This study introduces a spin invariant for Prym-Teichmüller curves in genus 3.
problem Sorting cusp prototypes of Prym-Teichmüller curves in genus 3.
method Develops a new invariant and describes the Galois action on these curves.
result Components of Prym-Teichmüller curves in genus 3 are homeomorphic.
Prototypal analysis improves archetypal analysis by penalizing distant prototypes, making it more robust and interpretable.
problem Sensitivity to outliers and non-locality in archetypal analysis limit its applicability as a learning tool.
method Prototypal analysis finds prototypes through convex combination of data points, penalizing distant prototypes.
result Prototypal analysis is more robust and interpretable than archetypal analysis.
ProtoryNet interprets text sequences using prototype trajectories for better understanding.
problem Improving text classification interpretability and accuracy.
method ProtoryNet uses prototype trajectories to interpret text sequences, with prototype pruning for better interpretability.
result ProtoryNet outperforms baseline models and reduces performance gap compared to black-box models.
Prototype networks on hyperspheres improve classification and regression.
problem Improving classification and regression performance.
method Using hyperspherical prototypes for classification and regression, optimizing prototypes through data-independent margin separation.
result Hyperspherical prototype networks outperform other methods in classification, regression, and their combination.
Infinite mixture prototypes adapt to complex data for few-shot learning.
problem Few-shot learning with complex data distributions.
method Adaptive representation of classes by clusters, inferring cluster number.
result 25% absolute accuracy improvement on alphabets, state-of-the-art semi-supervised clustering.
Optimal prototypes found for challenging pathological geometries.
problem Finding optimal prototypes for pathological geometries is challenging.
method Analytical and heuristic algorithms for finding nearly-optimal prototypes.
result Optimal prototypes can be found analytically for challenging geometries.
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.
Tree prototypes improve tree ensemble interpretability.
problem Making tree ensembles interpretable.
method Introducing prototypes, a new distance for GBTs, and adaptive selection methods.
result Prototypes can perform as well as or better than original tree ensembles when used as nearest-prototype classifiers.
Paper optimizes hyperspherical prototypes for better class separation.
problem Previous HPL approaches either lack principled optimisation or are limited to one latent dimension.
method Develops a principled optimisation procedure and uses linear block codes to create well-separated prototypes in various dimensions.
result Optimal prototype placement is characterized with achievable and converse bounds, showing near-optimality.
Prototype model improves model auditing and understanding.
problem Auditing and understanding modern language models is expensive and approximate.
method Introduced a sparse, non-negative mixture of learned prototypes trained with clustering objectives.
result Prototype models either surpass or remain within 2.5 percentage points of dense baselines on downstream tasks.
Prototypical networks simplify few-shot learning by using prototype representations.
problem Few-shot classification for new classes with limited training data.
method Learn a metric space with prototype representations for each class.
result Achieve excellent results compared to recent approaches.
New invariant cusp crossing density shows cusp densities of hyperbolic knots and links are dense.
problem Densities of cusp invariants for hyperbolic knots and links.
method Defined cusp crossing density as ratio of cusp volume to crossing number; showed densities are dense.
result Cusp crossing density for links is bounded above by 3.1263... and is dense in [0, 2.120...].
4-manifolds show every flat 3-manifold as cusp sections.
problem Realizing flat 3-manifolds as cusp sections of hyperbolic 4-manifolds.
method Transitive action on cusps, dense flat metrics realization.
result Existence of many cusp-transitive 4-manifolds.
Characterizes holonomies of convex projective cusps.
problem Understanding holonomies in strictly convex projective geometry.
method Complete characterization of holonomies for strictly convex and round cusps, building families of generalized cusps.
result Produces the first example of generalized cusps with non-virtually nilpotent fundamental group.
The paper uses learned prototypes to explain deep learning models for time-series data.
problem Lack of explainable AI in deep learning models for high-risk decisions.
method Learned prototypes in latent space of deep learning models.
result Prototypes improve classification decisions and provide explainable insights.
TPM improves medical image segmentation by separating foreground and background.
problem Few-shot medical image segmentation challenges due to background variability.
method Tied Prototype Model (TPM) focusing on foreground, adapting thresholds, and using class priors.
result TPM leads to improved segmentation accuracy compared to ADNet.
