Small generators found for cocompact arithmetic Fuchsian groups.
problem Determining generators for Fuchsian groups.
method Dynamical approach to construct fundamental regions.
result Set of small generators determined for cocompact arithmetic Fuchsian groups.
SHADOWCAST generates graphs with user-specified attributes.
problem Controlling graph generation with understandable structures.
method Conditional generative adversarial network guided by Markov model.
result Competitive performance in generating desired graphs.
Study on RCD(0,N) spaces with small linear diameter growth.
problem Understanding structure properties of RCD(0,N) spaces.
method Analyzing the (revised) fundamental group of RCD(0,N) spaces.
result Proved that the revised fundamental group is finitely generated for RCD(0,N) spaces with small linear diameter growth.
Generative Latent Implicit Conditional Optimization (GLICO) learns from small samples.
problem Learning from small labeled datasets.
method Generative Latent Implicit Conditional Optimization (GLICO) learns a latent space and generator from small labeled data.
result GLICO synthesizes new samples for every class using as few as 10 examples per class.
Connectedness of small clusters in Riemannian and Finsler manifolds proven.
problem Understanding connectedness of small clusters in Riemannian and Finsler manifolds.
method Proved connectedness and small diameter properties for clusters of small volume in both manifolds.
result Clusters in Riemannian manifolds are connected and have small diameter; in Finsler manifolds, they are at most m connected components of small diameter.
Augmentation improves machine learning model performance on small datasets.
problem Suboptimal generalization performance of machine learning models on small datasets.
method Data augmentation to increase sample size and diversity.
result Augmentation improves AUC by 15.55% on average for small datasets.
We investigate the general structure of optimal investment and consumption with small proportional transaction costs. For a safe asset and a risky asset with general continuous dynamics, traded with random and time-varying but small transaction costs, we derive simple formal asymptotics for the optimal policy and welfa…
The paper studies spheres with small diameter in 3D manifolds concentrating at scalar curvature critical points.
problem Understanding the behavior of Willmore spheres with small diameter in 3D manifolds.
method Analyzes spheres under bounded Willmore energy and small diameter constraints, focusing on scalar curvature critical points.
result Embedded Willmore spheres concentrate at critical points of scalar curvature under small diameter and bounded energy conditions.
GNA optimally identifies the best arm with small gaps.
problem Best arm identification in fixed-budget settings.
method Generalized Neyman Allocation (GNA) for asymptotically locally minimax optimal BAI.
result GNA's worst-case bounds match the lower and upper bounds in the small-gap regime.
Small bodies follow geodesics in general relativity.
problem Understanding the motion of small bodies in space-time.
method Analyzes the motion of small bodies as timelike geodesics or Lorentz-force curves in general relativity.
result Clarifies the relationship between modeling bodies as distributions or smooth fields.
OTS error shows small training error doesn't guarantee small test error.
problem The relationship between training and test errors is unclear.
method An analysis of the conditions under which small training set error guarantees small OTS error.
result The theorem is limited to models with distinct training and test distributions.
Metric surfaces can be divided into small triangles.
problem Decomposing metric surfaces into triangles.
method Proving any metric space homeomorphic to a surface can be divided into non-overlapping convex triangles of small diameter.
result Metric surfaces can be decomposed into triangles of arbitrarily small diameter.
Enhances classification performance with small, additive perturbations.
problem Improving classification performance using small, additive perturbations.
method Proposes a perturbation generation network (PGN) based on adversarial learning to enhance classifier performance.
result Demonstrates that PGN can enhance overall classification performance without altering the target classifier network.
Study finds small surfaces in space times with new functionals.
problem Investigating small surfaces in space times without symmetry assumptions.
method Introducing Hawking type functionals and analyzing their properties.
result Characterization of concentration points and expansion of critical surfaces.
Large initial learning rate helps neural nets generalize better.
problem Understanding why large initial learning rates lead to better neural net generalization.
method Developed a proof for a two-layer network and demonstrated with experiments on CIFAR-10.
result Proved that a two-layer network trained with a large initial learning rate and annealing generalizes better than one trained with a small learning rate.
Study of fundamental groups of 3D small covers using Morse theory.
problem Understanding the fundamental groups of 3D small covers.
method Morse-theoretic approach to get explicit, balanced presentations of fundamental groups.
result Explicit, balanced presentations of fundamental groups with minimal generators and minimal Heegaard splittings.
