Survey on broken ray transforms and open problems.
problem Understanding broken ray transforms and their applications.
method Survey of recent developments and open problems.
result Discussion of open problems in broken ray transforms.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “problem transformation”
This paper investigates efficient Transformers and finds they scale with problem size.
problem Finding suitable replacements for standard Transformers in large-scale tasks.
method Modeling efficient Transformers (Sparse and Linear) as Dynamic Programming problems and analyzing their reasoning capabilities.
result Efficient Transformers scale with problem size, but can be more efficient for certain DP problems.
Enhanced Transformer solves math problems better with explicit relation encoding.
problem Improving Transformer models for solving math word problems.
method Integrates Tensor-Product Representations and TP-Attention mechanism.
result Sets new state of the art on the Mathematics Dataset.
Sparse transformer architecture improves accuracy and speed in generative modeling and inverse problems.
problem Improving accuracy and speed in generative modeling and inverse problems.
method Proposes a sparse transformer architecture using regularized Wasserstein proximal operator with prior.
result Sparse transformer achieves higher accuracy and faster convergence than classical methods.
New Kelvin transform for anisotropic elliptic problems.
problem Semilinear and quasilinear anisotropic elliptic problems.
method Introducing a new Kelvin-type transform in the anisotropic setting.
result New insights into anisotropic elliptic problems.
Transformers improve solving mixed-integer programs, especially CLSP.
problem Solving Capacitated Lot Sizing Problem (CLSP) with mixed-integer programming.
method Employing transformer models to predict binary variables in CLSP.
result Transformer model outperforms CPLEX and LSTM in solving CLSP.
Equity-Transformer solves NP-hard min-max routing problems efficiently.
problem Min-max routing problems with multiple agents and large-scale applications.
method Sequential planning approach with Transformer and equitable workload distribution inductive biases.
result Significant runtime and cost reductions in min-max mTSP and min-max mPDP tasks.
Transform learning improves K-means clustering for document analysis.
problem Improving K-means clustering for document analysis.
method Embedding K-means clustering loss into transform learning framework and solving jointly using ADMM.
result Improves over state-of-the-art in document clustering.
Injectivity of geodesic ray transform on specific Finsler manifolds proven.
problem Injectivity of geodesic ray transform on spherically symmetric reversible Finsler manifolds.
method Reduction to invertibility of generalized Abel transforms using angular Fourier series and Taylor expansions of geodesics.
result Injectivity of geodesic ray transform proven on specified Finsler manifolds.
Solves problem of describing transformations for upper triangular Toeplitz operators.
problem Describing coordinate transformations preserving upper triangular Toeplitz form of operator fields.
method Implicit formulas involving matrix-valued functions for describing transformations and Nijenhuis operators.
result Formulas for coordinate transformations and Nijenhuis operators in upper triangular Toeplitz form.
CoT enhances transformer accuracy on serial tasks by enabling serial computation.
problem Improving accuracy of large language models on inherently serial problems.
method Integrating a chain of thought (CoT) into decoder-only transformers to enable serial computation.
result Constant-depth transformers with CoT can solve problems in AC^0, surpassing TC^0 without CoT.
Researchers improve transformer networks' optimization and understanding.
problem Improving the understanding and optimization of transformer networks.
method Introducing a convex alternative to the self-attention mechanism and reformulating the training problem as a convex optimization problem.
result Revealed an implicit regularization mechanism that promotes sparsity across tokens.
X-Transformer improves deep transformer performance on extreme multi-label text classification.
problem Classifying text with a large number of labels from a sparse label space.
method Fine-tuning deep transformer models for extreme multi-label text classification.
result X-Transformer achieves new state-of-the-art results on XMC benchmark datasets.
Kernel estimator optimally recovers function from noisy exponential Radon transform.
problem Inverting noisy exponential Radon transform of a function.
method Proposed a kernel estimator to estimate the true function.
result The estimator converges to the true function at minimax optimal rate.
