Implementing Boolean functions with circuits consisting of logic gates is fundamental in digital computer design. However, the implemented circuit must be exactly equivalent, which hinders generative neural approaches on this task due to their occasionally wrong predictions. In this study, we introduce a generative neural model, the “Circuit Transformer”, which eliminates such wrong predictions and produces logic circuits strictly equivalent to given Boolean functions. The main idea is a carefully designed decoding mechanism that builds a circuit step-by-step by generating tokens, which has beneficial “cutoff properties” that block a candidate token once it invalidate equivalence. In such a way, the proposed model works similar to typical LLMs while logical equivalence is strictly preserved. A Markov decision process formulation is also proposed for optimizing certain objectives of circuits. Experimentally, we trained an 88-million-parameter Circuit Transformer to generate equivalent yet more compact forms of input circuits, outperforming existing neural approaches on both synthetic and real world benchmarks, without any violation of equivalence constraints. Code: https://github.com/snowkylin/circuit-transformer

Self-consistent Field (SCF) equation is a type of nonlinear eigenvalue problem in which the matrix to be eigen-decomposed is a function of its own eigenvectors. It is of great significance in computational science for its connection to the Schrödinger equation. Traditional fixed-point iteration methods for solving such equations suffer from non-convergence issues. In this work, we present a novel perspective on such SCF equations as a principal component analysis (PCA) for non-stationary time series, in which a distribution and its own top principal components are mutually updated over time, and the equilibrium state of the model corresponds to the solution of the SCF equations. By the new perspective, online PCA techniques are able to engage in so as to enhance the convergence of the model towards the equilibrium state, acting as a new set of tools for converging the SCF equations. With several numerical adaptations, we then develop a new algorithm for converging the SCF equation, and demonstrated its high convergence capacity with experiments on both synthesized and real electronic structure scenarios.

An algebraic modeling system (AMS) is a type of mathematical software for optimization problems, which allows users to define symbolic mathematical models in a specific language, instantiate them with given source of data, and solve them with the aid of external solver engines. With the bursting scale of business models and increasing need for timeliness, traditional AMSs are not sufficient to meet the following industry needs: 1) million-variable models need to be instantiated from raw data very efficiently; 2) Strictly feasible solution of million-variable models need to be delivered in a rapid manner to make up-to-date decisions against highly dynamic environments. Grassland is a rapid AMS that provides an end-to-end solution to tackle these emerged new challenges. It integrates a parallelized instantiation scheme for large-scale linear constraints, and a sequential decomposition method that accelerates model solving exponentially with an acceptable loss of optimality. Extensive benchmarks on both classical models and real enterprise scenario demonstrate 6-10x speedup of Grassland over state-of-the-art solutions on model instantiation. Our proposed system has been deployed in the large-scale real production planning scenario of Huawei. With the aid of our decomposition method, Grassland successfully accelerated Huawei's million-variable production planning simulation pipeline from hours to 3-5 minutes, supporting near-real-time production plan decision making against highly dynamic supply-demand environment.

The 3-dimensional bin packing problem (3D-BPP) is not only fundamental in combinatorial optimization but also widely applied in real world logistics. In the modern logistics industry, the complexity of constraints, heterogeneity of cargoes and scale of orders are dramatically increased, leading to great challenges to devise packing plans up to standard. While the tree search algorithm is proved to be a successful paradigm to solve the 3D-BPP, it is too time-consuming to be applied in the aforementioned large-scale scenarios. To overcome the limitation, we propose a data-driven tree search algorithm (DDTS) to tackle the 3D-BPP. The solution space with complicated constraints is explored by a tree search algorithm, and a convolutional neural network trained with historical data guides pruning the tree so as to accelerate the search process. Computational experiments on real-world datasets show that our algorithm outperforms the state-of-the-art approach with a loading rate improvement of 2.47%. Moreover, the deep learning technique increases searching efficiency by 37.14% with only 0.04% performance loss. The algorithm has been deployed in Huawei Logistics System, which increases the loading rate by 3% and could reduce the logistics cost by millions of dollars per year. To the best of our knowledge, we are the first to embed pruning networks into tree search for the large-scale 3D-BPP.

Neural encoder-decoder models have been widely applied to conversational response generation, which is a research hot spot in recent years. However, conventional neural encoder-decoder models tend to generate commonplace responses like “I don’t know” regardless of what the input is. In this paper, we analyze this problem from a new perspective: latent vectors. Based on it, we propose an easy-to-extend learning framework named MEMD (Multi-Encoder to Multi-Decoder), in which an auxiliary encoder and an auxiliary decoder are introduced to provide necessary training guidance without resorting to extra data or complicating network’s inner structure. Experimental results demonstrate that our method effectively improve the quality of generated responses according to automatic metrics and human evaluations, yielding more diverse and smooth replies.