The Multi-Reference Alignment (MRA) problem aims at the recovery of an unknown signal from repeated observations under the latent action of a group of cyclic isometries, in the presence of additive noise of high intensity $\sigma$. It is a more tractable version of the celebrated cryo EM model. In the crucial high noise regime, it is known that its sample complexity scales as $\sigma^6$. Recent investigations have shown that for the practically significant setting of sparse signals, the sample complexity of the maximum likelihood estimator asymptotically scales with the noise level as $\sigma^4$. In this work, we investigate minimax optimality for signal estimation under the MRA model for so-called collision-free signals. In particular, this signal class covers the setting of generic signals of dilute sparsity (wherein the support size $s=O(L^{1/3})$, where $L$ is the ambient dimension. We demonstrate that the minimax optimal rate of estimation in for the sparse MRA problem in this setting is $\sigma^2/\sqrt{n}$, where $n$ is the sample size. In particular, this widely generalizes the sample complexity asymptotics for the restricted MLE in this setting, establishing it as the statistically optimal estimator. Finally, we demonstrate a concentration inequality for the restricted MLE on its deviations from the ground truth.

Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the generation of DPMs usually consumes much time due to the large number of function evaluations (NFE). Though recent works have accelerated the sampling to around 20 steps with high-order solvers, the sample quality with less than 10 NFE can still be improved. In this paper, we propose a unified sampling framework (USF) to study the optional strategies for solver. Under this framework, we further reveal that taking different solving strategies at different timesteps may help further decrease the truncation error, and a carefully designed \emph{solver schedule} has the potential to improve the sample quality by a large margin. Therefore, we propose a new sampling framework based on the exponential integral formulation that allows free choices of solver strategy at each step and design specific decisions for the framework. Moreover, we propose $S^3$, a predictor-based search method that automatically optimizes the solver schedule to get a better time-quality trade-off of sampling. We demonstrate that $S^3$ can find outstanding solver schedules which outperform the state-of-the-art sampling methods on CIFAR-10, CelebA, ImageNet, and LSUN-Bedroom datasets. Specifically, we achieve 2.69 FID with 10 NFE and 6.86 FID with 5 NFE on CIFAR-10 dataset, outperforming the SOTA method significantly. We further apply $S^3$ to Stable-Diffusion model and get an acceleration ratio of 2$\times$, showing the feasibility of sampling in very few steps without retraining the neural network.

With recent advancements in large language models, methods like chain-of-thought prompting to elicit reasoning chains have been shown to improve results on reasoning tasks. However, tasks that require multiple steps of reasoning still pose significant challenges to state-of-the-art models. Drawing inspiration from the beam search algorithm, we propose PathFinder, a tree-search-based reasoning path generation approach. It enhances diverse branching and multi-hop reasoning through the integration of dynamic decoding, enabled by varying sampling methods and parameters. Using constrained reasoning, PathFinder integrates novel quality constraints, pruning, and exploration methods to enhance the efficiency and the quality of generation. Moreover, it includes scoring and ranking features to improve candidate selection. Our approach outperforms competitive baselines on three complex arithmetic and commonsense reasoning tasks by 6% on average. Our model generalizes well to longer, unseen reasoning chains, reflecting similar complexities to beam search with large branching factors.

This paper delves into the realm of stochastic optimization for compositional minimax optimization - a pivotal challenge across various machine learning domains, including deep AUC and reinforcement learning policy evaluation. Despite its significance, the problem of compositional minimax optimization is still under-explored. Adding to the complexity, current methods of compositional minimax optimization are plagued by sub-optimal complexities or heavy reliance on sizable batch sizes. To respond to these constraints, this paper introduces a novel method, called Nested STOchastic Recursive Momentum (NSTORM), which can achieve the optimal sample complexity of $O(\kappa^3 /\epsilon^3 )$ to obtain the $\epsilon$-accuracy solution. We also demonstrate that NSTORM can achieve the same sample complexity under the Polyak-\L ojasiewicz (PL)-condition - an insightful extension of its capabilities. Yet, NSTORM encounters an issue with its requirement for low learning rates, potentially constraining its real-world applicability in machine learning. To overcome this hurdle, we present ADAptive NSTORM (ADA-NSTORM) with adaptive learning rates. We demonstrate that ADA-NSTORM can achieve the same sample complexity but the experimental results show its more effectiveness. All the proposed complexities indicate that our proposed methods can match lower bounds to existing minimax optimizations, without requiring a large batch size in each iteration. Extensive experiments support the efficiency of our proposed methods.