The paper proposes scalable methods for selecting prototypes from large dissimilarity datasets.
problem Selecting good prototypes from large dissimilarity datasets.
method Genetic algorithms, dissimilarity-based hashing, unsupervised and supervised criteria.
result The methods select good prototypes efficiently from large datasets.
A new neural network method improves interpretability and detection of outliers.
problem Improving interpretability and detection of outliers in neural networks.
method Prototype-based learning (PbL) using a winner-take-all (WTA) network with two prototypes: positive and negative.
result The negative prototype is similar to the positive one, aligning with the BCM theory.
We present the Bayesian Case Model (BCM), a general framework for Bayesian case-based reasoning (CBR) and prototype classification and clustering. BCM brings the intuitive power of CBR to a Bayesian generative framework. The BCM learns prototypes, the "quintessential" observations that best represent clusters in a data…
Gaussian prototypical networks improve few-shot learning on Omniglot.
problem Few-shot classification on the Omniglot dataset.
method Extends prototypical networks by incorporating uncertainty estimates as Gaussian covariance matrices to define a distance metric.
result Report state-of-the-art performance in 1-shot and 5-shot classification.
Study geodesics entering a fixed cusp neighborhood multiple times.
problem Understanding geodesics entering a specific cusp neighborhood multiple times.
method Investigate reciprocal geodesics entering a fixed cusp neighborhood a fixed number of times.
result Characterized the class of reciprocal geodesics entering a fixed cusp neighborhood a fixed number of times.
Proves methods for creating convex projective 3-manifolds with cusps.
problem Creating convex projective 3-manifolds with generalized cusps.
method Properly convex deformations of hyperbolic structures, controlling cusp types.
result First known example of a 1-cusped hyperbolic 3-manifold with a type 2 cusp.
Pantypes improve prototypical models by capturing diverse input distributions.
problem Prototypical models lack sufficient data representation in low density regions.
method Introducing pantypes, a sparse set of diverse objects to represent the full diversity of input distribution.
result Pantypes empower prototypical models to foster high diversity, interpretability, and fairness.
The paper classifies different types of cusps on plane curves.
problem Investigating various types of cusps on plane curves.
method Examining criteria for (n,n+1) cusps with differential conditions and relations to evolutes of fronts. result Complete classifications for (4,5)-cusps. The paper characterizes links in 3D from divides with cusps.
problem Characterizing links in 3D from divides with cusps.
method Defines and characterizes divides with cusps and their associated links.
result Every strongly invertible link and 2-periodic link can be described as the link of a divide with cusps.
Extends techniques to show existence of all cusp types in convex projective manifolds.
problem Existence of all cusp types in convex projective manifolds.
method Extension of techniques by Ballas-Marquis.
result Existence of all cusp types in all dimensions except diagonalizable.
Prototype sentences edited for better language models and quality.
problem Improving sentence generation quality and efficiency.
method Samples a prototype sentence, edits it, and uses a latent edit vector.
result Improves perplexity and generates higher quality sentences.
The paper explores cusp types in hyperbolic 4-manifolds and their commensurability classes.
problem Understanding cusp types in hyperbolic 4-manifolds and their commensurability.
method Criteria for commensurability classes containing specific cusp types.
result Infinitely many examples of commensurability classes without certain cusp types.
A neural network that explains its predictions through prototypes.
problem Lack of interpretability in deep neural networks.
method A novel network architecture with an autoencoder and prototype layer, trained with four terms.
result The network learns to explain its predictions through learned prototypes.
The paper classifies cusp types in hyperbolic knot complements.
problem Classifying cusp types in hyperbolic knot complements.
method Analyzing quotients of hyperbolic knot complements.
result All cusp types arise in the quotients of link complements.
IMKPL learns interpretable prototypes for better classification.
problem Efficient trade-offs between interpretability and prediction accuracy in kernel-based data.
method Local discrimination in feature space, condensed class-homogeneous neighborhoods, combined embedding.
result IMKPL achieves better interpretability and discriminative representation.
PTBCC improves accuracy in multi-class annotation aggregation by learning from prototype confusion matrices.
problem Inaccurate and insufficient confusion matrices for annotators in multi-class classification tasks.
method PTBCC (ProtoType learning-driven Bayesian Classifier Combination) uses prototype confusion matrices to capture annotator expertise.
result PTBCC achieves up to 15% accuracy improvement and 3% higher average accuracy compared to existing methods.
