Gradient-free optimizers are ineffective on barren plateaus in quantum computing.
problem Effect of barren plateaus on gradient-free optimization in quantum computing.
method Numerical simulations and theoretical analysis of gradient-free optimization algorithms.
result Gradient-free optimizers are not effective in barren plateau landscapes due to exponentially suppressed cost function differences.
Barren plateaus are not an average-case phenomenon, but a highly non-unique problem.
problem Avoiding barren plateaus in neural network training
method First-moment framework for initialization strategies
result Many families of inequivalent initialization strategies can avoid concentration
Quantum models avoiding barren plateaus can also be efficiently simulated classically.
problem Understanding the limitations of barren plateaus in quantum computing.
method Analyzing commonly used models and their ability to be simulated classically.
result Many quantum models with barren plateau-free landscapes can also be efficiently simulated classically.
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.
Quantum machine learning faces 'laziness' and 'barren plateaus', but noise can mitigate the latter.
problem Quantum machine learning's loss function landscape issues.
method Theoretical analysis of quantum variational circuits, neural tangent kernels, and noise effects.
result Noise can mitigate barren plateaus in quantum machine learning.
New methods optimize training VQAs without barren plateaus, improving efficiency and applicability.
problem Barren plateaus in training variational quantum algorithms.
method Derive adaptive learning rates and use Gaussian kernels to optimize movement in parameter space.
result Optimized training methods outperform other routines and can train VQAs free of barren plateaus.
New bound shows variational algorithms may struggle with barren plateaus.
problem Barren plateaus in quantum loss landscapes.
method General bound on loss variance and gradient decay.
result Exponential decay of gradients in subregions of barren plateaus.
Quantum models face barren plateaus, but specific losses can be trainable.
problem Barren plateaus and loss concentration in quantum generative models.
method Investigated explicit and implicit losses, and their interplay.
result Explicit losses lead to new barren plateaus, while implicit losses can be trainable.
Expressive quantum circuits are harder to train due to flatter cost landscapes.
problem Designing quantum circuits that are both expressive and trainable.
method Deriving a relationship between expressibility and gradient magnitude, extending barren plateau phenomenon.
result Highly expressive ansätze exhibit flatter cost landscapes, making them harder to train.
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.
Warm starts improve variational quantum algorithms by avoiding barren plateaus.
problem Barren plateaus in variational quantum algorithms limit scaling.
method Exploring warm starts in iterative variational methods for quantum circuits.
result Warm starts can lead to substantial gradients in small regions, suggesting trainability.
Variational quantum computing faces a flat optimization landscape problem.
problem Barren Plateaus (BP) in optimization landscapes.
method Theoretical and heuristic methods to understand and mitigate BPs.
result All algorithm components can lead to BPs if not well-suited.
Quantum machine learning faces challenges similar to variational quantum algorithms in training.
problem Challenges in training quantum machine learning models.
method Bridge between variational quantum algorithms and quantum machine learning, applying gradient scaling results.
result Gradient scaling results for variational quantum algorithms can also be applied to quantum machine learning models, revealing new trainability issues.
New approach connects quantum phases to VQA trainability, enabling better scaling.
problem Scalability issues in VQAs, especially barren plateaus.
method Analog VQA ansätze composed of quenches of a disordered Ising chain, tuning disorder strength.
result Thermalized and MBL phases reach maximal expressivity at large M, but barren plateaus emerge at smaller M in the thermalized phase. Quantum circuit models learn better with specific initialization strategies.
problem Understanding and improving the optimization landscape of IQP-based generative models.
method Proved barren plateaus for random initialization, established lower bounds, and developed data-dependent initialization.
result Data-dependent initialization leads to faster convergence and better minimums.
Quantum method detects financial stress regimes from market data.
problem Detecting financial stress regimes from market data.
method Adapted Pauli Correlation Encoding to quantum topological data analysis.
result Quantum method can recover Betti numbers exactly at every scale.
This work introduces a new quantum kernel, quantum tangent kernel, for improved performance.
problem Improving quantum machine learning performance beyond conventional methods.
method Developed a deep parameterized quantum circuit and used first-order expansion for training.
result The quantum tangent kernel outperforms conventional quantum kernel methods for ansatz-generated datasets.
