New method uses patchworking to represent oriented matroids.
problem Representing oriented matroids from polyhedral structures.
method Variant of Viro's patchworking, controlled cell merging process.
result Achieved a combinatorial manifestation of patchworking.
Cluster Quilting clusters fragmented data sets for neuroscience and genomics.
problem Clustering fragmented data sets in neuroscience and genomics.
method Cluster Quilting method using patch ordering, patchwise SVD, sequential linear mapping, and k-means.
result Cluster Quilting discovers more accurate clusters than other methods.
New Alexandrov-Patchwork construction for Lorentzian spaces with curvature bounds.
problem Understanding finite diameter constraints in Lorentzian geometry.
method Constructing Alexandrov-Patchwork and proving Bonnet-Myers theorem for Lorentzian spaces.
result Lorentzian spaces with curvature bounds have finite diameter.
A cumbersome hypothesis for Viro patchworking of real algebraic curves is the convexity of the given subdivision. It is an open question in general to know whether the convexity is necessary. In the case of trigonal curves we interpret Viro method in terms of dessins d'enfants. Gluing the dessins d'enfants in a coheren…
New method for constructing real algebraic surfaces from complex tropical hypersurfaces.
problem Constructing real algebraic surfaces from complex tropical hypersurfaces.
method Non-Abelian patchworking theory.
result The method reproduces all existing isotopy types of surfaces up to degree three.
Paper proposes a copula method to generate unfavorable VaR scenarios.
problem Creating unfavorable VaR scenarios for insurance models.
method Patchwork copulas to create unfavorable VaR scenarios with given marginal distributions.
result Demonstrated with a 19-dimensional real-life insurance losses data set.
The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegan…
In this article we focus on the study of special parabolic points in surfaces arising as graphs of polynomials, we give a theorem of Viro's patchworking type to build families of real polynomials in two variables with a prescribed number of special parabolic points in their graphs. We use this result to build a family …
This friendly introduction to tropical geometry is meant to be accessible to first year students in mathematics. The topics discussed here are basic tropical algebra, tropical plane curves, some tropical intersections, and Viro's patchworking. Each definition is explained with concrete examples and illustrations. To a …
We complete the topological classification of real algebraic non-singular curves of bidegree (5,5) on the quadric ellipsoid. We show in particular that previously known restrictions form a complete system for this bidegree. Therefore, the main part of the paper concerns the construction of real algebraic curves. Our…
Formula for Laplacian determinants on polygonal domains with slits.
problem Determining the ζ-regularized determinant of the Laplacian on polygonal domains with slits. method Patchwork method for heat trace asymptotics, comparison formula for smooth conformal metrics.
result Polyakov-Alvarez type formula for Laplacian determinants on polygonal domains with slits.
The paper shows averaging gradients leads to memorization, proposing an alternative algorithm to focus on invariances.
problem The principle that 'good explanations are hard to vary' in deep learning is investigated.
method Formalizing consistency for loss surface minima, proposing an alternative algorithm based on logical AND.
result The alternative algorithm prevents memorization and focuses on invariances.
Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families of conics. Patches of supercyclides can be adapted to a Q-net (a discrete quadrilateral net with planar faces) such that neighboring surface patches share tangent planes along common boundary curves. We call the result…
Doctors often rely on their past experience in order to diagnose patients. For a doctor with enough experience, almost every patient would have similarities to key cases seen in the past, and each new patient could be viewed as a mixture of these key past cases. Because doctors often tend to reason this way, an efficie…
This text is intended to become in the long run Chapter 3 of our long saga dedicated to Riemann, Ahlfors and Rohlin. Yet, as its contents evolved as mostly independent (due to our inaptitude to interconnect both trends as strongly as we wished), it seemed preferable to publish it separately. More factually, our account…
This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region. Unlike existing local partitioned GP approaches, we introduce a technique for patc…
Meta-learning adapts models for unseen tasks across AI, robotics, and NLP.
problem Adapting models to unseen tasks efficiently and accurately.
method Black-box, metric-based, layered, and Bayesian approaches.
result Meta-learning enhances model generalization and adaptation to unseen tasks.
