Akio Tomiya

We study a parameter optimization of domain-wall fermions to improve chiral symmetry based on machine learning. Domain-wall fermions involve coefficients along the fifth dimension, which can be treated as trainable parameters to reduce the chiral symmetry violation caused by the finite extent of the fifth dimension. As the loss function, we use the residual mass estimated stochastically on a single gauge configuration. Numerical tests on a $L^3\times T\times L_5=4^3\times8\times8$ lattice demonstrate the feasibility of this framework.

The chiral phase transition in QCD-like theories can be Coleman-Weinberg type supercooling. This is possible to see when Beyond the Standard Model (say, axionlike particle or baryogenesis) is coupled to QCD of the Standard Model (called ordinary QCD). Identifying such a supecooling chiral phase transition thus opens a new window to search for new physics associated with the QCD phase transition epoch of the thermal history, to be probed by gravitational wave and primordial black hole productions. We discuss this possibility by monitoring ordinary QCD setup in a view of a two-flavor Nambu-Jona-Lasinio model in hot and/or dense medium, at the mean-field approximation level. We find that the identification essentially follows the scale violation classification: soft-scale breaking and quantum scale anomaly.

Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling bottlenecks on large lattices. We present a novel machine learning framework for lattice gauge fixing, where Wilson lines are utilized to construct gauge transformation matrices within a convolutional neural network. The model parameters are optimized via backpropagation, and we introduce a hybrid strategy that combines a neural-network-based transformation with subsequent iterative methods. Preliminary tests on SU(3) gauge theory ensembles for Coulomb gauge demonstrate the potential of this approach to improve the efficiency of lattice gauge fixing. Furthermore, we show that the model exhibits lattice size transferability, where parameters optimized on smaller lattices remain effective for larger volumes without additional training. This framework provides a scalable path toward mitigating critical slowing down in high-precision gauge fixing.

We investigate a bias-corrected machine learning (ML) strategy for estimating traces of the inverse Dirac operator, $\text{Tr}\, M^{-n}$ ($n=1,2,3,4$), motivated by the need for higher-order cumulants of the chiral condensate near the finite-temperature QCD critical endpoint. Our supervised regression framework is trained on Wilson-clover ensembles with the Iwasaki gauge action, and we explore two input feature scenarios: one using $\text{Tr}\, M^{-1}$ and another relying solely on gauge observables (plaquette and rectangle), enabling a fully feature-based prediction pipeline. Using $\text{Tr}\, M^{-1}$ both as a physical input to cumulant construction and as a feature for predicting higher powers, we find that even with $\sim1\%$ labeled data, the resulting susceptibility, skewness, and kurtosis remain statistically consistent with fully measured baselines, reducing computational cost to about $26\%$. In the feature-only approach, where correlations rather than explicit stochastic traces drive the predictions, bias correction plays a more pronounced role. We quantify this impact through multi ensemble reweighting across nearby quark masses. Our results demonstrate that bias-corrected ML estimates can significantly reduce measurement overhead while preserving the stability of higher-order observables relevant for locating the QCD critical endpoint. Code for this work is available at https://github.com/saintbenjamin/Deborah.jl .

We enable the automatic construction of Hybrid Monte Carlo (HMC) forces in lattice gauge theory by performing reverse-mode automatic differentiation at the level of optimized LLVM intermediate representation, making the approach applicable to any language that lowers lattice action code to LLVM. In practice, this means that once the action evaluation routine is implemented, the corresponding HMC force can be generated automatically from the same code path, without deriving or maintaining a separate force routine. The method preserves conventional imperative, in-place implementations and enables a single-source workflow in which forces are generated directly from the action code while inheriting compiler optimizations. We perform end-to-end reverse-mode differentiation of both gauge and Wilson fermion actions. For the Wilson fermion case, we find that the force generated by automatic differentiation achieves performance comparable to a conventional hand-written fermion force implementation. The same differentiation pipeline targets both CPU and GPU backends, providing a practical route to performance-portable force construction for compositional lattice actions.