The motivation comes from a long-standing tension in the LHC programme. The Standard Model describes collider data superbly, yet it leaves basic observations unexplained, from dark matter to neutrino masses and the baryon asymmetry of the Universe. Most searches for physics beyond the Standard Model are optimised for specific benchmark signatures, which is powerful when the signal is known in advance but can blind experiments to the unexpected. Anomaly detection offers a complementary strategy: a model is trained only on typical background events, learns to compress and reconstruct them, and assigns large anomaly scores to events it reconstructs poorly. Reconstruction-based autoencoders have become a standard reference point in this field, but recent community comparisons have repeatedly emphasised that performance depends strongly on the input representation and the built-in structure of the model, not on reconstruction quality alone.

Jets, the collimated sprays of hadrons produced when energetic quarks or gluons fragment, are a natural testing ground for this idea. Ordinary QCD jets dominate proton-proton collisions, while jets from boosted heavy-particle decays, such as hadronic top-quark decays, carry richer internal substructure and more complex radiation patterns. Crucially, this substructure arises from a branching cascade: a high-energy parton radiates, its daughters radiate again, and the observable jet is built up through a nested sequence of splittings across several angular and momentum scales. Hard, large-angle splittings determine the coarse prong structure, while softer, more collinear radiation refines it at progressively smaller scales. A dense autoencoder treats its input as a largely unstructured vector and must learn any such hierarchy from scratch, which is flexible but wasteful. The authors therefore posed a concrete, testable hypothesis: if ordered jet constituents are locally compressible in a way that follows the shower geometry, a hierarchical architecture should model the background more economically than a dense map.

That is where MERA enters. Originally developed in quantum many-body physics, MERA is a tensor-network construction that alternates coarse-graining transformations with disentangling operations, allowing relevant correlations to be retained across length scales rather than being lost during compression. In the jet context, the coarse-graining steps resemble the progressive aggregation of information from nearby constituents into larger-scale features, while the disentangling operations are designed to reorganise short-range correlations before information is passed to the next scale. To the authors’ knowledge, a MERA-inspired autoencoder had not previously been proposed, and this architecture had not been explored in collider anomaly detection; earlier work had considered quantum autoencoders and matrix-product-state models, but not a MERA-inspired encoder-decoder acting directly on ordered jet constituents.

The mathematical case for the disentanglers is explicit. For a local pair of sites, a tree tensor network without disentanglers compresses the centred local fluctuation by direct projection onto a low-dimensional subspace. MERA first rotates the local basis and only then truncates. The expected local truncation error shows that, for a fixed rotation, the optimal projection is simply PCA in the rotated basis, so the role of the disentangler is to seek a basis in which the degrees of freedom retained by the subsequent coarse-graining step are as informative as possible. In jet language, this is exactly the mechanism one would want if short-distance angular correlations must be reorganised before a coarse description is formed. For moderate bond dimensions, each disentangler carries on the order of the fourth power of the bond dimension in parameters and each isometry its cube, while the total number of local tensors grows linearly with the number of sites, giving a parameter count that scales linearly with the input size for fixed bond dimension.

The implementation is a MERA-inspired neural architecture rather than a canonical tensor network. Each jet is represented by its 48 leading constituents, which retain on average 98.9 percent of the total constituent transverse momentum, described by three features each: transverse momentum and jet-centred angular coordinates, yielding a 144-dimensional input. Because jets are fundamentally unordered sets, the authors reorder constituents using a geometry-based nearest-neighbour walk in the angular plane, starting from the hardest constituent and repeatedly appending the nearest unvisited neighbour. The encoder then applies four binary coarse-graining stages, 48 to 24 to 12 to 6 to 3, with a fixed site dimension of 3 at every scale. At each layer, a learned local mixing map plays the role of a disentangler and a learned coarse-graining map plays the role of an isometry, followed by leaky-ReLU activations at intermediate levels. The decoder mirrors the hierarchy with untied tensors, since exact inversion is impossible once information has been discarded, and training uses soft orthogonality and isometry penalties rather than exact manifold constraints.