New findings on cusped Borel Anosov representations and their properties.
problem Characterizing and understanding cusped Borel Anosov representations.
method Analyzing representations of lattices in PGL2(R) to PGLd(R). result Cusped Borel Anosov representations with specific properties are Hitchin representations.
Cusped hyperbolic 3-manifolds can have up to 4 cusps under certain group actions.
problem Understanding the maximum number of cusps in hyperbolic 3-manifolds under group actions.
method Analyzing the isometry group actions on cusps of hyperbolic 3-manifolds.
result Constructing a family of manifolds with no upper bound on the number of cusps for k=2. A model finds interpretable prototypes for MIL datasets.
problem Finding interpretable prototypes for multiple instance learning.
method Permutation invariant maximally predictive prototype generator.
result The model outperforms existing approaches in accuracy and efficiency.
Study shows rigidity in cusp-decomposable manifolds' geometry.
problem Understanding the geometry of cusp-decomposable manifolds.
method Examined large scale geometry and quasi-isometries.
result Proved quasi-isometric rigidity for fundamental groups.
SPOT uses optimal transport to select important prototypes.
problem Summarizing datasets for better understanding and decision making.
method Modeling prototype selection as a submodular optimization problem and using a greedy algorithm.
result Our approach efficiently selects prototypes with optimal transport that best represent the target dataset.
Classifies low-volume hyperbolic 3-manifolds with a maximal cusp.
problem Identifying hyperbolic 3-manifolds with minimal volume and maximal cusps.
method Maximal cusp volume classification and analysis of low-volume manifolds.
result Figure-8 knot complement is unique in certain volume and filling categories.
The condensed nearest neighbor (CNN) algorithm is a heuristic for reducing the number of prototypical points stored by a nearest neighbor classifier, while keeping the classification rule given by the reduced prototypical set consistent with the full set. I present an upper bound on the number of prototypical points ac…
New subspace prototype flag median improves clustering on noisy data.
problem Finding robust prototypes for datasets of images and videos.
method Proposes flag median and introduces FlagIRLS algorithm for its calculation.
result Flag median is robust to outliers and improves cluster purity.
Study of isometries on hyperbolic 3-manifold cusps.
problem Understanding transitivity in hyperbolic 3-manifold actions.
method Analyzing multiply transitive actions of isometries on cusps.
result Proved a conjecture about the maximum transitivity and upper bounds on cusps.
Prototype selection improved using topological data analysis.
problem Improving prototype selection methods for data compression.
method Introducing two topological prototype selector variants: TPS and BoundaryTPS.
result BoundaryTPS achieves the lowest mean Friedman rank on H1 persistence-diagram preservation. Four hyperbolic 24-cell 4-manifolds with one cusp are identified.
problem Identifying hyperbolic 24-cell 4-manifolds with one cusp.
method Analyzing hyperbolic geometry and isometry.
result Found four one-cusped hyperbolic 4-manifolds of minimum volume.
DPTA improves CIL by adapting PTMs with dual prototypes.
problem Catastrophic forgetting in incremental learning with pre-trained models.
method Dual-Prototype Network with Task-wise Adaptation (DPTA).
result DPTA consistently outperforms recent methods by 1\%-5\% on multiple benchmarks.
ProtoBandit uses bandits to find prototypes efficiently.
problem Finding a compact set of prototypes from a large dataset.
method Stochastic greedy search and multi-armed bandits.
result ProtoBandit reduces similarity comparisons to O(k3∣S∣), independent of target set size. Computes cusp cobordism groups for Morse functions on manifolds.
problem Understanding the cusp cobordism groups of Morse functions.
method Employed Levine's cusp elimination technique and created pairs of cusps along fold lines.
result Both unoriented and oriented cusp cobordism groups are cyclic of order two in even dimensions and infinite order in odd dimensions.
Study of Eisenstein series linked to hyperbolic cusps.
problem Understanding Eisenstein series associated with hyperbolic cusps.
method Analyzing cohomology classes and intertwining operators.
result Different cusps correspond to linearly independent cohomology classes.
Algorithm generates new drug molecules from prototypes, showing diversity and validity.
problem Designing new drugs from existing prototypes is expensive and time-consuming.
method Conditional Diversity Networks (CDN) for unsupervised generation of drug molecules.
result Generated molecules are valid and significantly different from prototypes, including FDA-approved drugs.