Study shows limitations and universality of equivariant QNNs with Sn-equivariant gates.
problem Understanding the expressiveness of Sn-equivariant QNNs with k-body gates. method Investigated the interplay between symmetry and k-bodyness in Sn-equivariant QNN generators. result QNNs are semi-universal but not universal with one- and two-body Sn-equivariant gates. Theoretical guarantees for permutation-equivariant QNNs avoid barren plateaus.
problem Excessive local minima and barren plateaus in QNNs training landscapes.
method Designing Sn-equivariant QNNs to encode permutation symmetry. result Equivariant QNNs do not suffer from barren plateaus, quickly reach overparametrization, and generalize well.
Paper benchmarks quantum neural networks against classical ones for binary classification tasks.
problem Comparing quantum neural networks with classical ones for binary classification.
method Evaluated with two toy examples, focusing on model complexity and training data size.
result EQNN and QNN outperform ENN and DNN for smaller parameter sets and training data samples.
Overparametrization improves QNN trainability by reducing spurious local minima.
problem Understanding how overparametrization affects the loss landscape of QNNs.
method Rigorous analysis of overparametrization in QNNs with periodic structure.
result Overparametrization corresponds to a computational phase transition improving QNN trainability.
QNNs can't distinguish binary signals from their negations, revealing a new symmetry.
problem Understanding the behavior of QNNs in binary pattern classification.
method Presented and analyzed a new form of invariance (negational symmetry) in QNNs.
result QNNs cannot differentiate a quantum binary signal and its negational counterpart in binary classification tasks.
Proposes QNN to protect input privacy in neural networks.
problem Protecting input privacy in neural networks.
method Quaternion-valued neural network (QNN) to hide input information.
result QNN effectively protects input privacy without significant accuracy loss.
The paper explores the generalization of quantum neural networks using stability theory.
problem Understanding the generalization properties of quantum neural networks.
method The authors use algorithmic stability to establish generalization bounds for quantum neural networks.
result The paper provides practical insights into the design and training of quantum neural networks.
Paper proposes BQNs for efficient Bayesian quantized neural networks.
problem Learning with well-calibrated uncertainty in neural networks.
method Bayesian quantized networks (BQNs) with efficient algorithms for learning and prediction without sampling.
result BQNs achieve lower predictive errors and better-calibrated uncertainties than E-QNN with less than 20% negative log-likelihood.
Quantum neural networks approximate periodic functions more efficiently.
problem Approximating periodic functions with quantum neural networks.
method Using Jackson's inequality to construct a QNN that approximates a trigonometric polynomial of the function.
result Quantum neural networks can achieve better approximation results with fewer parameters for smoother functions.
Noise can affect the overparametrization of QNNs, enabling new directions but also suppressing sensitivity.
problem The overparametrization of QNNs in the presence of noise.
method Analyzing the Quantum Fisher Information Matrix (QFIM) to understand how noise affects the rank of QFIM.
result Noise can turn previously-zero eigenvalues of the QFIM to non-zero, enabling exploration of new directions.
A novel method quantizes Batch Normalization for QNNs, maintaining accuracy and efficiency.
problem Quantization challenges in Batch Normalization for QNNs.
method Converts BN to fixed-point operation with shared scale, suitable for hardware.
result Maintains same outputs through rigorous analysis and experiments.
Quantum neural networks improve causal inference in biomedical studies, especially for small samples.
problem Addressing selection bias in comparing surgical techniques using observational data.
method Developed QNN-based propensity score models focusing on four key covariates (Age, Sex, Stage, BMI). Employed a linear ZFeatureMap for data encoding, SummedPaulis for predictions, and CMA-ES for optimization. Integrated noise modeling to enhance predictive stability.
result QNNs, particularly with noise-aware strategies, outperformed classical models in small samples, achieving AUC up to 0.750 for n=100.
Quantum neural networks converge to Gaussian processes as they grow.
problem Understanding the convergence of quantum neural networks to Gaussian processes.
method Analyzing Haar random unitary and orthogonal deep QNNs, considering input states, measurement observables, and non-independence of unitary matrix entries.
result Quantum neural networks outputs converge to Gaussian processes in the limit of large Hilbert space dimension.
This paper proposes a learning framework for n-bit quantized neural networks that improves accuracy and speed on FPGAs.
problem Efficiently implementing quantized neural networks on FPGAs to maintain accuracy and speed.
method A novel learning framework for n-bit QNNs, constrained weights, reconstructed gradient function, n-BQ-NN structure, and SVPE array.
result Quantized models achieve almost the same accuracy as full-precision models and outperform typical low-precision QNNs.
QCNNs avoid barren plateaus, making them trainable.
problem Exponentially vanishing gradients in QNNs.
method Graph-based method to analyze Haar-distributed unitaries.
result QCNNs do not exhibit barren plateaus, implying trainability.