Develops a framework for designing quantum neural networks that respect symmetries.
problem Trainability and generalization issues in quantum neural networks.
method Equivariant quantum neural networks (EQNN) for any symmetry group.
result Efficient construction of equivariant layers for EQNNs, including QCNNs.
Study evaluates capacity and trainability of parametrized quantum circuits.
problem Finding the best type of circuits for hybrid quantum-classical algorithms.
method Geometric structure of parameter space, effective quantum dimension, and circuit expressiveness.
result Identifies a transition in quantum geometry leading to decay of quantum natural gradient for deep circuits.
Rapid mixing of Langevin dynamics on Riemannian manifolds
problem Mixing time of Langevin dynamics on Riemannian manifolds
method Relation between Langevin processes in domain and image
result Achievable polynomial mixing times
TensorHyper-VQC improves VQC scalability and robustness.
problem Scalability and noise sensitivity in VQC.
method Tensor-train-guided hypernetwork framework.
result TensorHyper-VQC achieves superior performance and robust noise tolerance.
New method uses adiabatic principles to improve ground-state preparation in quantum computing.
problem Challenges in variational training of complex energy landscapes.
method Iterative Hamiltonian deformation complemented with adiabatic principles.
result Consistent convergence to target ground state through sequence of intermediate problems.
Hybrid QAOA approach optimizes portfolios with strict constraints, outperforming classical methods.
problem Combinatorial optimization under strict cardinality constraints in portfolio management.
method Constraint-preserving QAOA with XY-mixers and Trotterized initialization.
result QAOA achieves a Sharpe Ratio of 1.81, significantly outperforming classical methods.
Study approximates Plateau's laws using the Allen-Cahn equation.
problem Approximating Plateau's laws with the Allen-Cahn equation.
method Minimizing the Allen-Cahn energy under volume and spanning constraints.
result Energy minimizing solutions approximate Plateau-type singularities.
Improves VQAs by balancing classical and quantum training resources.
problem Challenges in trainability and resource costs of VQAs on quantum hardware.
method Adopting HELIA Ansatz and combining classical and quantum methods for gradient estimation and training.
result Achieves higher accuracy and success rates in VQE and improved test accuracy in quantum phase classification.
Paper proves stable minimal surfaces in 3D are flat.
problem Understanding stable minimal surfaces in 3D.
method Analyzes quadratic area growth and stability conditions.
result Stable minimal Plateau surfaces in 3D are flat.
Paper proves uniqueness of weak solutions for Plateau flow.
problem Proving uniqueness of weak solutions for Plateau flow.
method Used natural energy condition and alternative methods from Struwe.
result Proves uniqueness of weak solutions under natural condition.
Researchers solve a Plateau problem for maximal surfaces in pseudo-hyperbolic spaces.
problem Finding maximal surfaces with given boundary curves in pseudo-hyperbolic spaces.
method Defined and proved the existence of unique solutions using asymptotic Plateau problem and analysis of pseudo-holomorphic curves.
result Existence and uniqueness of maximal surfaces with specified boundary conditions.
Solves Plateau problem for surfaces in pinched curvature manifolds.
problem Asymptotic Plateau problem for immersed surfaces in pinched curvature manifolds.
method Complete solution to asymptotic Plateau problem, providing dynamical stability of hypersurface laminations.
result Achieved complete solution to the asymptotic Plateau problem for immersed surfaces of constant extrinsic curvature in Cartan--Hadamard manifolds.
Solves area-minimizing surface problem for finite curves in H^2xR.
problem Asymptotic Plateau problem for area-minimizing surfaces.
method Complete solution for finite curves in $\BHH$.
result Fairly complete solution for finite curves in $\BHH$.
Unique solutions found for Plateau problems in smooth and continuous calibrations.
problem Finding unique solutions to the Plateau problem for specific types of currents.
method Boundary regularity theory for area-minimizing currents and unique continuation argument.
result Every compactly supported smoothly or continuously calibrated integral current is the unique solution to the Plateau problem for its boundary data.
CNN accurately reconstructs lattice topology with strong thermal fluctuations.
problem Reconstructing lattice topology with strong thermal fluctuations and unbalanced data.
method Deep convolutional neural network (CNN) mapping local magnetic moments to coupling probabilities.
result CNN accurately reconstructs lattice topology where thermal fluctuations dominate.