Study X-ray transform on conic spaces, proving injectivity under certain conditions.
problem Injectivity of geodesic X-ray transform on conic metrics.
method Injectivity under non-trapping and no conjugate point assumptions.
result Injectivity of geodesic X-ray transform for asymptotically conic metrics.
Study on determining metrics from minimal surface areas, extending earlier work.
problem Determining a Riemannian manifold with boundary from minimal surface areas.
method Linearized forward operator of minimal surface transform, double fibration transforms, Bolker condition.
result Invertibility of the minimal surface transform on analytic manifolds.
We reduce boundary determination of an unknown function and its normal derivatives from the (possibly weighted and attenuated) broken ray data to the injectivity of certain geodesic ray transforms on the boundary. For determination of the values of the function itself we obtain the usual geodesic ray transform, but for…
Transformer learns context and regularization for ICL in inverse problems.
problem Learning context and effective regularization for transformer-based in-context learning (ICL) in inverse problems.
method Introduced a linear transformer to learn inverse mapping from contextual examples to weight vectors, addressing rank-deficient problems.
result Transformer implicitly learns a prior distribution and effective regularization strategy, outperforming traditional methods.
In order to understand the linearization problem around a leaf of a singular foliation, we extend the familiar holonomy map from the case of regular foliations to the case of singular foliations. To this aim we introduce the notion of holonomy transformation. Unlike the regular case, holonomy transformations can not be…
Motivated by applications in computational anatomy, we consider a second-order problem in the calculus of variations on object manifolds that are acted upon by Lie groups of smooth invertible transformations. This problem leads to solution curves known as Riemannian cubics on object manifolds that are endowed with norm…
Study investigates ruin probability with random premiums and risky investments.
problem Ruin probability with random premiums and risky investments.
method Laplace transform applied to a model with geometric Brownian motion.
result Asymptotic behavior of ruin probability for large initial capital values.
Transformers learn chain-of-thought reasoning for longer problems, proving length generalization.
problem Challenging problems require deeper reasoning, but how do models generalize this to longer tasks?
method Theoretical analysis of transformers on synthetic state-tracking tasks, proving length generalization through attention concentration.
result Transformers can learn chain-of-thought reasoning for longer problems, proving length generalization.
Simplified Butterfly-Net2 improves CNN efficiency in solving PDEs and signal processing tasks.
problem Improving CNN efficiency in solving PDEs and signal processing tasks.
method Introducing BNet2, a simplified Butterfly-Net, and Fourier transform initialization.
result BNet2 achieves similar accuracy as CNN but with fewer parameters and improves accuracy over randomly initialized CNN.
New algebraic-geometry method for Ribaucour transformations.
problem Classical differential geometry problems.
method Algebraic-geometry approach to constructing orthogonal nets.
result Obtains smooth orthogonal nets as Ribaucour transformations.
Paper improves tensor completion using unitary transforms.
problem Robust tensor completion for various datasets.
method Transformed tensor SVD with unitary matrices.
result Recovered images have better PSNR than traditional methods.
On the broken ray transformmath.DG
This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is injective. We employ four different methods to approach this question, and each o…
Neural Canonical Transformation with Symplectic Flowscond-mat.stat-mech
Neural network models transform physical systems into latent Gaussian distributions.
problem Simplifying and solving classical Hamiltonian systems.
method Symplectic neural networks for canonical transformations.
result Captures nonlinear collective modes in latent space.
Darboux Wronskian formulas allow to construct Darboux transformations, but Laplace transformations, which are Darboux transformations of order one cannot be represented this way. It has been a long standing problem on what are other exceptions. In our previous work we proved that among transformations of total order on…
Transformers predict scattering amplitudes in theoretical physics.
problem Computing exact coefficients of scattering amplitudes in N = 4 SYM theory.
method Applied Transformers to predict integer coefficients of scattering amplitudes.
result Transformers achieve high (> 98%) accuracy on predicting scattering amplitudes.
Study inverse problems for twisted geodesic flows on manifolds.
problem Understanding inverse problems for twisted geodesic flows.
method Generalized ray transforms and tensor tomography.
result New insights into rigidity problems for twisted geodesic flows.
