A new Euclidean approach reveals the pentagram map's beauty.
problem Exploring the pentagram map through classical geometry.
method Introducing an alternative Euclidean approach.
result Demonstrates the pentagram map's elegance through classical geometry.
Modern statistical methods find the most common value in data.
problem Finding the most common value in data.
method Modern statistical methods applied to mode estimation.
result Traditional approaches to mode estimation are explored and modern methods are applied to new fields.
Paper compares modern regression methods for time series data.
problem Regression analysis of time series data with time-indexed predictors.
method Classical statistical and recent machine learning approaches compared.
result Advantages and disadvantages of current methods identified.
Modern differential cohomology explained with applications.
problem Understanding differential cohomology from a modern perspective.
method Sheaves on manifolds, Chern-Weil theory, differential characters, differential characteristic classes.
result Differential lift of the first Pontryagin class.
Surveying topological complexity of graph configurations, unifying traditional and modern approaches.
problem Understanding the topological complexity of configuration spaces of graphs.
method Exploring traditional cohomology methods and modern asphericity/fundamental group approaches.
result Unified understanding of topological complexity through both traditional and modern methods.
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of c…
The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models th…
New method uses impact IRR to assess impact investments.
problem Determining financial returns of impact investments remains challenging.
method Adapts modern portfolio theory and financial tools to evaluate impact investments.
result Demonstrates the feasibility and utility of impact IRR for optimizing impact investments.
Proposes ACP for efficient inference in noisy-or models.
problem Efficient inference in noisy-or models.
method Hybrid approach combining classical and modern variational inference.
result ACP outperforms or matches other approaches in noisy-or models.
Paper improves disaster damage detection using modern transfer learning.
problem Harder to obtain damaged examples than undamaged ones.
method Revisits classical bagging with modern transfer learning.
result Significantly outperforms existing methodologies.
Paper develops a novel approach for optimal control using kernel methods.
problem Optimal control of nonlinear stochastic systems.
method Infinitesimal generator approach in reproducing kernel Hilbert spaces.
result Data-driven solution to optimal control problems.
Improved functional data modeling with modern imputation methods.
problem Estimating complex non-linear models with sparsely and irregularly sampled functional data.
method Modified multiple imputation methods combining MissForest and Local Linear Forest.
result New imputation methods produce better estimates than existing methods.
DeepJet improves jet flavor classification and quark-gluon tagging.
problem Jet flavor classification in high-energy physics experiments.
method Proposes a novel deep learning architecture, DeepJet, for improved performance.
result Improves heavy flavor classification performance and extends to quark-gluon tagging.
Efficient sparse modern Hopfield models are introduced for memory retrieval and learning tasks.
problem Efficient modern Hopfield models for memory retrieval and learning tasks.
method Nonparametric interpretation of Hopfield models as a regression problem.
result Sparse-structured modern Hopfield models with sub-quadratic complexity.
The paper addresses optimal control in modern tontines with bequest preferences, showing a linear investment strategy.
problem Optimal controls and decreasing allocation in modern tontines with bequest preferences.
method Dual approach to solve optimal control problems with power utilities, modeling bequest preferences.
result Investment strategy almost linearly adjusts from 0% to 100% over time.
The paper proposes modern computational methods for optimizing reinsurance contracts.
problem Optimizing catastrophe excess-of-loss reinsurance contracts with realistic constraints and risk measures.
method Two approaches: simulated annealing for local search and quantum branch & bound for future potential.
result Quantum branch & bound approach shows potential for future optimization with quantum computers.
Unified framework for arbitrary conditional inference using AI and Bayesian methods.
problem Limited flexibility in existing conditional inference methods.
method Bayesian generative modeling with stochastic iterative algorithm.
result Single learned model for universal conditional prediction with uncertainty quantification.
Hopfield networks outperform deep-learning methods in portfolio optimization.
problem Optimizing portfolios and managing asset allocation efficiently.
method Application of Hopfield networks to portfolio optimization, using combinatorial purged cross-validation.
result Modern Hopfield Networks perform on par or better than deep-learning methods, with faster training times and better stability.