The benchmark is deliberately controlled. All methods, including the MERA-inspired model, the dense autoencoder, the corresponding tree-tensor-network limit, and classical unsupervised baselines such as PCA, a Gaussian Mahalanobis model, and Isolation Forest, are trained or fitted only on background QCD jets from the Top Quark Tagging Reference Dataset, generated with Pythia8 and passed through a fast Delphes detector simulation for 14 TeV proton-proton collisions with jets of 550 to 650 GeV. Signal jets from hadronically decaying top quarks enter only at validation and test time, and the top jets serve as a well-understood proxy anomaly rather than a literal model of new physics. In the nominal benchmark, the MERA-inspired model attains the largest mean test AUC at all three latent dimensions, reaching 0.7959, 0.7885, and 0.7963 at latent dimensions 8, 16, and 32, compared with 0.7616, 0.7487, and 0.7550 for the dense autoencoder. The mean gains of roughly 0.034 to 0.041 in AUC come with only about 5,000 to 5,500 trainable parameters, against 16,800 to 18,000 for the dense models.

The targeted follow-up studies then clarify why the multiscale construction works. A training-free local-compressibility diagnostic showed that the locality-preserving ordering reduces the mean adjacent-site separation to 0.131 in angular distance, compared with 0.361 for transverse-momentum ordering and about 0.397 for random permutations, and yields the highest retained-variance fractions in the first two local compression layers, 0.869 and 0.920 against 0.721 and 0.830 for the random control. Consistently, the completed ordering study gave the strongest MERA performance with the locality-preserving representation, with mean AUC values of 0.780, 0.777, and 0.774 at the three latent dimensions, versus 0.702, 0.698, and 0.702 for random orderings. Strikingly, the dense autoencoder does not share this benefit: it performs substantially better with transverse-momentum or random orderings, reaching mean AUC values above 0.819, while PCA shows no uniform locality advantage either. The locality gain therefore arises specifically when the event-dependent ordering is paired with an architecture whose first operations act on neighbouring sites, not as a generic consequence of preprocessing.

The authors also isolated the disentangling layers themselves through a direct ablation. At the strongest compression bottleneck, latent dimension 8, they compared the full model with a variant in which every disentangler is fixed to the identity, operationally mimicking the corresponding tree hierarchy while leaving everything else unchanged. The full model reached a mean test AUC of 0.8002, with a standard deviation of 0.0052, compared with 0.7922, with a standard deviation of 0.0138, for the identity-disentangler limit, and the mean true-positive rate at a false-positive rate of one in a thousand improved from 1.10 to 1.37 in units of one thousandth. Because the uncertainties overlap across the eight evaluation seeds, the authors are careful to describe this as a positive mean shift rather than a statistically resolved improvement. The structural diagnostic, however, is unambiguous: the trained mixing maps move substantially away from the identity, with a mean Frobenius distance of 3.898 from the six-dimensional identity matrix, showing that the disentangling step is an active, nontrivial component of the architecture.

The study comes with clear caveats. The numerical conclusions apply to the implemented neural architecture, with its within-pair connectivity, nonlinear activations, untied decoder, and soft structural constraints, and not to canonical MERA in general. Only a single proxy signal class was tested, and the authors note that a broader study involving multiple signal classes would be needed to assess how anomaly-detection performance generalises. Even so, the findings amount to a concrete empirical case that locality-aware, multiscale compression is a useful and parameter-efficient inductive bias for reconstruction-based jet anomaly detection. As the LHC programme increasingly seeks model-agnostic ways to probe the unknown, the message is that the physics of the background itself, the branching geometry of the QCD shower, can tell us how to build the detector that hunts for what lies beyond it.

Subject of Research: Quantum-inspired tensor network autoencoders for anomaly detection: a MERA-based approach

Article Title: Quantum-inspired tensor network autoencoders for anomaly detection: a MERA-based approach

Article References: Gurkanli, E., & Spannowsky, M. (2026). Quantum-inspired tensor network autoencoders for anomaly detection: a MERA-based approach. The European Physical Journal C, 86(10), Article 1211. https://doi.org/10.1140/epjc/s10052-026-16489-z

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16489-z

Keywords: Quantum-inspired, tensor, network, autoencoders, anomaly, detection, MERA-based, approach, scientific research