Transformers adapted to spherical geometry using space-filling curves.
problem Generalizing transformers to geometric domains like spheres.
method Attention heads following a space-filling curve.
result Introduction of the Spiroformer on a 2-sphere.
The study analyzes the convergence rate of a large transformer model.
problem Understanding the convergence rate of over-parameterized transformer models.
method Theoretical analysis focusing on gradient descent optimization.
result Theoretical upper bound on missclassification probability.
We prove that the global minimum of the backpropagation (BP) training problem of neural networks with an arbitrary nonlinear activation is given by the ridgelet transform. A series of computational experiments show that there exists an interesting similarity between the scatter plot of hidden parameters in a shallow ne…
The paper explains how microlocal analysis solves geometric inverse problems.
problem Recovering geometric information from boundary measurements.
method Microlocal analysis applied to three inverse problems.
result Microlocal techniques solve specific inverse problems in Riemannian geometry.
RNNs struggle with in-context retrieval, while Transformers excel.
problem In-context retrieval capability of RNNs.
method Theoretical analysis and experimental techniques (CoT, RAG, Transformer layer).
result Enhancing RNNs with techniques improves their in-context retrieval capability, closing the representation gap with Transformers.
We prove Transformers can learn diverse Gröbner bases.
problem Training Transformers for Gröbner basis computation.
method Prove generality of dataset generation algorithm; propose extended algorithm.
result Datasets are sufficiently general for diverse Gröbner bases learning.
New integral transforms solve multilayer heat equations.
problem Solving multilayer heat equations with moving boundaries.
method Expanding Dirac delta function in eigenfunctions, constructing oscillating integral transforms.
result Semi-analytical solutions for various problems.
We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result about preservation of lower curvature bounds under perturbation, which is new ev…
One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According to the Liouville Theorem, an important part of the conformal transformation is t…
Study solves inverse problems for real principal type operators using unique data sets and ray transforms.
problem Determining coefficients in real principal type equations from boundary data.
method Unique data sets, bicharacteristic ray transforms, and propagation of singularities.
result Global uniqueness results for determining coefficients in nonlinear real principal type equations.
The paper explores the injectivity of the light ray transform on Lorentzian manifolds.
problem Injectivity of the light ray transform on functions and tensors.
method Analyzes injectivity conditions for scalar and tensor fields on stationary and static Lorentzian manifolds.
result Injectivity of the light ray transform on functions and tensors is proven under specific conditions.
Quantum hybrid vision transformers improve event classification in high energy physics.
problem Excessive computational resources for training and deploying vision transformer models.
method Constructed quantum hybrid vision transformers for high energy physics event classification.
result Quantum hybrid models achieve comparable performance to classical models with fewer parameters.
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the approximation errors. Our aim is to design a method for moment transformation for …
The Funk--Minkowski transform associates a function on the sphere with its mean values (integrals) along all great circles of the sphere. Thepresented analytical inversion formula reconstruct the unknown function completely if two Funk--Minkowski transforms, and ${…
If is a finite group, is a function determined by its sums over all cosets of cyclic subgroups of ? In other words, is the Radon transform on injective? This inverse problem is a discrete analogue of asking whether a function on a compact Lie group is determined by its integrals over all ge…
We propose a novel multilinear dynamical system (MLDS) in a transform domain, named -MLDS, to model tensor time series. With transformations applied to a tensor data, the latent multidimensional correlations among the frontal slices are built, and thus resulting in the computational independence in the tra…
We consider the boundary rigidity problem for asymptotically hyperbolic manifolds. We show injectivity of the X-ray transform in several cases and consider the non-linear inverse problem which consists of recovering a metric from boundary measurements for the geodesic flow.
Study normal operators of double fibration transforms with conjugate points.
problem Normal operators of double fibration transforms with conjugate points.
method Stable conditions on the distribution of conjugate points, splitting into elliptic and Fourier integral operators.
result Normal operator splits into an elliptic pseudodifferential operator and Fourier integral operators.