Neural network architectures are at the core of powerful automatic speech recognition systems (ASR). However, while recent researches focus on novel model architectures, the acoustic input features remain almost unchanged. Traditional ASR systems rely on multidimensional acoustic features such as the Mel filter bank en…
We analyze the frequency spectrum of quantum neural networks using algebraic methods and prove maximality results.
problem Understanding the frequency spectrum and maximality properties of quantum neural networks.
method Using Minkowski sums and algebraic descriptions, we prove maximality results for QNN architectures.
result We establish spectral invariance under area-preserving transformations, showing the frequency spectrum depends only on the area A=RL. This work presents a novel fundamental algorithm for for defining and training Neural Networks in Quantum Information based on time evolution and the Hamiltonian. Classical Neural Network algorithms (ANN) are computationally expensive. For example, in image classification, representing an image pixel by pixel using cla…
Quantum Support Vector Classifier outperforms other QML models in finance fraud detection.
problem Detecting financial fraud using Quantum Machine Learning.
method Comparative study of four QML models: Quantum Support Vector Classifier, Variational Quantum Classifier, Estimator QNN, and Sampler QNN.
result Quantum Support Vector Classifier achieved the highest F1 scores (0.98) for fraud and non-fraud classes.
AskewSGD optimizes quantized neural networks with interval-constrained optimization.
problem Training deep neural networks with quantized weights.
method Formulates QNN training as smoothed interval-constrained optimization, proposes AskewSGD for solving each subproblem.
result AskewSGD avoids projections and allows infeasible iterates, performs better than state-of-the-art methods.
Hybrid QNN-LSTM predicts financial stock market trends using quantum computing.
problem Complex temporal dependencies and market fluctuations in financial time-series forecasting.
method Custom QNN regressor with hybrid optimization strategies.
result Hybrid models integrate quantum computing into financial forecasting workflows.
Study benchmarks classical models over quantum in DeFi yield prediction.
problem Accurate yield and performance forecasting for DeFi liquidity allocation.
method Benchmarked six models on Curve Finance pools' historical data.
result Classical models, especially XGBoost, outperform quantum models.
Quantized Neural Networks (QNNs) are often used to improve network efficiency during the inference phase, i.e. after the network has been trained. Extensive research in the field suggests many different quantization schemes. Still, the number of bits required, as well as the best quantization scheme, are yet unknown. O…
Quantum neural networks need both data-dependent and trainable unitaries for effective geometric deformation.
problem Quantum neural networks lack the geometric flexibility of classical networks due to limitations in state reachability.
method Viewing quantum states as embedded manifolds, we analyze infinitesimal unitary actions and introduce the CLA maps and aCLS criterion.
result Geometric flexibility in quantum neural networks requires a joint dependence on data and trainable weights.
Study of invariants on manifolds with boundary involving equivariant spectral flow and η-invariants.
problem Equivariant invariants on manifolds with boundary.
method Analysis of Dirac operators, winding numbers, spectral flow, Maslov indices, and η-invariants.
result Established relation between equivariant η-invariants and Maslov triple indices.
Group-equivariant subsampling layers improve CNNs' equivariance.
problem Non-translation equivariance in subsampling operations.
method Translation and group-equivariant subsampling/upsampling layers.
result Group-equivariant autoencoders learn equivariant representations.
Study of equivariant ribbon concordance using Khovanov homology.
problem Understanding equivariant ribbon concordance.
method Functoriality of equivariant Khovanov homology under equivariant cobordisms, and induced split injection.
result Equivariant ribbon concordances induce a split injection on equivariant Khovanov homology.
Defines a new homomorphism for strongly invertible knots, proving equivariant algebraic concordance.
problem Equivariant algebraic concordance of strongly invertible knots.
method Defining a homomorphism Φ from equivariant concordance group to a new equivariant algebraic concordance group, proving it lifts known homomorphisms and provides new obstructions. result Obtains a new obstruction to equivariant sliceness and novel lower bounds on equivariant slice genus.
Defines an equivariant Ruelle dynamical zeta function for flows on manifolds.
problem Defining a zeta function for equivariant flows on manifolds.
method Equivariant generalization of Guillemin's trace formula.
result Computes the equivariant Ruelle zeta function in various examples.
Study of equivariant movie moves for involutive links.
problem Equivariant cobordisms between involutive links.
method Equivariant Morse theory and singularity theory.
result 39 equivariant movie moves for isotopic cobordisms.
