Computer-generated proofs led to a mathematical result.
problem Discovering a mathematical result through computer-generated proofs.
method Combining computer-generated, human-readable proofs with mathematical abstraction.
result Abstracted lemma leading to an interesting mathematical result.
Computer generated academic papers have been used to expose a lack of thorough human review at several computer science conferences. We assess the problem of classifying such documents. After identifying and evaluating several quantifiable features of academic papers, we apply methods from machine learning to build a b…
Via a computer search, Altshuler and Steinberg found that there are 1296 +1 combinatorial 3-manifolds on nine vertices, of which only one is non-sphere. This exceptional 3-manifold K93 triangulates the twisted S2-bundle over S1. It was first constructed by Walkup. In this paper, we present a computer-…
Verified numerics prove existence of a curvature solution with known symmetries.
problem Existence of a curvature solution for the Nirenberg problem.
method Verified numerics and computer assistance.
result Existence of a genuine solution with known symmetry groups.
The minimum number of self-intersection points for members of a free homotopy class of curves on the punctured torus is bounded above in terms of the number L of letters required for a minimal description of the class in terms of the generators of the fundamental group and their inverses: it is less than or equal to (L…
Algorithm calculates Seifert matrices for colored links.
problem Computing Seifert matrices for colored links.
method Developed an algorithm implemented in Clasper software.
result Computes Seifert matrices, potential function, and signatures.
We use the Hopf fibration to explicitly compute generators of the second homotopy group of the flag manifolds of a compact Lie group. We show that these 2-spheres have nice geometrical properties such as being totally geodesic surfaces with respect to any invariant metric on the flag manifold. We characterize when th…
Simple ML models generate art completions.
problem Creating art through machine learning.
method Single-output classification and regression models trained on various image datasets.
result Generated images complete missing parts of input images.
We introduce a new fundamental domain for the cusp stabilizer of a Hilbert modular group over a real quadratic field K=Q(sqrt n). This is constructed as the union of Dirichlet domains for the maximal unipotent group, over the leaves in a foliation of the biplane. The region is the Cartesian product of the positive real…
Quantum GAN improves volatility modeling in finance.
problem Improving volatility modeling in finance using GANs.
method Developed a quantum GAN for volatility modeling.
result Quantum GAN provides exponential advantage over classical methods.
In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic function. We exploit the property of these risk measures of being the solution of an ele…
Study on random knot diagrams and their probability of forming specific knots.
problem Understanding the probability of forming specific knots from random knot diagrams.
method Analyzing free knot diagrams without over/under information and proving trefoil formation; making conjectures about unknot and trefoil probabilities.
result Every free knot diagram produces trefoil knots, and certain families of diagrams are completely worked out.
Let G be a two generator subgroup of PSL(2,C). The Jorgensen number J(G) of G is defined by J(G)=inf{ |tr^2 A-4|+|tr[A,B]-2| ; G=<A,B>}. If G is a non-elementary Kleinian group, then J(G) >= 1. This inequality is called Jorgensen's inequality. In this paper, we show that, for any r >= 1, there exists a non-elementary K…
Efficiently estimates online variational learning using importance sampling.
problem Online variational estimation in state-space models.
method Variational approach with Monte Carlo importance sampling.
result Proposed efficient algorithm for streaming data.
Study shows limits of certain normalizing flows in higher dimensions.
problem Understanding the representation power of normalizing flows in different dimensions.
method Rigorously established bounds on expressive power of basic normalizing flows.
result Limited representation power in higher dimensions, especially with moderate depth.
Four new methods for computing generalized chi-square distribution.
problem Computing the generalized chi-square distribution accurately and efficiently.
method Two exact and two approximate methods, with software for cdf, pdf, and inverse cdf.
result Comparison of methods' accuracy and speed, identifying best for different cases.
The paper proposes using path signatures for better inference in time series data.
problem Simulation models with time series data often lack tractable likelihood functions.
method Approximate Bayesian Computation with path signatures to handle sequential data.
result Theoretical guarantees on the resultant posteriors for Bayesian parameter inference.