However, these algorithms simply deem causal relationships stand exclusively at the level of individual variables Data science is moving from the data-centric paradigm forward (micro-variable), ignoring the collective interactions from the science-centric paradigm, and causal revolution multiple variables (macro-variable). For instance, the brain is sweeping across various research fields. Causality learning can be characterized at a micro granularity of neurons and endeavors to unearth causal relationships among variables their synapses, but high-order synergistic subsystems are from observational data and generate causal graph, widespread, which typically sit between canonical functional that is, directed acyclic graph (DAG). Unlike correlationbased networks and may serve an integrative role (Varley study, causality analysis reveals the causal mechanism et al. 2023). Actually, observational data can be regarded of data generation. Identifying causality holds paramount as knowledge in the lowest granularity level, while knowledge significance for stable inference and rational decisions can be regarded as the abstraction of data at different in many applications, such as recommendation systems granularity levels (Wang 2017; Wang et al. 2022). Similar (Wang et al. 2020), medical diagnostics (Richens, Lee, and viewpoints appear in the research of complex systems, Johri 2020), epidemiology (Vandenbroucke, Broadbent, and which suggests that causal relationship is more pronounced Pearce 2016) and many others (Von Kügelgen et al. 2022).

After the discovery of Shor's algorithm and Grover's search algorithm, there has been many researches covering the concept of quantum advantage, which insists quantum computers will exhibit specific advantages over classical computers. Google named the advantage as "Quantum Supremacy"[1] and explains for specific problems, quantum computers can surpass classical computer in computation time and required memory capacity. However, complex quantum algorithms such as Shor's algorithm requires number of qubits and gate fidelity exponentially more than currently we have, and therefore investigating executable algorithms that show quantum advantage even with noisy and few qubits have been arised as an important question in the NISQ (Noisy Intermediate-Scale Quantum) era[2]. Among them, VQAs (Variational Quantum Algorithms)[3] have been remarked as efficient algorithms that can been executed in NISQ devices with low limitation. VQA is a hybrid quantum algorithm that utilizes classical optimizer and Variational Quantum Circuit (VQC), it first measures a state's probability after quantum circuit, and passes the result to classical optimizer.

This short paper gives an overview of the XCSP3 solver implemented in Picat. Picat provides several constraint modules, and the Picat XCSP3 solver uses the sat module. The XCSP3 solver mainly consists of a parser implemented in Picat, which converts constraints from XCSP3 format to Picat. The solver demonstrates the strengths of Picat, a logic-based language, in parsing, modeling, and encoding constraints into SAT. The solver submitted to the 2022 XCSP competition is based on the one that won the 2019 XCSP competition.

Adversarial training is one of the most popular methods for training methods robust to adversarial attacks, however, it is not well-understood from a theoretical perspective. We prove and existence, regularity, and minimax theorems for adversarial surrogate risks. Our results explain some empirical observations on adversarial robustness from prior work and suggest new directions in algorithm development. Furthermore, our results extend previously known existence and minimax theorems for the adversarial classification risk to surrogate risks.

This short paper gives an overview of the XCSP3 solver implemented in Picat. Picat provides several constraint modules, and the Picat XCSP3 solver uses the sat module. The XCSP3 solver mainly consists of a parser implemented in Picat, which converts constraints from XCSP3 format to Picat. The solver demonstrates the strengths of Picat, a logic-based language, in parsing, modeling, and encoding constraints into SAT. The solver submitted to the 2022 XCSP competition is based on the one that won the 2019 XCSP competition.

Reinforcement learning and Imitation Learning approaches utilize policy learning strategies that are difficult to generalize well with just a few examples of a task. In this work, we propose a language-conditioned semantic search-based method to produce an online search-based policy from the available demonstration dataset of state-action trajectories. Here we directly acquire actions from the most similar manipulation trajectories found in the dataset. Our approach surpasses the performance of the baselines on the CALVIN benchmark and exhibits strong zero-shot adaptation capabilities. This holds great potential for expanding the use of our online search-based policy approach to tasks typically addressed by Imitation Learning or Reinforcement Learning-based policies.