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The development of Policy Iteration (PI) has inspired many recent algorithms for Reinforcement Learning (RL), including several policy gradient methods that gained both theoretical soundness and empirical success on a variety of tasks. The theory of PI is rich in the context of centralized learning, but its study under the federated setting is still in the infant stage. This paper investigates the federated version of Approximate PI (API) and derives its error bound, taking into account the approximation error introduced by environment heterogeneity. We theoretically prove that a proper client selection scheme can reduce this error bound. Based on the theoretical result, we propose a client selection algorithm to alleviate the additional approximation error caused by environment heterogeneity. Experiment results show that the proposed algorithm outperforms other biased and unbiased client selection methods on the federated mountain car problem and the Mujoco Hopper problem by effectively selecting clients with a lower level of heterogeneity from the population distribution.

Instructing the model to generate a sequence of intermediate steps, a.k.a., a chain of thought (CoT), is a highly effective method to improve the accuracy of large language models (LLMs) on arithmetics and symbolic reasoning tasks. However, the mechanism behind CoT remains unclear. This work provides a theoretical understanding of the power of CoT for decoder-only transformers through the lens of expressiveness. Conceptually, CoT empowers the model with the ability to perform inherently serial computation, which is otherwise lacking in transformers, especially when depth is low. Given input length $n$, previous works have shown that constant-depth transformers with finite precision $\mathsf{poly}(n)$ embedding size can only solve problems in $\mathsf{TC}^0$ without CoT. We first show an even tighter expressiveness upper bound for constant-depth transformers with constant-bit precision, which can only solve problems in $\mathsf{AC}^0$, a proper subset of $ \mathsf{TC}^0$. However, with $T$ steps of CoT, constant-depth transformers using constant-bit precision and $O(\log n)$ embedding size can solve any problem solvable by boolean circuits of size $T$. Empirically, enabling CoT dramatically improves the accuracy for tasks that are hard for parallel computation, including the composition of permutation groups, iterated squaring, and circuit value problems, especially for low-depth transformers.

Stacked intelligent metasurface (SIM) has emerged as a technology enabling wave domain beamforming through multiple stacked reconfigurable intelligent surfaces (RISs). SIM has been implemented so far with diagonal RIS (D-RIS), while SIM implemented with beyond diagonal RIS (BD-RIS) remains unexplored. Furthermore, a model of SIM accounting for mutual coupling is not yet available. To fill these gaps, we derive a physically consistent channel model for SIM-aided systems and clarify the assumptions needed to obtain the simplified model used in related works. Using this model, we show that 1-layer SIM implemented with BD-RIS achieves the performance upper bound with limited complexity.

Computability, in the presence of asynchrony and failures, is one of the central questions in distributed computing. The celebrated asynchronous computability theorem (ACT) charaterizes the computing power of the read-write shared-memory model through the geometric properties of its protocol complex: a combinatorial structure describing the states the model can reach via its finite executions. This characterization assumes that the memory is of unbounded capacity, in particular, it is able to store the exponentially growing states of the full-information protocol. In this paper, we tackle an orthogonal question: what is the minimal memory capacity that allows us to simulate a given number of rounds of the full-information protocol? In the iterated immediate snapshot model (IIS), we determine necessary and sufficient conditions on the number of bits an IIS element should be able to store so that the resulting protocol is equivalent, up to isomorphism, to the full-information protocol. Our characterization implies that $n\geq 3$ processes can simulate $r$ rounds of the full-information IIS protocol as long as the bit complexity per process is within $\Omega(r n)$ and $O(r n \log n)$. Two processes, however, can simulate any number of rounds of the full-information protocol using only $2$ bits per process, which implies, in particular, that just $2$ bits per process are sufficient to solve $\varepsilon$-agreement for arbitrarily small $\varepsilon$.

As Large Language Models (LLMs) are integrated into critical real-world applications, their strategic and logical reasoning abilities are increasingly crucial. This paper evaluates LLMs' reasoning abilities in competitive environments through game-theoretic tasks, e.g., board and card games that require pure logic and strategic reasoning to compete with opponents. We first propose GTBench, a language-driven environment composing 10 widely-recognized tasks, across a comprehensive game taxonomy: complete versus incomplete information, dynamic versus static, and probabilistic versus deterministic scenarios. Then, we investigate two key problems: (1) Characterizing game-theoretic reasoning of LLMs; (2) LLM-vs-LLM competitions as reasoning evaluation. We observe that (1) LLMs have distinct behaviors regarding various gaming scenarios; for example, LLMs fail in complete and deterministic games yet they are competitive in probabilistic gaming scenarios; (2) Open-source LLMs, e.g., CodeLlama-34b-Instruct, are less competitive than commercial LLMs, e.g., GPT-4, in complex games. In addition, code-pretraining greatly benefits strategic reasoning, while advanced reasoning methods such as Chain-of-Thought (CoT) and Tree-of-Thought (ToT) do not always help. Detailed error profiles are also provided for a better understanding of LLMs' behavior.