TabSurv adapts tabular neural networks for survival analysis.
problem Survival analysis on tabular data using deep learning methods.
method Adapts modern tabular architectures to survival analysis using Weibull distribution or non-parametric prediction. Optimizes SurvHL histogram loss function.
result TabSurv consistently outperforms classical and deep learning baselines on 10 real-world survival datasets.
Despite rapid advances in machine learning tools, the majority of neural decoding approaches still use traditional methods. Modern machine learning tools, which are versatile and easy to use, have the potential to significantly improve decoding performance. This tutorial describes how to effectively apply these algorit…
Georg de Buquoy, Lord de Vaux, lived in Nove Hrady, Prague and Cerveny Hradek for most of his productive life. From his extensive scientific contributions, both theoretical and experimental, we expand here the discussion of his contributions to mathematical economy. He is mainly celebrated as the first persons to defin…
Blackwell's theorems influence modern AI through information compression and decision making.
problem Information compression and decision making under uncertainty.
method Theorems developed in the 1940s and 1950s, applied to modern AI.
result Blackwell theorems remain relevant and influence modern AI subfields.
In this work we present a review of the state of the art of Learning Vector Quantization (LVQ) classifiers. A taxonomy is proposed which integrates the most relevant LVQ approaches to date. The main concepts associated with modern LVQ approaches are defined. A comparison is made among eleven LVQ classifiers using one r…
Differentiable programming aids in solving differential equations and their sensitivities.
problem Computing gradients of numerical solutions of differential equations.
method Review of existing techniques and mathematical foundations.
result Established a coherent framework for combining differential equations with data-driven approaches.
New math for deep learning tackles key questions about neural networks.
problem Understanding the exceptional performance of deep learning models.
method Analyzing overparametrized neural networks, depth, optimization, feature learning, and architecture effects.
result Partial answers to deep learning's outstanding generalization and optimization performance.
Modern neural networks tend to be overconfident on unseen, noisy or incorrectly labelled data and do not produce meaningful uncertainty measures. Bayesian deep learning aims to address this shortcoming with variational approximations (such as Bayes by Backprop or Multiplicative Normalising Flows). However, current appr…
Modern physics has demonstrated that matter behaves very differently as it approaches the speed of light. This paper explores the implications of modern physics to the operation and regulation of financial markets. Information cannot move faster than the speed of light. The geographic separation of market centers means…
SIMD operations boost Bayesian computations up to 6x faster.
problem Expensive Bayesian computations are computationally intensive and parallelizable.
method Demonstrated the utility of SIMD operations for Bayesian applications using standard libraries.
result Up to 6x improvement in floating point arithmetic performance.
The paper explains the importance of diffeological groupoids in modern geometry and physics.
problem None explicitly stated, focuses on the concept and applications.
method Expository review of the development and applications of diffeological groupoids.
result The diffeological groupoid serves as a powerful tool in various areas of modern geometry and physics.
A new method for fast, non-iterative graphical model estimation.
problem Scalability issues in iterative proportional fitting for high-dimensional data.
method Non-iterative approach for positive definite graphical model estimation.
result The proposed method outperforms state-of-the-art methods in high-dimensional settings.
Unified framework for non-linear attention using modern Hopfield networks.
problem Improving transformer model's understanding of complex relationships and efficiency.
method Proposes an energy functional based on Modern Hopfield Networks (MNH) to unify linear and non-linear attention mechanisms.
result Context wells encapsulate contextual relationships among tokens, offering a richer representation of non-linear data.
This paper deals with the numerical approximation of American-style option values governed by partial differential complementarity problems. For a variety of one- and two-asset American options we investigate by ample numerical experiments the temporal convergence behaviour of three modern splitting methods: the explic…
BiSHop tackles tabular data challenges with sparse Hopfield layers.
problem Non-rotationally invariant data structure and feature sparsity in tabular data.
method Sequential column-wise and row-wise processing through interconnected directional learning modules with generalized sparse modern Hopfield layers.
result BiSHop surpasses current SOTA methods with significantly less hyperparameter tuning.
