Paper discovers governing equations from data using differential invariants.
problem Discovering partial differential equations from data is challenging.
method The paper proposes a pipeline based on differential invariants to reduce the search space and adhere to symmetry.
result DI-SINDy method outperforms other symmetry-informed methods in PDE discovery.
New framework discovers non-affine continuous symmetries in neural networks.
problem Lack of efficient methods for detecting non-affine continuous symmetries in neural networks.
method Computational framework for discovering infinitesimal generators of multi-parameter group actions.
result Framework can discover non-affine continuous symmetries in neural networks.
Method discovers symmetries in data with neural networks.
problem Discovering symmetries in high-dimensional data.
method Fully connected neural networks trained with a loss function for symmetry.
result Generators for symmetries in latent space.
New method discovers symmetries in differential equations from data.
problem Directly identifying Lie symmetries from scattered data without explicit equations.
method Numerical scheme using manifold learning and linear system construction.
result Accuracy and robustness demonstrated in various differential equations.
New method detects symmetries beyond affine transformations.
problem Current methods limit symmetry detection to affine transformations.
method Framework for discovering continuous symmetry beyond affine transformations.
result Method is competitive for large sample sizes and superior for small sample sizes.
We demonstrate the possibility of classifying causal systems into kinds that share a common structure without first constructing an explicit dynamical model or using prior knowledge of the system dynamics. The algorithmic ability to determine whether arbitrary systems are governed by causal relations of the same form o…
Automatically learns flexible symmetry constraints in neural networks using gradients.
problem Fixed hard constraints on neural network functions that cannot be adapted.
method Improves parameterisations of soft equivariance and optimizes marginal likelihood using differentiable Laplace approximations.
result Achieves equivalent or improved performance on image classification tasks compared to baselines with hard-coded symmetry.
Method improves deep learning models for datasets with mixed approximate symmetries.
problem Improving deep learning models for datasets with mixed approximate symmetries.
method Regularizer-based approach to build models for datasets with mixed approximate symmetries.
result Our method achieves better accuracy than prior approaches while discovering the approximate symmetry levels correctly.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
problem Improving the stability and physical interpretability of Neural ODEs.
method Integrating Lie symmetries and conservation laws into the loss function.
result Symmetry-regularized Neural ODEs enhance model stability and interpretability.
Latent MoS learns multiple symmetries for efficient dynamic learning.
problem Efficiently learning dynamics from limited system measurements.
method Latent Mixture of Symmetries (Latent MoS) with hierarchical architecture.
result Latent MoS outperforms baselines in interpolation and extrapolation tasks.
Finite resources limit false discovery rate control in structured hypothesis spaces.
problem Controlling false discovery rate in hypothesis testing with finite data and structured hypothesis spaces.
method Framework for exact FDR control and adaptive power maximization.
result Exact FDR control and adaptive power maximization.
Minimal surfaces with dihedral symmetry are studied as angles converge to zero.
problem Understanding minimal surfaces with dihedral symmetry as angles approach zero.
method Analyzing the limit of minimal surfaces in wedges with varying angles and using the implicit function theorem.
result New minimal surfaces are discovered and existence proofs are simplified.
Abstraction plays a key role in concept learning and knowledge discovery; this paper is concerned with computational abstraction. In particular, we study the nature of abstraction through a group-theoretic approach, formalizing it as symmetry-driven---as opposed to data-driven---hierarchical clustering. Thus, the resul…
The singly periodic genus-one helicoid was in the origin of the discovery of the first example of a complete minimal surface with finite topology but infinite total curvature, the celebrated Hoffman-Karcher-Wei's genus one helicoid. The objective of this paper is to give a uniqueness theorem for the singly periodic gen…
Unified framework for enforcing, discovering, and promoting symmetry in machine learning.
problem Symmetry in machine learning models and data.
method Unified mathematical framework using Lie derivatives, convex regularization, and nuclear norm relaxation.
result Unified approach to symmetry in machine learning tasks.
Study shows directional convergence for neural networks under spherical symmetry.
problem Learning linear predictors with neural networks under spherically symmetric data.
method Analysis of gradient flow and gradient descent for two-layer and deep linear networks.
result Directional convergence guarantees with exact convergence rate for specific network architectures.
Constructs a unique surface in a ball with specific properties.
problem Creating a minimal surface with specific topological and geometric constraints.
method Variational methods, equivariant min-max theory, nontrivial sweepout.
result First genus one critical catenoid in a unit ball.
This paper finds ReLU restores symmetry in SCL under class imbalances.
problem Symmetry break in SCL under class imbalances.
method Analytical proof and experiments with ReLU activation and batch selection.
result ReLU restores symmetry in SCL-learned representations without loss in test accuracy.
The paper explains emergent phenomena in deep learning using entropic forces.
problem Understanding the cause of emergent phenomena in deep learning and large language models.
method Proposes a rigorous entropic-force theory for neural networks trained with SGD and variants.
result Shows that representation learning is governed by emergent entropic forces that break continuous symmetries and preserve discrete ones.
Unified framework connects different neural network models.
problem Understanding the geometry of neural network loss landscapes.
method Unified framework capturing four symmetry classes.
result First discovery of low- and zero-barrier linear interpolation paths.
