The core mechanical system is built around three stepper motors for physical manipulation, a microcontroller for hardware control, a camera and YOLO detection model for real-time cube state detection. A significant software component is the development of a user-friendly graphical user interface (GUI) designed in Unity. The initial state after detection from real-time YOLOv8 model (Precision 0.98443, Recall 0.98419, Box Loss 0.42051, Class Loss 0.2611) is virtualized on GUI. To get the solution, the system employs the Kociemba's algorithm while physical manipulation with a single degree of freedom is done by combination of stepper motors' interaction with the cube achieving the average solving time of ~2.2 minutes.

Federated learning (FL) offers a promising paradigm for collaborative model training while preserving data privacy. However, its susceptibility to gradient inversion attacks poses a significant challenge, necessitating robust privacy protection mechanisms. This paper introduces a novel theoretical framework to decipher the intricate interplay between attack and protection complexities in privacy-preserving FL. We formally define "Attack Complexity" as the minimum computational and data resources an adversary requires to reconstruct private data below a given error threshold, and "Protection Complexity" as the expected distortion introduced by privacy mechanisms. Leveraging Maximum Bayesian Privacy (MBP), we derive tight theoretical bounds for protection complexity, demonstrating its scaling with model dimensionality and privacy budget. Furthermore, we establish comprehensive bounds for attack complexity, revealing its dependence on privacy leakage, gradient distortion, model dimension, and the chosen privacy level. Our findings quantitatively illuminate the fundamental trade-offs between privacy guarantees, system utility, and the effort required for both attacking and defending. This framework provides critical insights for designing more secure and efficient federated learning systems.

Integer programming lies at the heart of crucial combinatorial optimization tasks but remains challenging due to its NP-hard nature. An effective approach for practically solving integer programs is the manual design of acceleration cuts, i.e. inequalities that improve solver performance. However, this creative process demands deep expertise and is yet to be automated. Our proposed framework, EvoCut, automates the generation of acceleration cuts by combining large language models (LLMs) with an evolutionary search. EvoCut (i) initializes a diverse population of candidate cuts via an LLM-based initializer agent; (ii) for each cut empirically evaluates both preservation of the optimal solution and its ability to cut off fractional solutions across a verification set; and (iii) iteratively refines the population through evolutionary crossover and mutation agents. We quantify each cut's utility by its relative reduction in the solver's optimality gap. Our comparisons against standard integer programming practice show that EvoCut reduces optimality gap by 17-57% within a fixed time. It obtains the same solutions up to 4 times as fast, and obtains higher-quality solutions within the same time limit. Requiring no human expert input, EvoCut reliably generates, improves, and empirically verifies cuts that generalize to unseen instances. The code is available at https://github.com/milad1378yz/EvoCut.

Scaling inference-time computation has substantially improved the reasoning capabilities of language models. However, existing methods have significant limitations: serialized chain-of-thought approaches generate overly long outputs, leading to increased latency and exhausted context windows, while parallel methods such as self-consistency suffer from insufficient coordination, resulting in redundant computations and limited performance gains. To address these shortcomings, we propose Adaptive Parallel Reasoning (APR), a novel reasoning framework that enables language models to orchestrate both serialized and parallel computations end-to-end. APR generalizes existing reasoning methods by enabling adaptive multi-threaded inference using spawn() and join() operations. A key innovation is our end-to-end reinforcement learning strategy, optimizing both parent and child inference threads to enhance task success rate without requiring predefined reasoning structures. Experiments on the Countdown reasoning task demonstrate significant benefits of APR: (1) higher performance within the same context window (83.4% vs. 60.0% at 4k context); (2) superior scalability with increased computation (80.1% vs. 66.6% at 20k total tokens); (3) improved accuracy at equivalent latency (75.2% vs. 57.3% at approximately 5,000ms). APR represents a step towards enabling language models to autonomously optimize their reasoning processes through adaptive allocation of computation.

Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems.

Stabilizing an unknown control system is one of the most fundamental problems in control systems engineering. In this paper, we provide a simple, model-free algorithm for stabilizing fully observed dynamical systems. While model-free methods have become increasingly popular in practice due to their simplicity and flexibility, stabilization via direct policy search has received surprisingly little attention. Our algorithm proceeds by solving a series of discounted LQR problems, where the discount factor is gradually increased. We prove that this method efficiently recovers a stabilizing controller for linear systems, and for smooth, nonlinear systems within a neighborhood of their equilibria. Our approach overcomes a significant limitation of prior work, namely the need for a pre-given stabilizing control policy. We empirically evaluate the effectiveness of our approach on common control benchmarks.

To provide a systematic study of the performance of NAS algorithms on a macro search space, we release Blox - a benchmark that consists of 91k unique models trained on the CIFAR-100 dataset. The dataset also includes runtime measurements of all the models on a diverse set of hardware platforms.