Vinod Nair

David Warde-Farley, Vinod Nair, Yujia Li et al. · deepmind

We propose an incomplete algorithm for Maximum Satisfiability (MaxSAT) specifically designed to run on neural network accelerators such as GPUs and TPUs. Given a MaxSAT problem instance in conjunctive normal form, our procedure constructs a Restricted Boltzmann Machine (RBM) with an equilibrium distribution wherein the probability of a Boolean assignment is exponential in the number of clauses it satisfies. Block Gibbs sampling is used to stochastically search the space of assignments with parallel Markov chains. Since matrix multiplication is the main computational primitive for block Gibbs sampling in an RBM, our approach leads to an elegantly simple algorithm (40 lines of JAX) well-suited for neural network accelerators. Theoretical results about RBMs guarantee that the required number of visible and hidden units of the RBM scale only linearly with the number of variables and constant-sized clauses in the MaxSAT instance, ensuring that the computational cost of a Gibbs step scales reasonably with the instance size. Search throughput can be increased by batching parallel chains within a single accelerator as well as by distributing them across multiple accelerators. As a further enhancement, a heuristic based on unit propagation running on CPU is periodically applied to the sampled assignments. Our approach, which we term RbmSAT, is a new design point in the algorithm-hardware co-design space for MaxSAT. We present timed results on a subset of problem instances from the annual MaxSAT Evaluation's Incomplete Unweighted Track for the years 2018 to 2021. When allotted the same running time and CPU compute budget (but no TPUs), RbmSAT outperforms other participating solvers on problems drawn from three out of the four years' competitions. Given the same running time on a TPU cluster for which RbmSAT is uniquely designed, it outperforms all solvers on problems drawn from all four years.

Michael Schaarschmidt, Dominik Grewe, Dimitrios Vytiniotis et al.

The rapid rise in demand for training large neural network architectures has brought into focus the need for partitioning strategies, for example by using data, model, or pipeline parallelism. Implementing these methods is increasingly supported through program primitives, but identifying efficient partitioning strategies requires expensive experimentation and expertise. We present the prototype of an automated partitioner that seamlessly integrates into existing compilers and existing user workflows. Our partitioner enables SPMD-style parallelism that encompasses data parallelism and parameter/activation sharding. Through a combination of inductive tactics and search in a platform-independent partitioning IR, automap can recover expert partitioning strategies such as Megatron sharding for transformer layers.

Nicolas Sonnerat, Pengming Wang, Ira Ktena et al.

Large Neighborhood Search (LNS) is a combinatorial optimization heuristic that starts with an assignment of values for the variables to be optimized, and iteratively improves it by searching a large neighborhood around the current assignment. In this paper we consider a learning-based LNS approach for mixed integer programs (MIPs). We train a Neural Diving model to represent a probability distribution over assignments, which, together with an off-the-shelf MIP solver, generates an initial assignment. Formulating the subsequent search steps as a Markov Decision Process, we train a Neural Neighborhood Selection policy to select a search neighborhood at each step, which is searched using a MIP solver to find the next assignment. The policy network is trained using imitation learning. We propose a target policy for imitation that, given enough compute resources, is guaranteed to select the neighborhood containing the optimal next assignment amongst all possible choices for the neighborhood of a specified size. Our approach matches or outperforms all the baselines on five real-world MIP datasets with large-scale instances from diverse applications, including two production applications at Google. It achieves $2\times$ to $37.8\times$ better average primal gap than the best baseline on three of the datasets at large running times.