bounds the repeated ReLU as tight as possible up to the sign invariance inherent in quadratic forms. We derive a similar complete set of incremental QCs for repeated ReLU, which can potentially lead to less conservative Lipschitz bounds for ReLU networks than the standard LipSDP approach. The basic constructions are also used to derive the complete sets of QCs for other piecewise linear activation functions such as leaky ReLU, MaxMin, and HouseHolder. Finally, we illustrate the use of the complete set of QCs to assess stability and performance for recurrent neural networks with ReLU activation functions. We rely on a standard copositivity relaxation to formulate the stability/performance condition as a semidefinite program. Simple examples are provided to illustrate that the complete sets of QCs and incremental QCs can yield less conservative bounds than existing sets.
There has been a lot of recent research on improving the efficiency of fine-tuning foundation models. In this paper, we propose a novel efficient fine-tuning method that allows the input image size of Segment Anything Model (SAM) to be variable. SAM is a powerful foundational model for image segmentation trained on huge datasets, but it requires fine-tuning to recognize arbitrary classes. The input image size of SAM is fixed at 1024 x 1024, resulting in substantial computational demands during training. Furthermore, the fixed input image size may result in the loss of image information, e.g. due to fixed aspect ratios. To address this problem, we propose Generalized SAM (GSAM). Different from the previous methods, GSAM is the first to apply random cropping during training with SAM, thereby significantly reducing the computational cost of training. Experiments on datasets of various types and various pixel counts have shown that GSAM can train more efficiently than SAM and other fine-tuning methods for SAM, achieving comparable or higher accuracy.
In this paper, we focus on numerical approximations of Piecewise Diffusion Markov Processes (PDifMPs), particularly when the explicit flow maps are unavailable. Our approach is based on the thinning method for modelling the jump mechanism and combines the Euler-Maruyama scheme to approximate the underlying flow dynamics. For the proposed approximation schemes, we study both the mean-square and weak convergence. Weak convergence of the algorithms is established by a martingale problem formulation. Moreover, we employ these results to simulate the migration patterns exhibited by moving glioma cells at the microscopic level. Further, we develop and implement a splitting method for this PDifMP model and employ both the Thinned Euler-Maruyama and the splitting scheme in our simulation example, allowing us to compare both methods.
In this paper, we present a simulation system called AgentCourt that simulates the entire courtroom process. The judge, plaintiff's lawyer, defense lawyer, and other participants are autonomous agents driven by large language models (LLMs). Our core goal is to enable lawyer agents to learn how to argue a case, as well as improving their overall legal skills, through courtroom process simulation. To achieve this goal, we propose an adversarial evolutionary approach for the lawyer-agent. Since AgentCourt can simulate the occurrence and development of court hearings based on a knowledge base and LLM, the lawyer agents can continuously learn and accumulate experience from real court cases. The simulation experiments show that after two lawyer-agents have engaged in a thousand adversarial legal cases in AgentCourt (which can take a decade for real-world lawyers), compared to their pre-evolutionary state, the evolved lawyer agents exhibit consistent improvement in their ability to handle legal tasks. To enhance the credibility of our experimental results, we enlisted a panel of professional lawyers to evaluate our simulations. The evaluation indicates that the evolved lawyer agents exhibit notable advancements in responsiveness, as well as expertise and logical rigor. This work paves the way for advancing LLM-driven agent technology in legal scenarios. Code is available at //github.com/relic-yuexi/AgentCourt.
In this paper, we suggest new SAT encodings of the partial-ordering based ILP model for the graph coloring problem (GCP) and the bandwidth coloring problem (BCP). The GCP asks for the minimum number of colors that can be assigned to the vertices of a given graph such that each two adjacent vertices get different colors. The BCP is a generalization, where each edge has a weight that enforces a minimal "distance" between the assigned colors, and the goal is to minimize the "largest" color used. For the widely studied GCP, we experimentally compare our new SAT encoding to the state-of-the-art approaches on the DIMACS benchmark set. Our evaluation confirms that this SAT encoding is effective for sparse graphs and even outperforms the state-of-the-art on some DIMACS instances. For the BCP, our theoretical analysis shows that the partial-ordering based SAT and ILP formulations have an asymptotically smaller size than that of the classical assignment-based model. Our practical evaluation confirms not only a dominance compared to the assignment-based encodings but also to the state-of-the-art approaches on a set of benchmark instances. Up to our knowledge, we have solved several open instances of the BCP from the literature for the first time.
