Genetic Algorithms for Tractable Bayesian Network Fusion via Pre-Fusion Edge Pruning

Bayesian Network (BN) fusion combines multiple input networks into a single structure, balancing dependency preservation with computational tractability. While unrestricted fusion retains all dependencies, it often results in overly complex networks with high treewidth, which affects inference scalability. Limited fusion mitigates this by pruning edges to control treewidth but risks overfitting to input-specific noise and omitting dependencies from the original BNs. This paper introduces a consensus framework that prioritizes shared structures among input networks while enforcing treewidth constraints, ensuring a good consensus. We propose genetic algorithms with advanced initialization, specialized operators, and a tailored fitness function. Additionally, we adapt existing methods to this problem and implement greedy baselines for benchmarking and further optimization. Experiments on synthetic and real-world BNs show the superiority of the proposed genetic algorithms over the adapted methods and greedy baselines.

Tensor Seeks Layout: Formalizing Layout Selection for ML Compilers

Modern machine learning compilers select tensor memory layouts to minimize execution cost under hardware constraints. Layout selection is global: an operator may be fastest under one layout while its consumers prefer another, and aligning these preferences requires explicit layout conversions that can hurt model performance. Despite its practical importance, layout selection lacks a formal basis, so current compilers rely on ad-hoc heuristics. This paper presents the first formal study of layout selection in machine learning compilers. We formulate the problem as combinatorial optimization over dataflow graphs, minimizing the sum of operator execution costs and the per-tensor cost of these conversions. Our theoretical analysis shows that optimal layout selection is computationally hard, even for programs containing only matrix multiplications over two-dimensional tensors. We design an optimal polynomial-time algorithm for dataflow graphs of bounded treewidth. For general instances, we give a weighted MaxSAT encoding that an off-the-shelf solver can optimize. The formulation unifies several existing layout optimization strategies, including XLA's layout assignment, partition dimension selection in systolic array compilers, and layout planning in mobile GPU optimizers. We implement the formalization in a production compiler for an AI accelerator and measure the execution time of the compiled models under greedy heuristics, the compiler's rule-based strategy, and an optimal solver. Simple heuristics degrade execution time by up to $5\times$ on some workloads. Where the compiler's cost model is accurate, the solver matches or beats the rule-based strategy. On workloads with complex data movement it falls behind, and since the solver minimizes the stated objective exactly, that gap isolates cost-model error from search quality, showing where compiler effort actually pays off.

Fixed-Parameter Tractability of Private Synthetic Data Generation

We study the problem of generating synthetic data under differential privacy. We establish fixed-parameter tractability (FPT) for this problem where the parameter is the treewidth of the query family's incidence graph. Our algorithms attain optimal error rates across all regimes and are realized by two different approaches: the first is based on linear programming (LP) and the FPT of the separation problem for the LP dual; the second is based on a subsampled private multiplicative weights method, where we obtain FPT for sampling from Gibbs distributions. Both approaches are unified by a dynamic programming framework over a tree decomposition.