Reduces constructing multiplicative connections to simpler tasks.
problem Constructing multiplicative connections on proper Lie groupoids.
method Reduction to simpler tasks involving proper and regular Lie groupoids.
result Simpler methods for constructing multiplicative connections.
A simpler 3D Möbius strip design without twists.
problem Creating a Möbius strip without twists.
method A simple rational function on a polynomial subset of R^2.
result The new design is a union of a segment and a graph of a rational function.
Simpler method detects trivial rational 3-tangle.
problem Detecting trivial rational 3-tangle.
method Bridge arc replacement method.
result Simpler method detects trivial rational 3-tangle.
A simpler proof for apex graphs in McCarty and Thomas' conjecture.
problem Proving a conjecture about apex graphs and their linklessly embeddable properties.
method Shorter and simpler proof for the apex case.
result A shorter and simpler proof for the apex case of the conjecture.
KL-LIME explains Bayesian models by projecting them locally to simpler models.
problem Explaining predictions of complex Bayesian models.
method Combines LIME with Bayesian projection methods.
result Demonstrates improved explanation of MNIST classifications.
Machine learning factors outperform traditional portfolio optimization methods.
problem Comparing machine learning and traditional portfolio optimization methods.
method Examined machine learning and factor-based portfolio optimization using autoencoder neural networks and dimensionality reduction techniques.
result Minimum-variance portfolios using latent factors derived from autoencoders and sparse methods outperform simpler benchmarks in risk minimization.
Simpler algorithm learns shallow networks faster.
problem Learning a linear combination of ReLU activations.
method A simpler one-stage algorithm with improved runtime.
result Runs in (d/ε)O(k2) time. Simpler proof for Kielak's virtual fibering criterion.
problem Virtual fibering criterion for RFRS groups
method Simpler proof
result Simplified proof of Kielak's criterion
Tree ensembles, such as random forest and boosted trees, are renowned for their high prediction performance, whereas their interpretability is critically limited. In this paper, we propose a post processing method that improves the model interpretability of tree ensembles. After learning a complex tree ensembles in a s…
A new method creates simpler, more interpretable decision trees from complex ensembles.
problem Complex tree ensembles reduce interpretability and control over machine learning models.
method Dynamic-programming based algorithm for finding a minimum-size decision tree.
result Optimal born-again trees are simpler and more interpretable than original ensembles.
We define a new Hurwitz problem which is essentially a small core of the simple Hurwitz problem. The corresponding Hurwitz numbers have simpler formulae, satisfy effective recursion relations and determine the simple Hurwitz numbers. We also apply this idea of finding a smaller simpler enumerative problem to orbifold H…
Simpler proof for quaternionic Calabi conjecture
problem Quaternionic Monge-Ampère equation on compact hyperKähler manifolds
method Proves C0 estimate for quaternionic Monge-Ampère equation
result Simpler proof for quaternionic Calabi conjecture
We provide an alternative, simpler proof of the existence of thick triangulations for noncompact C1 manifolds. Moreover, this proof is simpler than the original one given in \cite{pe}, since it mainly uses tools of elementary differential topology. The role played by curvatures in this construction is also…
Simpler method derived for path geometries on surfaces, characterizing projective path geometries.
problem Characterizing projective path geometries on surfaces.
method Solving the equivalence problem of sub-Riemannian geometry of signature (1,1) on a contact 3-manifold.
result Characterization of projective path geometries in terms of their chains.
Simpler method for separating and manipulating latent attributes in autoencoders.
problem Separating and manipulating latent attributes in autoencoders.
method Matrix subspace projection
result Our method allows for changing selected attributes while preserving other information.
Simpler linear models outperform complex GCN encoders for graph tasks.
problem Complex graph autoencoders and variational autoencoders.
method Replacing GCN encoders with one-hop linear models.
result Simpler linear models achieve competitive performance with fewer operations and parameters.
SGD tends to favor simpler subnetworks, improving generalization.
problem SGD's tendency to favor simpler subnetworks over complex ones.
method Identifying invariant sets and analyzing SGD's behavior around them.
result SGD collapses networks to simpler subnetworks, improving generalization.
