FERMI-ML: Machine Learning in Fermionic Systems

• FERMI-ML is a collection of methods integrating fermionic physics with machine learning, enabling extraction of quantum many-body observables and robust data classification.
• It encompasses CNN frameworks for SU(N) Fermi gases, supervised and unsupervised pipelines for astrophysical γ-ray source classification, and quantum-inspired kernel techniques that achieve high accuracy.
• The paradigm drives advances in accelerator control through deep reinforcement learning, mixed-precision neural Fermi-operator expansions, and energy-efficient in-memory hardware for embedded TinyML.

FERMI-ML refers to a set of distinct but thematically related machine learning and quantum-inspired paradigms, each of which integrates fermionic physics or Fermi-instrumentation data with contemporary machine learning, computational, or accelerator hardware. The term encompasses frameworks spanning neural-network analysis of quantum gases, data-driven classification of high-energy astrophysical sources, quantum-inspired and quantum-native machine learning architectures, and specialized hardware for ultra-efficient embedded AI. Below, representative research groups and subfields are detailed, with emphasis on published methodological, theoretical, and applied advances.

1. Neural-Network Extraction of Thermodynamic and Many-Body Observables in SU(N) Fermi Gases

FERMI-ML in ultracold atom experiments refers to a heuristic convolutional neural network (CNN) framework for directly classifying and interpreting spin and thermodynamic observables from experimental single-shot density and momentum profiles of SU(N) Fermi gases. The architecture consists of a 5-layer CNN operating on 201×201 pixel absorption images (input layer → 24 convolutional kernels → average pooling → dropout → 4-class softmax output). The model is trained for supervised classification of the spin symmetry class (SU(1), SU(2), SU(5), SU(6)) at 94% accuracy using 200 images/class, with rigorous preprocessing (PCA fringe removal, normalization, post-selection on atomic cloud width) and no need for artificial data augmentation.

Crucially, FERMI-ML enables the inference of subtle many-body effects—most notably, thermodynamic compressibility and Tan’s contact—by decomposing classification performance on systematically filtered images. Manipulating momentum-space images to suppress or isolate features (high-$k$ tails, azimuthal density fluctuations, etc.) precisely identifies the physical observables contributing to spin discrimination and compressibility measures. This establishes a model-agnostic ML protocol for extracting interaction-driven quantities in regimes where analytic Fermi-liquid formulas are unknown or single-shot resolution is unattainable by human or direct statistical analysis.

Potential generalizations include:

• Extension to regression architectures for continuous observable extraction (e.g., $(T/T_F)$, $k_Fa_s$).
• Application in lattice systems, topological phases, and strongly correlated fluids where standard fluctuation-dissipation analysis fails.
• Cross-domain adoption for quantum gas microscopes and correlated solid-state imaging.

This approach provides a template for ML-guided physical discovery in quantum matter, leveraging manipulated data workflows and accuracy-trace-based feature interpretability (Zhao et al., 2020).

2. Machine Learning for Fermi-LAT Source Catalog Classification and All-Sky Map Inference

FERMI-ML in the astrophysical context refers to a suite of supervised and unsupervised machine learning pipelines for classifying $\gamma$-ray sources in the Fermi Large Area Telescope (LAT) catalogs as well as for denoising, sharpening, and analyzing variable structure in all-sky gamma-ray maps.

Catalog Classification: Multiple efforts utilize features spanning spatial (GLON, GLAT), spectroscopic (energy flux, indices, curvature), and temporal (variability indices and hardness ratios) dimensions to train classifiers such as Random Forests, Boosted Decision Trees, Neural Networks, Logistic Regression, and ensemble frameworks. Key challenges include sample impurity, class imbalance, and population-shift between well-identified, bright sources and unassociated, fainter objects.

Three-class (AGN/PSR/OTHER) or two-class (AGN/PSR) probabilistic models assign soft class probabilities $P(c|x)$, which are then exploited for population studies and source-count distribution $N(>S)$. Notable advances include algorithmic correction (post hoc or direct multi-class learning) for misclassified or interspersed "OTHER" objects, Bayesian-Gaussian outlier filtering to counteract erroneous soft-spectrum assignments, and ensemble-based balanced accuracy maximization.

All-Sky Map Sharpening and Variability Detection: Image-processing ML (dictionary learning, U-net, Noise2Noise) can recover one-year-equivalent structural features (RMSE, SSIM performance up to 0.85) from week-long photon count maps, providing sharper all-sky representations and automated variable-source (blazar/AGN) detection by analyzing ML-GT systematic residuals. This pipeline is broadly model-independent, scalable to all-sky monitors across wavebands, and suitable for transient or structure forecasting (Zhu et al., 2023, Bhat et al., 2021, Xiao et al., 2020, Sato et al., 2021).

3. Quantum-Inspired and Quantum-Native Machine Learning: FermiML and the Fermi Machine

Fermionic Machine Learning (FermiML) denotes a quantum kernel learning framework in which classical data are embedded via parameterized matchgate circuits—i.e., circuits simulating free, non-interacting Majorana fermions—mapping directly to efficiently simulable Gaussian unitary evolutions. In this model, support vector machine kernels are generated by computing the overlap

$$\mathcal{K}(x,x') = \left| \langle 0 | U_{\text{MG}}(x)^\dagger U_{\text{MG}}(x') | 0 \rangle \right|^2$$

where $U_{\text{MG}}(x)$ is the matchgate circuit encoding the data point $x$.