Recent advances in Large Language Models (LLMs) have highlighted the need for robust, comprehensive, and challenging benchmarks. Yet, research on evaluating their Emotional Intelligence (EI) is considerably limited. Existing benchmarks have two major shortcomings: first, they mainly focus on emotion recognition, neglecting essential EI capabilities such as emotion regulation and thought facilitation through emotion understanding; second, they are primarily constructed from existing datasets, which include frequent patterns, explicit information, and annotation errors, leading to unreliable evaluation. We propose EmoBench, a benchmark that draws upon established psychological theories and proposes a comprehensive definition for machine EI, including Emotional Understanding and Emotional Application. EmoBench includes a set of 400 hand-crafted questions in English and Chinese, which are meticulously designed to require thorough reasoning and understanding. Our findings reveal a considerable gap between the EI of existing LLMs and the average human, highlighting a promising direction for future research. Our code and data will be publicly available from //github.com/Sahandfer/EmoBench.

Contextualized embeddings are the preferred tool for modeling Lexical Semantic Change (LSC). Current evaluations typically focus on a specific task known as Graded Change Detection (GCD). However, performance comparison across work are often misleading due to their reliance on diverse settings. In this paper, we evaluate state-of-the-art models and approaches for GCD under equal conditions. We further break the LSC problem into Word-in-Context (WiC) and Word Sense Induction (WSI) tasks, and compare models across these different levels. Our evaluation is performed across different languages on eight available benchmarks for LSC, and shows that (i) APD outperforms other approaches for GCD; (ii) XL-LEXEME outperforms other contextualized models for WiC, WSI, and GCD, while being comparable to GPT-4; (iii) there is a clear need for improving the modeling of word meanings, as well as focus on how, when, and why these meanings change, rather than solely focusing on the extent of semantic change.

SRAM bitcells in retention mode behave as autonomous stochastic nonlinear dynamical systems. From observation of variability-aware transient noise simulations, we provide an unidimensional model, fully characterizable by conventional deterministic SPICE simulations, insightfully explaining the mechanism of intrinsic noise-induced bit flips. The proposed model is exploited to, first, explain the reported inaccuracy of existing closed-form near-equilibrium formulas aimed at predicting the mean time to failure and, secondly, to propose a closer estimate attractive in terms of CPU time.

Network Intrusion Detection Systems (NIDS) are a fundamental tool in cybersecurity. Their ability to generalize across diverse networks is a critical factor in their effectiveness and a prerequisite for real-world applications. In this study, we conduct a comprehensive analysis on the generalization of machine-learning-based NIDS through an extensive experimentation in a cross-dataset framework. We employ four machine learning classifiers and utilize four datasets acquired from different networks: CIC-IDS-2017, CSE-CIC-IDS2018, LycoS-IDS2017, and LycoS-Unicas-IDS2018. Notably, the last dataset is a novel contribution, where we apply corrections based on LycoS-IDS2017 to the well-known CSE-CIC-IDS2018 dataset. The results show nearly perfect classification performance when the models are trained and tested on the same dataset. However, when training and testing the models in a cross-dataset fashion, the classification accuracy is largely commensurate with random chance except for a few combinations of attacks and datasets. We employ data visualization techniques in order to provide valuable insights on the patterns in the data. Our analysis unveils the presence of anomalies in the data that directly hinder the classifiers capability to generalize the learned knowledge to new scenarios. This study enhances our comprehension of the generalization capabilities of machine-learning-based NIDS, highlighting the significance of acknowledging data heterogeneity.

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of GNNs. Although most of GNNs basically follow a message passing manner, litter effort has been made to discover and analyze their essential relations. In this paper, we establish a surprising connection between different propagation mechanisms with a unified optimization problem, showing that despite the proliferation of various GNNs, in fact, their proposed propagation mechanisms are the optimal solution optimizing a feature fitting function over a wide class of graph kernels with a graph regularization term. Our proposed unified optimization framework, summarizing the commonalities between several of the most representative GNNs, not only provides a macroscopic view on surveying the relations between different GNNs, but also further opens up new opportunities for flexibly designing new GNNs. With the proposed framework, we discover that existing works usually utilize naive graph convolutional kernels for feature fitting function, and we further develop two novel objective functions considering adjustable graph kernels showing low-pass or high-pass filtering capabilities respectively. Moreover, we provide the convergence proofs and expressive power comparisons for the proposed models. Extensive experiments on benchmark datasets clearly show that the proposed GNNs not only outperform the state-of-the-art methods but also have good ability to alleviate over-smoothing, and further verify the feasibility for designing GNNs with our unified optimization framework.