Simplified construction of p-adic transformation group action.
problem Constructing an action of p-adic integers on a compactum.
method Simpler construction of the p-adic transformation group action.
result A simpler example of p-adic transformation group action.
Simpler proof for non-basic sets in 2D.
problem Proving non-basic sets in 2D.
method Defining Sternfeld arrays and proving non-basic sets.
result Simpler proof of non-basic sets in 2D.
Simpler neural architecture search method using random architectures and regression.
problem Complex algorithms in neural architecture search.
method Train N random architectures, use them to train a regression model, predict validation accuracies, and select top-K architectures.
result More sample efficient and competitive with complex approaches.
Contrastive learning struggles with class collapse and feature suppression, revealing bias towards simpler solutions.
problem Contrastive learning struggles with class collapse and feature suppression, especially in supervised and unsupervised settings.
method Unified theoretical framework to determine which features are learnt by CL, revealing bias towards simpler solutions.
result Bias towards simpler solutions is a key factor in class collapse and feature suppression.
Simplified proof for Frank and Lieb's inequality on Heisenberg group.
problem Proving the sharp Frank-Lieb inequality on the Heisenberg group.
method Simpler proof based on 2nd variation of subcritical functionals.
result A simpler proof of the inequality without the need for minimizer existence.
Defines basic sections of LA-groupoids for simpler modeling.
problem Modeling sections of stacky Lie algebroids.
method Introduces basic sections with injective core-anchor map.
result Basic sections are Morita invariant and equivalent to multiplicative sections.
We address the issue of edge detection in Synthetic Aperture Radar imagery. In particular, we propose nonparametric methods for edge detection, and numerically compare them to an alternative method that has been recently proposed in the literature. Our results show that some of the proposed methods display superior res…
Local probabilistic models simplify Bayesian classification for complex data.
problem Complex real-world data requires simpler models than global ones.
method Establish local probabilistic models for local regions, relaxing global assumptions.
result Local probabilistic models improve classification accuracy on real-world datasets.
Simplified derivation and simulation of Feller Diffusion.
problem Deriving the probability density function of Feller Diffusion.
method Fourier Transform and Method of Characteristics for derivation; simulation algorithms for validation.
result Confirmation of hitting time probabilities via simulation.
Consider the problem of sparse clustering, where it is assumed that only a subset of the features are useful for clustering purposes. In the framework of the COSA method of Friedman and Meulman, subsequently improved in the form of the Sparse K-means method of Witten and Tibshirani, a natural and simpler hill-climbing …
Noise increases the Rashomon ratio, leading simpler models to perform similarly to complex ones.
problem Why simpler models perform similarly to complex models on noisy datasets.
method Analyzed the data generation process and model training choices, introduced pattern diversity.
result Noisier datasets lead to larger Rashomon ratios, explaining simpler models' performance.
Paper proposes a new method to minimize submodular functions with fewer calls to simpler oracles.
problem Minimizing the sum of submodular set functions with limited information.
method Introduces a modified convex problem requiring constrained total variation oracles that can be solved with fewer calls to minimization oracles.
result Shows significant reduction in the number of calls to minimization oracles.
Transformers prefer simpler explanations in hierarchical tasks.
problem Navigating tasks with varying complexity levels.
method Well-controlled testbeds based on Markov chains and linear regression.
result Transformers favor the least complex sufficient explanation when presented with simpler data.
Proposes a simpler method for quantifying uncertainty in time-series with volatility clustering.
problem Uncertainty quantification for time-series with volatility clustering.
method Proposes a Scale Mixture Distribution to quantify return forecast uncertainty in neural networks.
result The proposed method provides a favorable complexity-accuracy trade-off and separates model parameters into subnetworks.
The Adomian decomposition method is shown to be equivalent to the Taylor series approach.
problem Incorrectly perceived complexity of the Adomian decomposition method.
method Demonstrates the Adomian decomposition method as equivalent to the Taylor series approach.
result The Adomian decomposition method is simpler and more straightforward.
