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We explore the fairness of a redistricting game introduced by Mixon and Villar, which provides a two-party protocol for dividing a state into electoral districts, without the participation of an independent authority. We analyze the game in an abstract setting that ignores the geographic distribution of voters and assumes that voter preferences are fixed and known. We show that the minority player can always win at least $p-1$ districts, where $p$ is proportional to the percentage of minority voters. We give an upper bound on the number of districts won by the minority based on a "cracking" strategy for the majority.

Memory bandwidth is known to be a performance bottleneck for FPGA accelerators, especially when they deal with large multi-dimensional data-sets. A large body of work focuses on reducing of off-chip transfers, but few authors try to improve the efficiency of transfers. This paper addresses the later issue by proposing (i) a compiler-based approach to accelerator's data layout to maximize contiguous access to off-chip memory, and (ii) data packing and runtime compression techniques that take advantage of this layout to further improve memory performance. We show that our approach can decrease the I/O cycles up to $7\times$ compared to un-optimized memory accesses.

The classic question of whether one should walk or run in the rain to remain the least wet has inspired a myriad of solutions ranging from physically performing test runs in raining conditions to mathematically modeling human movement through rain. This manuscript approaches the classical problem by simulating movement through rainfall using MATLAB. Our simulation was generalizable to include snowfall as well. An increase in walking speed resulted in a corresponding decrease in raindrop and snowflake collisions. When raindrops or snowflakes were given a horizontal movement vector due to wind, a local minimum in collisions was achieved when moving in parallel with the same horizontal speed as the raindrop; no local minimum was detected with antiparallel movement. In general, our simulation revealed that the faster one moves, the drier one remains.

We propose a novel stereo-confidence that can be measured externally to various stereo-matching networks, offering an alternative input modality choice of the cost volume for learning-based approaches, especially in safety-critical systems. Grounded in the foundational concepts of disparity definition and the disparity plane sweep, the proposed stereo-confidence method is built upon the idea that any shift in a stereo-image pair should be updated in a corresponding amount shift in the disparity map. Based on this idea, the proposed stereo-confidence method can be summarized in three folds. 1) Using the disparity plane sweep, multiple disparity maps can be obtained and treated as a 3-D volume (predicted disparity volume), like the cost volume is constructed. 2) One of these disparity maps serves as an anchor, allowing us to define a desirable (or ideal) disparity profile at every spatial point. 3) By comparing the desirable and predicted disparity profiles, we can quantify the level of matching ambiguity between left and right images for confidence measurement. Extensive experimental results using various stereo-matching networks and datasets demonstrate that the proposed stereo-confidence method not only shows competitive performance on its own but also consistent performance improvements when it is used as an input modality for learning-based stereo-confidence methods.

Software vulnerabilities are a major cyber threat and it is important to detect them. One important approach to detecting vulnerabilities is to use deep learning while treating a program function as a whole, known as function-level vulnerability detectors. However, the limitation of this approach is not understood. In this paper, we investigate its limitation in detecting one class of vulnerabilities known as inter-procedural vulnerabilities, where the to-be-patched statements and the vulnerability-triggering statements belong to different functions. For this purpose, we create the first Inter-Procedural Vulnerability Dataset (InterPVD) based on C/C++ open-source software, and we propose a tool dubbed VulTrigger for identifying vulnerability-triggering statements across functions. Experimental results show that VulTrigger can effectively identify vulnerability-triggering statements and inter-procedural vulnerabilities. Our findings include: (i) inter-procedural vulnerabilities are prevalent with an average of 2.8 inter-procedural layers; and (ii) function-level vulnerability detectors are much less effective in detecting to-be-patched functions of inter-procedural vulnerabilities than detecting their counterparts of intra-procedural vulnerabilities.

We systematically analyze the accuracy of Physics-Informed Neural Networks (PINNs) in approximating solutions to the critical Surface Quasi-Geostrophic (SQG) equation on two-dimensional periodic boxes. The critical SQG equation involves advection and diffusion described by nonlocal periodic operators, posing challenges for neural network-based methods that do not commonly exhibit periodic boundary conditions. In this paper, we present a novel approximation of these operators using their nonperiodic analogs based on singular integral representation formulas and use it to perform error estimates. This idea can be generalized to a larger class of nonlocal partial differential equations whose solutions satisfy prescribed boundary conditions, thereby initiating a new PINNs theory for equations with nonlocalities.

Despite their popularity in non-English NLP, multilingual language models often underperform monolingual ones due to inter-language competition for model parameters. We propose Cross-lingual Expert Language Models (X-ELM), which mitigate this competition by independently training language models on subsets of the multilingual corpus. This process specializes X-ELMs to different languages while remaining effective as a multilingual ensemble. Our experiments show that when given the same compute budget, X-ELM outperforms jointly trained multilingual models across all considered languages and that these gains transfer to downstream tasks. X-ELM provides additional benefits over performance improvements: new experts can be iteratively added, adapting X-ELM to new languages without catastrophic forgetting. Furthermore, training is asynchronous, reducing the hardware requirements for multilingual training and democratizing multilingual modeling.

Language is often considered a key aspect of human thinking, providing us with exceptional abilities to generalize, explore, plan, replan, and adapt to new situations. However, Reinforcement Learning (RL) agents are far from human-level performance in any of these abilities. We hypothesize one reason for such cognitive deficiencies is that they lack the benefits of thinking in language and that we can improve AI agents by training them to think like humans do. We introduce a novel Imitation Learning framework, Thought Cloning, where the idea is to not just clone the behaviors of human demonstrators, but also the thoughts humans have as they perform these behaviors. While we expect Thought Cloning to truly shine at scale on internet-sized datasets of humans thinking out loud while acting (e.g. online videos with transcripts), here we conduct experiments in a domain where the thinking and action data are synthetically generated. Results reveal that Thought Cloning learns much faster than Behavioral Cloning and its performance advantage grows the further out of distribution test tasks are, highlighting its ability to better handle novel situations. Thought Cloning also provides important benefits for AI Safety and Interpretability, and makes it easier to debug and improve AI. Because we can observe the agent's thoughts, we can (1) more easily diagnose why things are going wrong, making it easier to fix the problem, (2) steer the agent by correcting its thinking, or (3) prevent it from doing unsafe things it plans to do. Overall, by training agents how to think as well as behave, Thought Cloning creates safer, more powerful agents.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.

The concept of causality plays an important role in human cognition . In the past few decades, causal inference has been well developed in many fields, such as computer science, medicine, economics, and education. With the advancement of deep learning techniques, it has been increasingly used in causal inference against counterfactual data. Typically, deep causal models map the characteristics of covariates to a representation space and then design various objective optimization functions to estimate counterfactual data unbiasedly based on the different optimization methods. This paper focuses on the survey of the deep causal models, and its core contributions are as follows: 1) we provide relevant metrics under multiple treatments and continuous-dose treatment; 2) we incorporate a comprehensive overview of deep causal models from both temporal development and method classification perspectives; 3) we assist a detailed and comprehensive classification and analysis of relevant datasets and source code.