Abstract--The Minimum Bisection Problem is a well-known NP-hard problem in combinatorial optimization, with practical applications in areas such as parallel computing, network design, and machine learning. In this paper, we examine the potential of using D-Wave Systems' quantum annealing solvers to solve the Minimum Bisection Problem, which we formulate as a Quadratic Unconstrained Binary Optimization model. A key challenge in this formulation lies in choosing an appropriate penalty parameter, as it plays a crucial role in ensuring both the quality of the solution and the satisfaction of the problem's constraints. T o address this, we introduce a novel machine learning-based approach for adaptive tuning of the penalty parameter . Specifically, we use a Gradient Boosting Regressor model trained to predict suitable penalty parameter values based on structural properties of the input graph, the number of nodes and the graph's density. This method enables the penalty parameter to be adjusted dynamically for each specific problem instance, improving the solver's ability to balance the competing goals of minimizing the cut size and maintaining equally sized partitions. We test our approach on a large dataset of randomly generated Erd os-R enyi graphs with up to 4000 nodes, and we compare the results with classical partitioning algorithms, Metis and Kernighan-Lin. Experimental findings demonstrate that our adaptive tuning strategy significantly improves the performance of quantum annealing hybrid solver and consistently outperforms the classical methods used, indicating its potential as an alternative for graph partitioning problem. RAPH partitioning is a fundamental problem in combinatorial optimization with applications in task scheduling for multiprocessor computers with focus on parallel computation, partitioning the circuit with applications in microchips design, social network analysis e.g. The problem involves dividing a given graph G into two or more subsets while optimizing certain objective, such as minimizing the number of inter-edges and/or assigned costs between them and producing balanced partitions. While general Graph Partitioning Problem (GPP) allow for flexible partition sizes, a significant special case is the Minimum Bisection Problem (MBP), where the graph is partitioned into two equal-sized subsets while minimizing the number of inter-edges [1].

Protein-ligand binding affinity (PLBA) prediction is the fundamental task in drug discovery. Recently, various deep learning-based models predict binding affinity by incorporating the three-dimensional structure of protein-ligand complexes as input and achieving astounding progress. However, due to the scarcity of highquality training data, the generalization ability of current models is still limited. In addition, different bioassays use varying affinity measurement labels (i.e., IC50, Ki, Kd), and different experimental conditions inevitably introduce systematic noise, which poses a significant challenge to constructing high-precision affinity prediction models. To address these issues, we (1) propose Multi-task Bioassay Pre-training (MBP), a pre-training framework for structure-based PLBA prediction; (2) construct a pre-training dataset called ChEMBL-Dock with more than 300k experimentally measured affinity labels and about 2.8M docked three-dimensional structures. By introducing multi-task pre-training to treat the prediction of different affinity labels as different tasks and classifying relative rankings between samples from the same bioassay, MBP learns robust and transferrable structural knowledge from our new ChEMBL-Dock dataset with varied and noisy labels. Experiments substantiate the capability of MBP as a general framework that can improve and be tailored to mainstream structure-based PLBA prediction tasks. To the best of our knowledge, MBP is the first affinity pre-training model and shows great potential for future development. All codes and data are available on the online platform https://github.com/jiaxianyan/MBP.

For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is smooth at every iterate, the corresponding local models are unstable and the number of cutting planes invoked by traditional remedies is difficult to bound, leading to convergences guarantees that are sublinear relative to the cumulative number of gradient evaluations. We instead propose a multipoint generalization of the gradient descent iteration for local optimization. While designed with general objectives in mind, we are motivated by a ``max-of-smooth'' model that captures the subdifferential dimension at optimality. We prove linear convergence when the objective is itself max-of-smooth, and experiments suggest a more general phenomenon.

Animals execute goal-directed behaviours despite the limited range and scope of their sensors. To cope, they explore environments and store memories maintaining estimates of important information that is not presently available. Recently, progress has been made with artificial intelligence (AI) agents that learn to perform tasks from sensory input, even at a human level, by merging reinforcement learning (RL) algorithms with deep neural networks, and the excitement surrounding these results has led to the pursuit of related ideas as explanations of non-human animal learning. However, we demonstrate that contemporary RL algorithms struggle to solve simple tasks when enough information is concealed from the sensors of the agent, a property called "partial observability". An obvious requirement for handling partially observed tasks is access to extensive memory, but we show memory is not enough; it is critical that the right information be stored in the right format. We develop a model, the Memory, RL, and Inference Network (MERLIN), in which memory formation is guided by a process of predictive modeling. MERLIN facilitates the solution of tasks in 3D virtual reality environments for which partial observability is severe and memories must be maintained over long durations. Our model demonstrates a single learning agent architecture that can solve canonical behavioural tasks in psychology and neurobiology without strong simplifying assumptions about the dimensionality of sensory input or the duration of experiences.

We demonstrate that any physical object, as long as its volume is conserved when coupled with suitable operations, provides a sophisticated decision-making capability. We consider the problem of finding, as accurately and quickly as possible, the most profitable option from a set of options that gives stochastic rewards. These decisions are made as dictated by a physical object, which is moved in a manner similar to the fluctuations of a rigid body in a tug-of-war game. Our analytical calculations validate statistical reasons why our method exhibits higher efficiency than conventional algorithms. The computing principles in modern digital paradigms have been designed to be dissociated from the underlying physics of natural phenomena [1].

In our experiments with four well-known systems for solving partially observable planning problems  (Contingent-FF, MBP, PKS, and POND), we were greatly surprised to find that they could only solve problems with a small number of contingencies. Apparently they were repeatedly trying to solve many combinations of contingencies at once, thus unnecessarily using up huge amounts of time and space. This difficulty can be alleviated if the planner can maintain focus on the contingency that it is currently trying to solve. We provide a way to accomplish this by incorporating focusing information directly into the planning domain's operators, without any need to modify the planning algorithm itself. This enables the above planners to solve larger problems and to solve them much more quickly. We also provide a new planner, FOCUS, in which focusing information can be provided as a separate input. This provides even better performance by allowing the planner to utilize more extensive focusing information.