Federated Learning (FL) is a promising distributed model training paradigm without the leakage of local data. In wireless communication networks, energy-constrained mobile devices may encounter outage when uploading local gradients to edge server due to fading channels, leading to lost devices and thus performance degradation. Retransmission is a classical mechanism to address the outage issue, which however increases energy consumption and delay of mobile devices. To this end, we propose an adaptive retransmission strategy for wireless FL, where the server decides whether to request retransmission according to the number of transmission outage, and devices decide whether to respond based on their channel conditions and remaining energy. A convergence analysis is conducted for the proposed FL framework. Based on this, we aim to minimize the convergence error by jointly optimizing the retransmission decisions and the allocation of retransmission slots, under the devices’ long-term energy budget and the communication resource constraints. Since the decisions are coupled across different iterations, we design a Lyapunov-based online algorithm to solve this problem. Through experiments, we find that the effect of outage is trivial sometimes and retransmission is not always necessary in FL because channel conditions and data distributions affect the degree of the retransmission gain, and that the retransmission strategy benefits wireless FL.

Federated learning (FL) is a promising distributed machine learning paradigm to train a machine learning model without the leakage of local data. However, as the sizes of models are increasing while Internet of Things (IoT) devices are heterogeneous and capability-limited, FL faces performance bottleneck. In this article, we propose a cooperative device-to-device (D2D)-based partial training scheme for wireless FL. Specifically, the IoT devices in each cluster extract and train the nonoverlapping submodels from the global model, and the trained submodels are transmitted to the cluster head (CH) to form a whole local model via D2D links. Then the CHs upload the local models to the server for global aggregation. We first conduct the convergence analysis for the proposed wireless FL scheme. Then a joint optimization problem is formulated to minimize the average delay by the optimization of model division, device selection, and bandwidth allocation. An efficient algorithm is proposed to solve this nonconvex problem. Comprehensive experiments verify the efficiency of the proposed scheme.

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.

Formal verification (FV) has witnessed growing significance with current emerging program synthesis by the evolving large language models (LLMs). However, current formal verification mainly resorts to symbolic verifiers or hand-craft rules, resulting in limitations for extensive and flexible verification. On the other hand, formal languages for automated theorem proving, such as Isabelle, as another line of rigorous verification, are maintained with comprehensive rules and theorems. In this paper, we propose FVEL, an interactive Formal Verification Environment with LLMs. Specifically, FVEL transforms a given code to be verified into Isabelle, and then conducts verification via neural automated theorem proving with an LLM. The joined paradigm leverages the rigorous yet abundant formulated and organized rules in Isabelle and is also convenient for introducing and adjusting cutting-edge LLMs. To achieve this goal, we extract a large-scale FVELER. The FVELER dataset includes code dependencies and verification processes that are formulated in Isabelle, containing 758 theories, 29,304 lemmas, and 201,498 proof steps in total with in-depth dependencies. We benchmark FVELER in the FVEL environment by first fine-tuning LLMs with FVELER and then evaluating them on Code2Inv and SV-COMP. The results show that FVEL with FVELER fine-tuned Llama3-8B solves 17.39% (69→81) more problems, and Mistral-7B 12% (75→84) more problems in SV-COMP. And the proportion of proof errors is reduced. Project page: https://fveler.github.io/.

Attractor networks require neuronal connections to be highly structured in order to maintain attractor states that represent information, while excitation and inhibition balanced networks (E-INNs) require neuronal connections to be random and sparse to generate irregular neuronal firings. Despite being regarded as canonical models of neural circuits, both types of networks are usually studied in isolation, and it remains unclear how they coexist in the brain, given their very different structural demands. In this study, we investigate the compatibility of continuous attractor neural networks (CANNs) and E-INNs. In line with recent experimental data, we find that a neural circuit can exhibit both the traits of CANNs and E-INNs if the neuronal synapses consist of two sets: one set is strong and fast for irregular firing, and the other set is weak and slow for attractor dynamics. Our results from simulations and theoretical analysis reveal that the network also exhibits enhanced performance compared to the case of using only one set of synapses, with accelerated convergence of attractor states and retained E-I balanced condition for localized input. We also apply the network model to solve a real-world tracking problem and demonstrate that it can track fast-moving objects well. We hope that this study provides insight into how structured neural computations are realized by irregular firings of neurons.

Spatio-temporal information processing is fundamental in both brain functions and AI applications. Current strategies for spatio-temporal pattern recognition usually involve explicit feature extraction followed by feature aggregation, which requires a large amount of labeled data. In the present study, motivated by the subcortical visual pathway and early stages of the auditory pathway for motion and sound processing, we propose a novel brain-inspired computational model for generic spatio-temporal pattern recognition. The model consists of two modules, a reservoir module and a decision-making module. The former projects complex spatio-temporal patterns into spatially separated neural representations via its recurrent dynamics, the latter reads out neural representations via integrating information over time, and the two modules are linked together using known examples. Using synthetic data, we demonstrate that the model can extract the frequency and order information of temporal inputs. We apply the model to reproduce the looming pattern discrimination behavior as observed in experiments successfully. Furthermore, we apply the model to the gait recognition task, and demonstrate that our model accomplishes the recognition in an event-based manner and outperforms deep learning counterparts when training data is limited.