Meta-learning improves neural networks by adapting learning algorithms.
problem Conventional AI approaches solve tasks from scratch, but meta-learning aims to improve the learning algorithm.
method Meta-learning adapts a learning algorithm based on multiple learning episodes.
result Meta-learning can tackle deep learning challenges like data and computation bottlenecks.
Survey explores how transfer learning improves deep reinforcement learning.
problem Challenges in reinforcement learning efficiency and effectiveness.
method Categorizes and analyzes transfer learning approaches.
result Transfer learning enhances reinforcement learning performance.
Machine learning models adapt to motor learning but face challenges.
problem Adapting machine learning to handle motor variability and differentiate new movements from known ones.
method Parameter adaptation, transfer and meta-learning, reinforcement learning.
result Challenges in applying machine learning models for motor learning support systems.
New method uses bi-level optimization to learn useful representations for imitation learning.
problem Learning useful representations for multiple tasks in imitation learning settings.
method Formulates representation learning as a bi-level optimization problem.
result Bi-level optimization framework provides sample complexity benefits for imitation learning.
Tabular Q-Learning with learned state abstractions solves continuous control tasks.
problem Challenging reinforcement learning problems in continuous control.
method Learned state abstraction to transform continuous state-space into discrete.
result Tabular Q-Learning with learned abstractions achieves efficient learning in unseen tasks.
Study Whittle index learning algorithms for restless bandits with constant stepsizes.
problem Optimizing decisions in restless multi-armed bandits with constant stepsizes.
method Developed Q-learning algorithms with constant stepsizes for index learning in restless bandits, extending to DQN and function approximations.
result The algorithms learn the Whittle index effectively.
Paper discusses flaws in traditional RL for lifelong learning.
problem Traditional RL fails to model lifelong learning systems.
method Simplified prototype of lifelong RL system.
result Insights into lifelong RL, showing traditional RL's limitations.
AI learns to learn sequentially without forgetting.
problem Preventing catastrophic forgetting in machine learning models.
method Meta-learning a neuromodulatory activation-gating function to control selective activation in deep neural networks.
result State-of-the-art continual learning performance with 600 classes (9,000 updates).
Poisson learning doesn't solve graph semi-supervised learning issues.
problem Global information loss in graph-based semi-supervised learning.
method Poisson learning is Laplace regularization with thresholding.
result Poisson learning cannot overcome the global information loss problem.
New unsupervised learning technique learns independent kernels for better machine learning tasks.
problem Improving unsupervised representation learning for machine learning tasks.
method Stacking convolutional transforms using alternating proximal minimization scheme.
result DCTL outperforms shallow version CTL on benchmark datasets.
Meta-learning helps models learn quickly from few samples.
problem Deep learning requires many samples, which are hard to get.
method Meta-learning optimizes models to adapt quickly to new tasks.
result Meta-learning can improve model efficiency and adaptability.
New self-imitation learning method improves performance in continuous control tasks.
problem Improving off-policy learning in continuous control tasks.
method Proposes a n-step lower bound to generalize lower-bound Q-learning and introduces a new family of self-imitation learning algorithms.
result n-step lower bound Q-learning achieves a better trade-off between bias and contraction rate, leading to improved performance.
Deep reinforcement learning finds optimal learning policies for adaptive systems.
problem Finding individualized learning plans for learners with unknown latent traits.
method Formulated as a Markov decision process, applied deep Q-learning with a transition model estimator.
result The algorithm efficiently discovers optimal learning policies with small data sets.
Unified framework explains all types of learning, including brain.
problem Lack of clear explanation for deep learning success.
method Constructing a learning principle that equates all learning to probability estimation.
result Unified understanding of learning across different fields.
Cyclical learning rates improve DRL performance without manual tuning.
problem Manual hyperparameter tuning in DRL is time-consuming and error-prone.
method Proposes cyclical learning rates for DRL problems.
result Cyclical learning achieves similar or better results than fixed learning rates.