We describe a novel optimization method for finite sums (such as empirical risk minimization problems) building on the recently introduced SAGA method. Our method achieves an accelerated convergence rate on strongly convex smooth problems. Our method has only one parameter (a step size), and is radically simpler than o…
Deep learning methods are useful for high-dimensional data and are becoming widely used in many areas of software engineering. Deep learners utilizes extensive computational power and can take a long time to train-- making it difficult to widely validate and repeat and improve their results. Further, they are not the b…
We consider the problem of estimating a function defined over n locations on a d-dimensional grid (having all side lengths equal to n1/d). When the function is constrained to have discrete total variation bounded by Cn, we derive the minimax optimal (squared) ℓ2 estimation error rate, parametrized by …
A new method for creating simpler models from complex ones.
problem Creating accurate approximations of complex models at reduced costs.
method Sequential adaptive surrogate modeling based on locally spectral expansions.
result Stochastic spectral embedding (SSE) shows good approximation capabilities and scalability.
Automates molecule design with simpler SMILES generation and reinforcement learning.
problem Designing molecules with specific chemical properties.
method Combines context-free grammar for SMILES strings and reinforcement learning with a Transformer model.
result Significantly reduces model steps per atom and beats previous baselines.
ODCGM solves non-convex optimization on manifolds with simpler projections.
problem Minimizing non-convex functions over smooth manifolds.
method Orthogonal Directions Constrained Gradient Method (ODCGM) that projects onto a vector space.
result ODCGM converges to the manifold with near-optimal oracle complexities.
Simpler CNN model with spatial attention and temporal pooling outperforms complex models.
problem Emotion recognition from videos with small face deformations and identity variations.
method Spatial attention mechanism and temporal softmax pooling applied to a pre-trained CNN.
result The approach achieves higher accuracy than state-of-the-art methods on the EmotiW dataset.
Method constructs complex symplectic Lie algebras from simpler ones.
problem Classifying complex symplectic Lie algebras of various dimensions.
method Complex symplectic oxidation method
result Classification of eight-dimensional nilpotent complex symplectic Lie algebras.
In this note, we present a new averaging technique for the projected stochastic subgradient method. By using a weighted average with a weight of t+1 for each iterate w_t at iteration t, we obtain the convergence rate of O(1/t) with both an easy proof and an easy implementation. The new scheme is compared empirically to…
New method trains neural ODEs faster with fewer layers.
problem Training neural ODEs on large datasets is computationally expensive.
method Combines optimal transport and stability regularizations.
result Significant reductions in training time with no performance loss.
New method for estimating firm linkages using CVLs and QCML.
problem Estimating firm linkages for profitable trading strategies.
method Characteristic Vector Linkages (CVLs) and Quantum Cognition Machine Learning (QCML).
result QCML similarity outperforms Euclidean similarity in constructing profitable trading strategies.
Finding simpler models is often hard, but this work introduces a new tool to check if they might exist.
problem Finding accurate yet simple models is NP-hard and often not known to exist.
method Introducing the Rashomon ratio to gauge simplicity and check for the existence of simple models.
result The Rashomon ratio can help determine if a simpler model might exist before searching for it.
The study examines how automorphism growth rates of a group can be deduced from its simpler decompositions.
problem Determine automorphism growth rates of a group from its simpler decompositions.
method Analyze group decompositions into simpler pieces (direct products, free products, graph of groups) and deduce growth rates.
result Information about automorphism growth rates of a group can be deduced from its simpler decompositions.
Simpler algorithms for morphing planar and toroidal graphs.
problem Constructing smooth transitions between isomorphic drawings of planar and toroidal graphs.
method Barycentric interpolation and scaling strategy.
result Simplified and more natural morphs with improved computational efficiency.
Deep learning system generates new Chinese fonts via style variables.
problem Efficiently design new Chinese fonts.
method End-to-end deep learning system generating new style fonts via interpolation of latent style-related embedding variables.
result Smooth transition between different font styles achieved.
We present new, unified proofs for the cell-like, Z/p-, and Q-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems involving cohomology groups by converting them into problems about homology groups…