MIT Center for Theoretical Physics – a Leinweber Institute

The 1D flux power spectrum ($P_{\mathrm{1D}}$) of the Ly$α$ forest provides an exceptionally high-resolution probe of structure formation down to small scales ($k\approx1-10~\text{$h~$Mpc$^{-1}$}$). These scales carry the imprints of massive neutrinos, warm dark matter, and the running of the primordial power spectrum spectral index. The effective field theory (EFT) is a promising perturbative approach to systematically and efficiently describe the Ly$α$ forest, but it faces challenges in its application to $P_{\mathrm{1D}}$, as many EFT parameters become degenerate when projected along the line of sight. In addition, this projection generates new stochastic terms from the integration over small-scale modes. In this work, we address these issues by compressing the EFT model space using the Fisher matrix formalism and linearizing the resulting compression directions, enabling analytic template marginalization and significantly reducing the computational cost of likelihood evaluation. We use hydrodynamical simulations to obtain a baseline estimate of EFT parameters, and use the DESI DR1 $P_{\mathrm{1D}}$ measurements to derive compression directions. We then marginalize over deviations from the baseline using these compression directions and forecast the constraining power of our formalism. We find that even in conservative scenarios where each data redshift bin requires its own set of EFT parameters, the cosmological constraints saturate with the linear bias, two leading-order 1D stochastic terms, and three principal combinations of the remaining EFT templates. In this case, our forecasted precision of the amplitude ($Δ^2_p$) and the logarithmic slope ($n_p$) of the linear matter power spectrum at the pivot scale ($k_p=0.7~\text{Mpc}^{-1}$) is $10\%$ and $2.0\%$, respectively, which is similar to emulator-based analyses that include observational data systematics.

We present a solvable Hamiltonian that realizes an exact lattice chiral $U(1)_V \times U(1)_A$ symmetry. Nielsen-Ninomiya-type no-go theorems are evaded by using lattice bosons rather than fermions. The continuum limit is a compact boson field theory with an axion-like coupling. The $U(1)_V$ symmetry shifts the scalar, while $U(1)_A$ acts on local operators associated with short axion strings and is transmuted into a higher-form symmetry in the continuum limit. We demonstrate the chiral anomaly by showing that the lattice theta angle is shifted by an axial rotation when $U(1)_V$ is gauged. Gauging either $U(1)_V$ or $U(1)_A$ leads to lattice non-invertible and 2-group symmetries, respectively, matching the continuum picture.

In particle physics, as in many areas of science, parameter inference relies on simulations to bridge the gap between theory and experiment. Recent developments in simulation-based inference have boosted the sensitivity of analyses; however, biases induced by simulation-data mismodeling can be difficult to control within standard inference pipelines. In this work, we propose a Template-Adapted Mixture Model to confront this problem in the context of signal fraction estimation: inferring the population proportion of signal in a mixed sample of signal and background, both of which follow arbitrarily complex distributions. We harness many biased simulations to perform data-driven estimates of each process distribution in the signal region, substantially reducing the bias on the signal fraction due to the domain shift between simulation and reality. We explore different methodological choices, including model selection, feature representation, and statistical method, and apply them to a Gaussian toy example and to a semi-realistic di-Higgs measurement. We find that the presented methods successfully leverage the biased simulations to provide estimates with well-calibrated uncertainties.

We introduce Sven (Singular Value dEsceNt), a new optimization algorithm for neural networks that exploits the natural decomposition of loss functions into a sum over individual data points, rather than reducing the full loss to a single scalar before computing a parameter update. Sven treats each data point’s residual as a separate condition to be satisfied simultaneously, using the Moore-Penrose pseudoinverse of the loss Jacobian to find the minimum-norm parameter update that best satisfies all conditions at once. In practice, this pseudoinverse is approximated via a truncated singular value decomposition, retaining only the $k$ most significant directions and incurring a computational overhead of only a factor of $k$ relative to stochastic gradient descent. This is in comparison to traditional natural gradient methods, which scale as the square of the number of parameters. We show that Sven can be understood as a natural gradient method generalized to the over-parametrized regime, recovering natural gradient descent in the under-parametrized limit. On regression tasks, Sven significantly outperforms standard first-order methods including Adam, converging faster and to a lower final loss, while remaining competitive with LBFGS at a fraction of the wall-time cost. We discuss the primary challenge to scaling, namely memory overhead, and propose mitigation strategies. Beyond standard machine learning benchmarks, we anticipate that Sven will find natural application in scientific computing settings where custom loss functions decompose into several conditions.