We define the equivariant holonomy of an invariant connection on a principal U(1)-bundle. The properties of the ordinary holonomy are generalized to the equivariant setting. In particular, equivariant U(1)-bundles with connection are shown to be classified by its equivariant holonomy modulo isomorphisms. We also show t…
A bound on knot unknotting using equivariant signature.
problem Equivariant unknotting of knots.
method Analysis of strongly invertible knots and application of equivariant unknotting moves.
result The equivariant signature provides a lower bound for the equivariant unknotting number.
New proof for 4D symplectic manifolds: equivariant cohomology determines diffeotype.
problem Determining if 4D symplectic manifolds are diffeomorphic based on their equivariant cohomology.
method Proved that equivariant cohomology rings of Hamiltonian circle actions on 4D symplectic manifolds determine their equivariant diffeotypes.
result Isomorphism of equivariant cohomology rings implies equivariant diffeomorphism for 4D symplectic manifolds.
The paper develops methods for calculating equivariant homology from Morse functions.
problem Calculating equivariant homology from equivariant Morse functions.
method Alter equivariant Morse functions to stable ones, use generic equivariant metrics, and analyze the Morse spectral sequence.
result Equivariant Morse functions induce a filtration that computes equivariant homology.
Efficiently samples and learns densities with symmetries using equivariant methods.
problem Efficiently sampling and learning densities with symmetries.
method Equivariant Stein Variational Gradient Descent (SVGD) and equivariant energy based models.
result Improves and scales up training of energy based models.
Study shows non-equivariant and equivariant non-orientable 4-genus of periodic knots can differ.
problem Exploring differences in non-orientable 4-genus for periodic knots.
method Analyzed p-periodic knots, showing differences in equivariant and non-equivariant non-orientable 4-genus.
result Differences exist in non-equivariant and equivariant non-orientable 4-genus for periodic knots.
In this paper, we establish an infinitesimal equivariant index formula in the noncommutative geometry framework using Greiner's approach to heat kernel asymptotics. An infinitesimal equivariant index formula for odd dimensional manifolds is also given. We define infinitesimal equivariant eta cochains, prove their regul…
Equivariant trisections for group actions on 4-manifolds are introduced and studied.
problem Understanding the equivariant topology of G-manifolds and their quotients. method Introducing G-equivariant trisections and bridge trisections, and establishing their existence for G-manifolds. result Any G-manifold X admits a G-equivariant trisection such that a G-invariant surface S is in equivariant bridge trisection position. This work introduces a method for almost equivariance in neural networks using Lie algebra convolutions.
problem Real-world data often does not conform to strict group equivariances, leading to underperformance in models.
method Definition and practical implementation of almost equivariance through Lie algebra convolutions.
result Demonstrated the validity of the approach through benchmarking against fully equivariant settings.
Equivariant neural networks use symmetry to interpret complex data.
problem Interpreting and understanding the behavior of equivariant neural networks.
method Decompose layers into simple representations and analyze nonlinear activation functions.
result Equivariant neural networks can be interpreted using a filtration generalizing Fourier series.
Study on equivariant Heegaard genus of reducible 3-manifolds with group actions.
problem Understanding the equivariant Heegaard genus of reducible 3-manifolds with group actions.
method Thin position theory for 3-dimensional orbifolds to establish bounds on equivariant Heegaard genus.
result Sharp bounds on equivariant Heegaard genus of reducible manifolds, similar to tunnel number results.
New equivariant version of Khovanov homology for annuli.
problem Developing a new mathematical framework for annular Khovanov homology.
method Using Frobenius algebra and equivariant cohomology of CP1. result Introduced an equivariant version of the Temperley-Lieb algebra.
For a compact Lie group acting on a smooth manifold, we define the differential cohomology of a certain quotient stack involving principal bundles with connection. This produces differential equivariant cohomology groups that map to the Cartan-Weil equivariant forms and to Borel's equivariant integral cohomology. We sh…
We show that J. Lott's equivariant higher analytic torsion for compact group actions depends only on the equivariant Euler characteristic.
Develops a theory for equivariant networks with partial domain symmetry.
problem Limited analysis of equivariant networks with partial domain symmetry.
method Proposes pointwise definitions of correct, incorrect, and extrinsic equivariance.
result Establishes error lower bounds for networks with partial symmetry.
In this work we develop a cellular equivariant homology functor and apply it to prove an equivariant Euler-Poincare formula and an equivariant Lefschetz theorem.
Paper develops equivariant basic cohomology for Lie groupoids.
problem Equivariant cohomology for Lie groupoids with weak actions.
method Using Kan fibrations and fiber structures, constructing models and comparing with existing theories.
result Equivariant basic cohomology theory for orbifolds and Lie groupoids.
On the basis of Brylinski's work, we introduce a notion of equivariant smooth Deligne cohomology group, which is a generalization of both the ordinary smooth Deligne cohomology and the ordinary equivariant cohomology. Using the cohomology group, we classify equivariant circle bundles with connection, and equivariant ge…