Study on minimal submanifolds in curved spaces with unique solution to asymptotic Plateau problem.
problem Minimal submanifolds in negatively curved spaces with small curvature.
method Analysis of spheres at infinity and asymptotic Plateau problem.
result Complete minimal submanifolds bound a class of spheres with uniquely solvable asymptotic Plateau problem.
Derives equilibrium law for Plateau borders in wet soap films and foams.
problem Equilibrium law for Plateau borders in wet foams and films.
method Rigorous derivation using Gauss' capillarity theory, homotopic spanning condition, and effective compactness theorems.
result Sharp regularity properties of energy minimizers for Plateau borders in wet foams and films.
Spherical Plateau problem studies minimal surfaces in quotients of spheres.
problem Minimal surfaces in quotients of spheres.
method Metric currents, barycenter map method.
result Intrinsic uniqueness of solutions for negatively curved manifolds.
Solves Plateau's Problem in Heisenberg group for graphs.
problem Plateau's Problem in the Heisenberg group for intrinsic graphs.
method Geometric construction and calibration argument.
result Solves Plateau's Problem under smallness conditions.
Solves the asymptotic Plateau problem in hyperbolic space for specific curvature.
problem Existence of complete hypersurfaces with prescribed asymptotic boundary.
method Curvature estimates.
result Solves the problem for a wider range of curvature values.
Noise causes learning plateaus in neural networks.
problem Plateau phenomena in online learning due to vanishing gradients.
method Analysis of stochastic gradient descent in multi-layer perceptrons.
result Noise induces synchronisation leading to strong plateaus.
Plateau's problem is to show the existence of an area minimizing surface with a given boundary, a problem posed by Lagrange in 1760. Experiments conducted by Plateau showed that an area minimizing surface can be obtained in the form of a film of oil stretched on a wire frame, and the problem came to be called Plateau's…
Unified approach for quantum and classical learning from evaluation oracles.
problem Learning from evaluation oracles in quantum and classical settings.
method Inspired by Kearns' SQ and Valiant's weak evaluation oracle, a unified framework is established.
result Characterizes query complexity for learning linear function classes and extends learnability results for quantum circuits.
Paper finds invariant solutions for Plateau problem in hyperbolic space.
problem Finding minimal surfaces with specific symmetries in hyperbolic space.
method Proved existence of foliations by invariant minimal surfaces, used to solve the Plateau problem.
result Existence of invariant minimal surfaces solving the asymptotic Plateau problem.
This study investigates abrupt learning dynamics in Transformers, revealing plateau formation and internal representation collapse.
problem Abrupt learning in Transformers, particularly during the loss plateau.
method Investigates mechanisms of abrupt learning in shallow Transformers, focusing on attention maps and hidden states.
result Reveals plateau formation, internal representation collapse, and strong repetition bias in outputs.
We give a solution of Plateau's problem for singular curves possibly having self-intersections. The proof is based on the solution of Plateau's problem for Jordan curves in very general metric spaces by Alexander Lytchak and Stefan Wenger and hence works also in a quite general setting. However the main result of this …
This is a survey of old and recent results about the asymptotic Plateau problem. Our aim is to give a fairly complete picture of the field, and present the current situation.
This research solves Plateau's problem for CRPC surfaces.
problem Constructing surfaces with constant ratio of principal curvatures.
method Proposed a family of surfaces containing a given minimal surface without flat points.
result Obtained a partial solution to Plateau's problem for CRPC surfaces.
New energy model avoids self-intersections in curve optimization.
problem Avoiding self-intersections in curve optimization under elastic boundary energies.
method Introduced Möbius-Plateau energy to minimize curve variations.
result Screw-like solutions are plentiful, ribbon-like solutions have constraints.
The plateau phenomenon, wherein the loss value stops decreasing during the process of learning, has been reported by various researchers. The phenomenon is actively inspected in the 1990s and found to be due to the fundamental hierarchical structure of neural network models. Then the phenomenon has been thought as inev…
Study on the Euler-Plateau energy with elastic modulus, focusing on minimizers and critical surfaces.
problem Minimizing the Euler-Plateau energy with elastic modulus.
method Analyzing the energy functional and its minimizers, considering different boundary conditions and topological constraints.
result Potential minimizers are highly dependent on physical rigidity parameters, and the area of critical surfaces can be computed from boundary data.