FermiML kernels, due to polynomial scaling ($O(N^3)$ for $N$ qubits/features), enable systematic benchmarking of quantum learning protocols in regimes inaccessible to generic PQC (parameterized quantum circuit) simulations. Empirically, FermiML achieves $\sim94$–$96\%$ accuracy on canonical classification tasks (Wisconsin Breast Cancer, Digits) for $N \gtrsim 15$, typically matching or exceeding unrestricted PQC kernels in expressivity for both binary and multi-class SVM settings (Gince et al., 29 Apr 2024).

Fermi Machine refers to a variational neural-network ansatz for quantum many-body ground states, leveraging exact correspondences between interacting fermion models (e.g., the Hubbard model) and noninteracting multi-component fermionic systems. By fractionalizing each physical fermion into a visible and a hierarchy of hidden Majorana modes, and by constructing the trial wavefunction as a Slater determinant on this augmented noninteracting Hilbert space, Fermi Machine achieves exact representation of the 1- and 2-site Hubbard model and highly accurate solutions ($<10^{-6}$ relative error) for 4-site benchmarks. The method generalizes to systematically improvable architectures with deep hidden layers and nonlocal hybridization, enabling scalable, sign-problem-free many-body solver construction (Imada, 30 Jul 2024).

4. Machine-Learning Enhanced Control and Numerical Linear Algebra for Fermionic Systems

FERMI-ML designates a collection of ML and deep RL algorithms for direct control of physical systems governed by Fermi statistics and Hamiltonians, as well as for developing efficient algorithms for quantum calculations.

Reinforcement Learning for Accelerator Optimization: For the FERMI Free Electron Laser (FEL), both model-free and model-based deep RL agents (twin-network NAF2 for Q-learning; AE-DYNA for Bayesian-model-based RL) perform intensity optimization in continuous voltage-action spaces. Model-based agents employ DYNA-style synthetic rollouts and anchored ensemble regularization to achieve near-optimal policies (95% intensity) within $<1000$ real transitions, demonstrating high sample efficiency and robustness to noise—a requirement for practical deployment on physical accelerators (Hirlaender et al., 2020).

Mixed-Precision Neural Fermi-Operator Expansion: In quantum chemistry, the recursive Fermi-operator expansion (SP2) for building the electronic density matrix is recast as a deep neural network with polynomial activations (matrix square) and learnable weight/bias parameters. This "unrolled" network architecture is ideally matched to GPU tensor cores for mixed-precision computations, yielding $>100$ TFLOPs and $10\times$ speedup compared to diagonalization, while maintaining high-precision occupation number fidelity even at finite temperature. Optimization of layer weights can accelerate purification and enable explicit learning of the finite-$T$ Fermi-Dirac distribution (Finkelstein et al., 2021).

5. In-Memory and Resource-Efficient Hardware for Embedded TinyML (FERMI-ML SRAM)

FERMI-ML in hardware design contexts specifies a digital memory-in-situ (MIS) SRAM macro for low-power, area-optimized TinyML inference. The macro features:

• A 9T XNOR-capable bit-cell (RX9T) merging storage with in-situ compute (XNOR/MAC, binary/ternary CAM).
• A 22-transistor (C22T) logarithmic-depth compressor-tree with $O(\log N)$ accumulation latency for 1–64-bit MACs, drastically reducing power (30–40%) and area (1.9$\times$) compared to contemporary adders.
• Run-time reconfigurability for integer, 4-bit floating-point, and Posit encoding with dual in-situ compute/CAM lookup, facilitating LUT-based non-linear activations in-memory.
• Post-layout metrics: 1.93 TOPS throughput, 364 TOPS/W efficiency at 350 MHz (65 nm CMOS), and $>$97.5% QoR for deep CNN workloads.

FERMI-ML's design paradigm demonstrates an integrated, energy-optimal path for embedded AI in edge AIoT domains, supporting high-density mixed-precision MAC and advanced search/activation primitives (Lokhande et al., 16 Nov 2025).

6. Broader Implications and Future Directions

FERMI-ML strategies highlight the intersection of fermionic modeling, hardware-aware algorithm design, and ML for high-sensitivity physical diagnostics. They provide foundational methodologies for:

• Nonparametric observable extraction in quantum matter using ML feature-causality tracing.
• Robust, uncertainty-calibrated source classification in astrophysics, critical for population statistics and dark matter searches as in the systematic-feature approach for unassociated sources (Gammaldi et al., 2022).
• Quantum-inspired machine learning pipelines that balance expressivity and tractability, directly informing the design of near-term quantum and hybrid computing architectures.
• Efficient, end-to-end AI pipelines from data collection to computation and inference, minimizing relaxation, readout, and processing bottlenecks.

Future research directions include integration of Fermi-ML frameworks with tensor-network and quantum-circuit architectures for many-body simulation, adaption for real-time control in high-dimensional systems, and hardware/algorithms co-design for increasingly resource-constrained AI deployments. Domain-agnostic extensions and cross-fertilization with other statistical physics-ML paradigms—such as deformation-driven quantum statistics (Seifi et al., 2 Nov 2025)—are plausible avenues, potentially yielding further insights into nonequilibrium, nonextensive, or highly correlated regimes.