Hopfield networks improve reaction template prediction for few/zero-shot scenarios.
problem Predicting reaction templates for new molecules in CASP.
method Adapted Hopfield networks to associate reaction templates, molecules, and structural information.
result Significantly improved performance for templates with few or zero training examples.
We analyze computational limits of modern Hopfield models based on pattern norms.
problem Understanding the efficiency of modern Hopfield models from a fine-grained complexity perspective.
method Fine-grained complexity analysis and upper bound criterion for pattern norms.
result Below a specific norm threshold, efficient variants of modern Hopfield models exist.
Bayesian approach scores influential training examples for model predictions.
problem Enhance interpretability and safety of machine learning models.
method Formulate TDA as a Bayesian information-theoretic problem, scoring subsets by information loss.
result Method aligns with classical influence scores while promoting diversity for subsets.
Surveying probabilistic real algebraic geometry.
problem Classical problems in real algebraic geometry.
method Probabilistic perspective on classical topics.
result Modern approach to Hilbert's Sixteenth Problem.
How useful can machine learning be in a quantum laboratory? Here we raise the question of the potential of intelligent machines in the context of scientific research. A major motivation for the present work is the unknown reachability of various entanglement classes in quantum experiments. We investigate this question …
A database of objects discovered in houses in the Roman city of Pompeii provides a unique view of ordinary life in an ancient city. Experts have used this collection to study the structure of Roman households, exploring the distribution and variability of tasks in architectural spaces, but such approaches are necessari…
Modern treatment of space curve evolutes and involutes.
problem Understanding space curve evolutes and involutes.
method Unified treatment with novel observations and computer graphics.
result Illustration of space curve evolutes and involutes with computer graphics.
In 1896 Tresse gave a complete description of relative differential invariants for the pseudogroup action of point transformations on the 2nd order ODEs. The purpose of this paper is to review, in light of modern geometric approach to PDEs, this classification and also discuss the role of absolute invariants and the eq…
Modern health data science applications leverage abundant molecular and electronic health data, providing opportunities for machine learning to build statistical models to support clinical practice. Time-to-event analysis, also called survival analysis, stands as one of the most representative examples of such statisti…
Modern technologies are generating ever-increasing amounts of data. Making use of these data requires methods that are both statistically sound and computationally efficient. Typically, the statistical and computational aspects are treated separately. In this paper, we propose an approach to entangle these two aspects …
FF layers in transformers are nearly as interpretable as sparse autoencoders.
problem Comparing interpretability of feature vectors in FF layers vs. sparse autoencoders.
method Revisited interpretability of FF layers as key-value memories using modern benchmarks.
result FF and SAE feature vectors are similarly interpretable, but FFs can be better in some aspects.
AI improves credit rating predictions over traditional methods.
problem Improving credit rating predictions for global corporate entities.
method Applying deep learning techniques, specifically neural networks with categorical embeddings, to a large dataset of corporate obligations.
result Deep learning models achieve adequate accuracy in predicting different credit rating classes.
TensorFlow Probability MCMC toolkit improves MCMC efficiency for modern hardware.
problem Inefficient MCMC algorithms on modern hardware.
method Design and implementation of a new MCMC toolkit for TensorFlow.
result Improved MCMC efficiency on modern hardware.
New scaling laws optimize model size, training, and inference for better performance.
problem Trade-off between model size and inference cost in modern LLMs.
method Train-to-Test (T2) scaling laws that jointly optimize model size, training tokens, and inference samples. result Optimal pretraining decisions shift into overtraining regime, leading to stronger performance.
Investigates sports betting strategies using modern portfolio theory and Kelly criterion.
problem Mitigating risk in sports betting investments.
method Modern portfolio theory and Kelly criterion, with modifications for practical risk control.
result Adaptive fractional Kelly method is suitable across various sports settings.