This paper presents a novel multi-channel speech enhancement approach, FoVNet, that enables highly efficient speech enhancement within a configurable field of view (FoV) of a smart-glasses user without needing specific target-talker(s) directions. It advances over prior works by enhancing all speakers within any given FoV, with a hybrid signal processing and deep learning approach designed with high computational efficiency. The neural network component is designed with ultra-low computation (about 50 MMACS). A multi-channel Wiener filter and a post-processing module are further used to improve perceptual quality. We evaluate our algorithm with a microphone array on smart glasses, providing a configurable, efficient solution for augmented hearing on energy-constrained devices. FoVNet excels in both computational efficiency and speech quality across multiple scenarios, making it a promising solution for smart glasses applications.
This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions, our approach leverages the relationship between MGFs and distribution moments to extend high-order uncertainty propagation techniques to non-Gaussian scenarios. This significantly broadens the applicability of these methods to a wider range of problems and uncertainty types. High-order moment computations are performed one-off and symbolically, reducing the computational burden of the technique to the calculation of Taylor series coefficients around a nominal trajectory, achieved by efficiently integrating the system's variational equations. Furthermore, the use of the proposed approach in combination with event transition tensors, allows for accurate propagation of uncertainties at specific events, such as the landing surface of a celestial body, the crossing of a predefined Poincar\'e section, or the trigger of an arbitrary event during the propagation. Via numerical simulations we demonstrate the effectiveness of our method in various astrodynamics applications, including the unperturbed and perturbed two-body problem, and the circular restricted three-body problem, showing that it accurately propagates non-Gaussian uncertainties both at future times and at event manifolds.
In this paper, we propose a data-driven method to learn interpretable topological features of biomolecular data and demonstrate the efficacy of parsimonious models trained on topological features in predicting the stability of synthetic mini proteins. We compare models that leverage automatically-learned structural features against models trained on a large set of biophysical features determined by subject-matter experts (SME). Our models, based only on topological features of the protein structures, achieved 92%-99% of the performance of SME-based models in terms of the average precision score. By interrogating model performance and feature importance metrics, we extract numerous insights that uncover high correlations between topological features and SME features. We further showcase how combining topological features and SME features can lead to improved model performance over either feature set used in isolation, suggesting that, in some settings, topological features may provide new discriminating information not captured in existing SME features that are useful for protein stability prediction.
In this paper, we propose a new framework called YOWOv3, which is an improved version of YOWOv2, designed specifically for the task of Human Action Detection and Recognition. This framework is designed to facilitate extensive experimentation with different configurations and supports easy customization of various components within the model, reducing efforts required for understanding and modifying the code. YOWOv3 demonstrates its superior performance compared to YOWOv2 on two widely used datasets for Human Action Detection and Recognition: UCF101-24 and AVAv2.2. Specifically, the predecessor model YOWOv2 achieves an mAP of 85.2% and 20.3% on UCF101-24 and AVAv2.2, respectively, with 109.7M parameters and 53.6 GFLOPs. In contrast, our model - YOWOv3, with only 59.8M parameters and 39.8 GFLOPs, achieves an mAP of 88.33% and 20.31% on UCF101-24 and AVAv2.2, respectively. The results demonstrate that YOWOv3 significantly reduces the number of parameters and GFLOPs while still achieving comparable performance.
In this paper, we consider deploying multiple Unmanned Aerial Vehicles (UAVs) to enhance the computation service of Mobile Edge Computing (MEC) through collaborative computation among UAVs. In particular, the tasks of different types and service requirements in MEC network are offloaded from one UAV to another. To pursue the goal of low-carbon edge computing, we study the problem of minimizing system energy consumption by jointly optimizing computation resource allocation, task scheduling, service placement, and UAV trajectories. Considering the inherent unpredictability associated with task generation and the dynamic nature of wireless fading channels, addressing this problem presents a significant challenge. To overcome this issue, we reformulate the complicated non-convex problem as a Markov decision process and propose a soft actor-critic-based trajectory optimization and resource allocation algorithm to implement a flexible learning strategy. Numerical results illustrate that within a multi-UAV-enabled MEC network, the proposed algorithm effectively reduces the system energy consumption in heterogeneous tasks and services scenarios compared to other baseline solutions.
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