Study batch reinforcement learning methods for personalized medical treatments.
problem Batch reinforcement learning for personalized medical treatments.
method Direct policy learning and model-based learning approaches.
result Model-based learning is impossible with finite model classes but feasible with relaxed conditions.
A new meta-meta classification method tackles few-shot learning tasks.
problem Learning with limited data in small-data settings.
method Designing an ensemble of learners for a large set of problems, then learning how to combine them for a new problem.
result Meta-meta classification outperforms traditional meta-learning and ensembling approaches in one-shot learning tasks.
The paper proposes a learning algorithm that improves adaptability and generalization.
problem Improving adaptability and generalization in learning models.
method Learning to meta-learn by meta-finetuning on related tasks before adapting to specific tasks.
result Learning to meta-learn improves adaptability and generalization across various tasks.
Bayesian meta-learning improves few-shot learning with deep kernels.
problem Few-shot learning with small labeled datasets.
method Bayesian treatment of meta-learning using deep kernels.
result Deep Kernel Transfer (DKT) outperforms state-of-the-art algorithms.
Transfer learning improves algorithm recommendation performance.
problem Improving algorithm recommendation with limited data.
method Train a neural network on meta-datasets, then transfer knowledge to similar datasets.
result Transfer learning enhances meta-learning for algorithm recommendation.
This paper surveys meta-learning, online, and continual learning.
problem Combining and understanding meta-learning, online, and continual learning.
method Organizing various problem settings using consistent terminology and formal descriptions.
result Fosters further advancements in meta-learning, online, and continual learning.
Relational logistic regression (RLR) is a representation of conditional probability in terms of weighted formulae for modelling multi-relational data. In this paper, we develop a learning algorithm for RLR models. Learning an RLR model from data consists of two steps: 1- learning the set of formulae to be used in the m…
Survey on curriculum learning for reinforcement learning.
problem Efficiently learning complex tasks in reinforcement learning.
method Framework for curriculum learning in reinforcement learning.
result Survey and classification of existing CL methods.
Contrastive learning works well with redundant data views.
problem Improving unsupervised learning with redundant data views.
method Theoretical analysis of contrastive learning in a multi-view setting.
result Linear functions of learned representations are nearly optimal on prediction tasks when views are redundant.
Paper analyzes iterative learning for concept classes and learns half-spaces.
problem Learning concept classes efficiently with iterative learners.
method Analyzes various settings of iterative learning and provides a constructive algorithm for half-spaces.
result Constructive iterative algorithm for learning half-spaces from informant.
This paper introduces Dex, a reinforcement learning environment toolkit specialized for training and evaluation of continual learning methods as well as general reinforcement learning problems. We also present the novel continual learning method of incremental learning, where a challenging environment is solved using o…
Bayesian approach adapts deep network structure for continual learning.
problem Training neural networks with sequential or streaming tasks.
method Bayesian approach to learn deep network structure for each task.
result Model performs comparably or better than recent advances in continual learning.
Study shows cliff-learning in transfer learning from foundation models.
problem Data-scaling of transfer learning from foundation models in low data regimes.
method Investigation of cliff-learning phenomenon through foundation-model analysis and toy models.
result Cliff-learning reflects compatibility between priors and tasks.
Meta-strategy learns tuning parameters for online learning methods.
problem Difficulty in setting tuning parameters for online learning methods.
method Meta-learning approach to learn parameters from past tasks.
result Meta-strategy improves on learning each task in isolation.
This article reviews statistical methods for learning data representations.
problem Learning meaningful representations of data.
method Statistical perspective on unsupervised and supervised representation learning.
result Recent advances in representation learning from a statistical viewpoint.
We discuss a general method to learn data representations from multiple tasks. We provide a justification for this method in both settings of multitask learning and learning-to-learn. The method is illustrated in detail in the special case of linear feature learning. Conditions on the theoretical advantage offered by m…