A surgery formula for a specific 4-manifold invariant.
problem Computing the Casson-Seiberg-Witten invariant of a specific 4-manifold.
method Surgery formula and application to mapping tori.
result Computed the invariant for mapping tori of 3-manifolds.
Novel deep learning approach for fast, differentiable fluid simulations.
problem Challenges in solving incompressible fluid dynamics equations efficiently.
method Physics-constrained training approach for convolutional neural networks.
result Trained models can handle various fluid phenomena and offer fast simulations.
Invariants for singular knots and links using non-commutative cocycles.
problem Creating invariants for singular knots and links.
method Defining universal group and functions for non-commutative cocycles, and computing examples.
result Invariants for singular knots and links defined using non-commutative cocycles.
Algorithms for equilibrium computation generally make no attempt to ensure that the computed strategies are understandable by humans. For instance the strategies for the strongest poker agents are represented as massive binary files. In many situations, we would like to compute strategies that can actually be implement…
The Cheap Gradient Principle (Griewank 2008) --- the computational cost of computing the gradient of a scalar-valued function is nearly the same (often within a factor of 5) as that of simply computing the function itself --- is of central importance in optimization; it allows us to quickly obtain (high dimensional) …
New approach to compute generalization performance using known risk distribution.
problem Computing generalization performance in machine learning.
method Assumes known risk distribution ρ(r), computes expected error using empirical risk minimization, and considers power-law behavior of ρ(r). result Corrected typical behavior of generalization performance due to chance correlations in training set.
Survey on GANs for generating visual arts, music, and literature.
problem Tackles the challenge of generating art using GANs.
method Uses generative adversarial networks (GANs) to generate visual arts, music, and literary text.
result Performance comparison and description of various GAN architectures presented.
The paper connects ABC to GBI, suggesting ABC as a robustification strategy.
problem Approximate Bayesian Computation struggles with tractability in complex simulators.
method Reinterpreting ABC as an implicitly defined error model and suggesting GBI.
result ABC can be seen as a robustification strategy for approximating Bayesian posteriors.
SVM algorithm extracts digits from audio CAPTCHAs.
problem Recognizing audio CAPTCHAs from computer programs.
method Used RastaPLP features and SVM algorithm.
result Successfully extracted digits from audio CAPTCHAs.
Meta-learning base distributions for efficient PDE solutions.
problem Efficiently solving parametric parabolic PDEs across different scenarios.
method Meta-learning base distributions to compute PDE solutions.
result Improves generalization to new parameter regimes.
Study improves trading decisions by predicting profit and loss outcomes.
problem Inconsistent profitability of machine learning forecasts in financial markets.
method Developed a novel algorithm for forecasting profit and loss outcomes, integrating with market trend predictions.
result Significantly improved performance of trading strategies, including traditional and algorithmic trading.
Bardo Composer generates tabletop RPG music based on player speech.
problem Creating immersive background music for tabletop RPGs.
method Speech recognition, emotion classification, and music generation using a novel beam search algorithm.
result Generated music pieces can be accurately identified by human subjects as conveying the intended emotion.
We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure…
Linear time algorithm for random walk kernels on sparse graphs.
problem Efficient computation of general random walk kernels for large graphs.
method Sample dependent random walks to compute graph embeddings without direct graph product.
result Up to 27x faster and scalable to 128x larger graphs than previous methods.
Reduces a complex hypersurface to a simplified equation with primary invariants.
problem Analyzing Levi degenerate CR manifolds in 5 dimensions.
method Applying Lie's theory, integrating and straightening chains, and using Poincaré-Moser reduction.
result Shows a convergent change of coordinates that simplifies the equation of the manifold.
This study reveals efficient finite-difference computation for gradient regularization in deep learning.
problem Improving generalization performance in deep learning through gradient regularization.
method Analyzes and reveals a specific finite-difference computation that reduces computational cost and improves generalization performance.
result Finite-difference computation strengthens the implicit bias towards rich regimes and enhances generalization performance.