Deep residual networks trained with gradient descent have small generalization gap.
problem Limited theoretical understanding of why residual networks generalize well.
method Analyzing overparameterized deep residual networks trained by gradient descent.
result Demonstrates that residual networks have a small generalization gap between training and test error.
Generative model initializes 2-layer network weights for small datasets.
problem Approximating functions with 2-layer networks using small datasets and gradient-based training.
method Initialize hidden weights with a learned proposal distribution parameterized as a deep generative model. Refine with gradient-based post-processing and regularization.
result Demonstrates effectiveness of the approach with numerical examples.
Small sub-Riemannian balls have diameter close to twice their radius.
problem Understanding the diameter of small sub-Riemannian balls.
method Analyzing C1,1 and C0 sub-Riemannian manifolds. result The diameter of small sub-Riemannian balls equals twice the radius in C1,1 manifolds, and is close to twice the radius in C0 manifolds. Study evaluates synthetic data augmentation for small datasets, highlighting inconsistencies in traditional metrics.
problem Inconsistent validation of synthetic data generated for small sample sizes.
method Proposes a normalized Bottleneck distance metric to evaluate synthetic tabular data.
result Common metrics like propensity scoring and MMD fail for small datasets, showing instability and high variability.
In the present paper we find a bijection between the set of small covers over an n-cube and the set of acyclic digraphs with n labeled nodes. Using this, we give a formula of the number of small covers over an n-cube (generally, a product of simplices) up to Davis-Januszkiewicz equivalence classes and $\mathbf{Z}…
Proposes a new signal model for high-dimensional, small-sample-size data.
problem Signal detection in high-dimensional, small-sample-size datasets.
method Intrinsic signal model based on dynamical system assumption.
result Taguchi method effectively detects signals in the proposed model.
MolGAN generates valid small molecular graphs without graph matching.
problem Generating valid small molecular graphs efficiently.
method Adapts GANs to generate graph-structured data with reinforcement learning.
result MolGAN generates close to 100% valid compounds.
Paper solves isomorphism problem for specific Baumslag-Solitar groups.
problem Isomorphism problem for small rose non-ascending generalized Baumslag-Solitar groups.
method Analyzed group actions on trees with specific stabilizers.
result Isomorphism problem solvable for the specified groups.
In these notes we give a shortened and more direct proof of Goto's generalized Kaehler stability theorem stating that if (J_1,J_2) is a generalized kaehler structure for which J_2 is determined by a nowhere vanishing closed form, then small deformations of J_1 can be coupled with small deformations of J_2 so that the p…
Improved graph generation model for small organic molecules.
problem Graph generation models struggle with matching training distributions and require expensive graph matching.
method Introduced a message passing neural network into the GVAE's encoder and decoder.
result Demonstrated improved graph generation for small organic molecules.
We examine geometric properties of a knot J that are unchanged by taking a (p,q)-cable K of J. Specifically, we relate w(K) to w(J), where w(K) is the width of K in the sense of Gabai. We use this information to demonstrate that thin position is a minimal bridge position of J if and only if the same is true for K, and …
This paper uses synthetic data to improve machine learning performance on small, imbalanced datasets.
problem Improving machine learning performance on small and imbalanced datasets.
method Generates synthetic data through convex combination and uses it in a semi-supervised learning framework with support vector machines.
result Synthetic data over-sampling supports the cluster assumption in semi-supervised learning, leading to outstanding results for small high-dimensional datasets and imbalanced learning problems.
A new model speeds up MRF learning from small datasets.
problem Intractable MRF learning and high computational cost.
method Characterized MRF subset with Lattice, Homogeneity, and Inertia; designed a non-Markov model.
result Learning algorithm is much faster (O(U log U) vs. general-purpose MRF's time complexity).
A small cover was introduced by Davis and Januszkiewicz as an n-dimensional closed manifold with a locally standard Z2)n-action such that its orbit space is a simple convex polytope. There exist a one-to-one correspondence between small covers and (Z2)n-colored polytopes. In this paper we study a construction…
New algorithm achieves small-loss bounds in online learning with improved rates.
problem Achieving strong stability in online learning algorithms.
method Introduces ρ-separation to enforce strong stability, unifying previous approaches. result Oracle-efficient algorithm achieves small-loss bounds with improved rates.
New bounds on diameters and generators for specific lattices and graphs.
problem Finding bounds on diameters and generators for arithmetic lattices and Ramanujan graphs.
method Analyzing arithmetic lattices from Eichler orders in quaternion algebras, applying techniques to definite quaternion algebras.
result Bounds on diameters and generators for arithmetic lattices and Ramanujan graphs.