New MBQC algorithm uses randomness for generative modeling.
problem Designing efficient quantum algorithms for generative modeling.
method Proposes a variational MBQC algorithm that treats randomness as a resource.
result Randomness in MBQC can lead to significant gains in generative modeling performance.
Machine learning discovers equations from simulated data.
problem Discovering equations from computer-generated data.
method Sparse regression for equation learning.
result Machine learning can discover equations from complex data.
A new model for latent class analysis with weighted responses.
problem Limitation of latent class model for real-world data with continuous or negative responses.
method Proposed a novel generative model, the weighted latent class model (WLCM).
result The proposed WLCM is more realistic and general than the latent class model.
The study investigates how data variability impacts the generalization of neural networks.
problem Understanding the impact of data variability on neural network generalization.
method Developed a field-theoretic formalism to compute generalization properties of neural networks, focusing on data variability.
result Data variability leads to non-Gaussian action, affecting the learning curve and generalization properties of neural networks.
DO-EM framework for quantum models improves generative tasks.
problem Lack of Expectation-Maximization framework for density operators.
method Demonstrated inequality for density operators, derived DO-EM framework.
result DO-EM framework outperforms probabilistic models in generative tasks.
DiMMSB models directed mixed membership networks, identifying distinct community structures.
problem Modeling directed mixed membership networks with distinct community structures.
method Directed Mixed Membership Stochastic Blockmodel (DiMMSB) with DiSP algorithm.
result DiSP algorithm is asymptotically consistent and outperforms competitors.
New method computes discriminative classifiers from generative models.
problem Discriminative vs generative classifiers are often seen as distinct, but this work shows they can be equivalent.
method General theoretical result showing generative classifiers can be computed discriminatively.
result Bayesian Maximum Posterior classifier from generative models matches discriminative classifier definition.
Paper presents a new VMBQC model with fewer parameters for better generative modeling.
problem Limited generative power of VMBQC due to more parameters than unitary models.
method Introduces a restricted VMBQC model with a single additional trainable parameter.
result Minimal extension of VMBQC model generates distributions not learnable by unitary models.
Big T-Rex solves FDR-controlled sparse regression on laptops with millions of variables.
problem Scalable FDR-controlled variable selection for high-dimensional data.
method Early terminated random experiments with memory-mapping and permutation-based dummy generation.
result Solves FDR-controlled Lasso problems with 5 million variables on a laptop in 30 minutes.
Generative adversarial networks transform streetscape images to improve health and wellbeing.
problem Improving health and wellbeing outcomes through better streetscape design.
method Generative adversarial networks were used to translate Google Street View images, preserving structure while changing the style from bad health to good health areas.
result Translated images show that good health areas have more green space and compact urban design, while good social capital areas have more footpaths and less fencing.
Generative AI reduces IR evaluation costs but introduces errors; this work provides reliable CIs.
problem Generating relevance annotations using AI introduces errors that affect IR evaluation metrics.
method Proposes two methods: prediction-powered inference and conformal risk control to place reliable CIs around IR metrics.
result Proposed methods accurately capture both variance and bias in evaluation based on AI-generated annotations.
New bounds improve deep learning performance efficiently.
problem Improving generalization and robustness of deep learning models.
method Deriving four provable upper bounds on spectral norm of convolution layers, differentiable and efficient.
result Minimum of four bounds is a tight, differentiable and efficient upper bound on spectral norm.
Existing guarantees in terms of rigorous upper bounds on the generalization error for the original random forest algorithm, one of the most frequently used machine learning methods, are unsatisfying. We discuss and evaluate various PAC-Bayesian approaches to derive such bounds. The bounds do not require additional hold…
Unified framework for blending ML and mechanistic models in dynamical systems.
problem Learning dynamical systems from noisy, partially observed data.
method A unifying framework that combines mechanistic and machine learning approaches.
result Proves that hybrid models can learn memory-dependent model error.
This paper simplifies computing higher-order U-statistics efficiently.
problem The inefficiency of computing higher-order U-statistics in practice. method Decomposition, connection to Einstein summation, and treewidth-based complexity estimate.
result A new, more efficient algorithm to compute U-statistics.