Proves a small set generates a subgroup of surface mapping classes.
problem Generating a subgroup of Torelli group efficiently.
method Proves genus one BP-maps generate handlebody subgroup.
result Proves a normal generating set for handlebody subgroup.
The paper investigates why GNNs struggle to generalize from small to large graphs.
problem Challenges in graph neural networks' ability to generalize across different graph sizes.
method Identified and studied the effect of local structure on size generalization; proposed a novel SSL task.
result GNNs can converge to non-generalizing solutions when there is a discrepancy in local structure.
Improves probability estimates for small datasets in multi-class problems.
problem Inaccurate probability estimates in classification tasks, especially on small datasets.
method Introduced Data Generation and Grouping algorithm to improve calibration on small datasets, then applied to multi-class problems.
result Calibration error can be decreased using the proposed approach.
Improves generalization in learning problems with small parameter method.
problem Improving generalization in learning problems with high-dimensional nonlinear functions.
method Perturbation theory applied to a weakly-controlled gradient system.
result Approximate optimal solutions for improving generalization with small noise.
EnLSTM network improves log generation from small datasets.
problem Generating well logs from small datasets with high accuracy.
method Combining ENN and C-LSTM networks with perturbation methods.
result 34% reduction in mean-square-error compared to existing models.
Random feature model shows slow self-correction of generalization gap.
problem Slow deterioration of generalization error in random feature model.
method Examined the dynamic behavior of gradient descent in the model's resonance regime.
result Gradient descent exhibits a self-correction mechanism, reducing generalization gap over time.
CoDistill-GRPO improves small models in GRPO by distilling knowledge from a larger model.
problem Small models in GRPO struggle with sparse rewards on difficult tasks.
method Simultaneously trains a large and small model using co-distillation and GRPO objectives.
result Significant improvement in small model performance over standard GRPO on mathematical benchmarks.
An investor with constant absolute risk aversion trades a risky asset with general Itô-dynamics, in the presence of small proportional transaction costs. In this setting, we formally derive a leading-order optimal trading policy and the associated welfare, expressed in terms of the local dynamics of the frictionless op…
Optimizes trading frequencies for multi-asset portfolios with small transaction costs.
problem Investment with multiple assets and small transaction costs.
method Optimizes trading frequencies explicitly for multidimensional diffusion setting, compares to alternatives.
result Explicit formulas for optimal trading frequencies and welfare losses.
The lifespan of Ricci flows is analyzed and generalized to noncompact manifolds.
problem Analyzing the lifespan and transfer rate of Ricci flows on manifolds with small Ricci curvature.
method Generalized lifespan estimate for local Ricci flow, proving short-time existence on noncompact manifolds with small curvature.
result Spatial transfer rate of Ricci flow resembles that of the heat equation under certain conditions.
We generalize the notion of a small sheaf of sets over a topological space or manifold to define the notion of a small stack of groupoids over an étale topological or differentiable stack. We then provide a construction analogous to the étalé space construction in this context, establishing an equivalence of 2-categori…
Paper tackles object detection in limited data scenarios.
problem Limited annotated data for object detection.
method Generative modeling with a novel unrolling mechanism to optimize both generation and detection.
result Improves object detection performance on NIH Chest X-ray dataset by 20%.
Method generates prototypes from small datasets for efficient learning.
problem Efficiently learning from small datasets with soft labels.
method Modular method for generating soft-label prototypical lines and Hierarchical Soft-Label Prototype k-Nearest Neighbor algorithm.
result High classification accuracy with significantly fewer prototypes than classes.
Small LLMs outperform large ones on simple tasks without extra labelling costs.
problem Performance of large commercial models in simple classification tasks.
method Logistic Regression on small LLM embeddings.
result Small LLMs equal or outperform large LLMs in 'tens-of-shot' classification tasks.
Develops a method for manifold learning with small sample size datasets.
problem Improving manifold learning performance for multiple tasks with limited samples.
method Uses instance and model transfer to integrate manifold models from similar tasks.
result Successfully estimates manifolds with tiny sample sizes across multiple tasks.
We prove that for every P there is a bound B depending only on P so that the mapping torus of every P--small irreducible train-track map can be obtained by surgery from one of B mapping tori. We show that given an integer P>0 there is a bound M depending only on P, so that there exists a presentation of the fundament…