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the fundamental solution to the sub-Laplacian. This system is known to admit closed orb…
The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a new general method for any rank of CKT. This method can also be applied to other…
The main aim of this thesis is to study the properties of trapped surfaces in spacetimes with symmetries and their possible relation with the theory of black holes. We will concetrate specially on one aspect of this possible equivalence, namely whether the static black hole uniqueness theorems extend to static spacetim…
Deep learning has proven to yield fast and accurate predictions of quantum-chemical properties to accelerate the discovery of novel molecules and materials. As an exhaustive exploration of the vast chemical space is still infeasible, we require generative models that guide our search towards systems with desired proper…
The volume conjecture is proven for twist knots after Dehn filling.
problem Proving the volume conjecture for twist knots after Dehn filling.
method Constructing a new ideal triangulation of the Whitehead link complement.
result Chen-Yang's volume conjecture holds for sufficiently large parameters.
Differentiable causal discovery methods perform robustly under model violations.
problem Causal discovery algorithms struggle with real-world data due to unverifiable causal assumptions.
method Benchmarked differentiable causal discovery methods under eight model assumption violations.
result Differentiable causal discovery methods exhibit robust performance under Structural Hamming Distance and Structural Intervention Distance metrics.
New framework uses background knowledge to speed up causal discovery.
problem Scalable causal discovery for large datasets.
method Utilizes background knowledge during causal discovery process.
result Background knowledge reduces computational requirements and improves structure quality.
New method prevents invalid inference after causal discovery.
problem Invalid inference after causal discovery.
method Developed tools for valid post-causal-discovery inference.
result Our method provides reliable coverage while achieving more accurate causal discovery.
Unified approach to causal representation learning using invariance principles.
problem Identifying latent causal variables from high-dimensional observations.
method Guiding identification of causal variables with invariance principles rather than causal hierarchies.
result Unified method that mixes causal and non-causal assumptions improves treatment effect estimation.
Sparse regression models CMs from oscillatory shear data efficiently.
problem Discovering parsimonious constitutive models from oscillatory shear experiments.
method Sparse regression with tensor basis functions, l1 regularization, and greedy two-stage algorithm.
result Inferred CMs extrapolate well beyond training data and flow conditions.
LDP speeds up causal discovery by partitioning, improving VAS recall and runtime.
problem Hard causal discovery in nonparametric settings with exponential complexity.
method Local Discovery by Partitioning (LDP) for causal inference around exposure-outcome pairs.
result LDP yields less biased and more precise estimates than baseline methods.
In 1985, physicists Dixon, Harvey, Vafa and Witten studied string theories on Calabi-Yau orbifolds (cf. [DHVW]). An interesting discovery in their paper was the prediction that a certain physicist's Euler number of the orbifold must be equal to the Euler number of any of its crepant resolutions. This was soon related t…
Proposes LLM-DCD for improved causal discovery from data.
problem Challenges in discovering causal relationships from observational data.
method Uses LLM to initialize DCD optimization, incorporating priors.
result Higher accuracy on benchmark datasets compared to state-of-the-art.
Probabilistic grammars improve equation discovery from data.
problem Discovering scientific laws from data using equations.
method Proposed probabilistic context-free grammars to encode soft constraints and a Monte-Carlo algorithm.
result Probabilistic grammars lead to more efficient equation discovery.
Causal discovery improves fMRI analysis, but faces challenges.
problem Challenges in applying causal discovery to fMRI data.
method Identifying and addressing nine challenges in fMRI causal discovery.
result Current methods for fMRI causal discovery need improvement.
New methods for Markov Blanket discovery using MML outperform existing approaches.
problem Causal discovery from large datasets.
method Developed three new methods of Markov Blanket discovery using Minimum Message Length.
result Our best MML method is consistently competitive and has advantageous features.
L2D-CD learns to defer expert recommendations in causal discovery.
problem Combining expert knowledge with data-driven results in causal discovery when expert recommendations may contradict data.
method Adapting learning-to-defer algorithms for pairwise causal discovery, L2D-CD learns a deferral function to select between expert recommendations and data-driven methods.
result L2D-CD outperforms both causal discovery methods and the expert used in isolation, identifying domains where the expert's performance is strong or weak.
Review of automation's role in chemical discovery, emphasizing future challenges.
problem Improving automation's contribution to chemical discovery.
method Analysis of exemplary studies and open research directions.
result Future autonomous systems need improvement in data handling, model building, and experiment automation.
New method controls false discoveries in financial asset pricing.
problem Controlling false discoveries in time series with unknown correlations.
method Double bootstrapping method to control false discovery rate.
result Superior statistical power and controlled false discovery rate.
Interpretable ML helps discover insights from big data.
problem Validating data-driven discoveries from complex datasets.
method Statistical and machine learning techniques for interpretable models.
result Challenges in validating data-driven discoveries remain.
We introduce interactive structure discovery, a generic framework that encompasses many interactive learning settings, including active learning, top-k item identification, interactive drug discovery, and others. We adapt a recently developed active learning algorithm of Tosh and Dasgupta (2017) for interactive structu…
Review of automation's role in chemical discoveries.
problem Improving autonomous discovery in chemistry.
method Classification of discovery types, assessment of autonomy, case studies.
result Rapid advancements in automation and machine learning are transforming experimentation and modeling.
KEEL improves causal discovery with fuzzy knowledge and complex data.
problem Challenges in causal discovery due to prior knowledge, domain inconsistencies, and small sample sizes.
method Weakly-supervised fuzzy knowledge and data co-driven causal discovery method (KEEL).
result KEEL outperforms state-of-the-art methods in accuracy, robustness, and computational efficiency.
Cluster-DAGs improve causal discovery with prior knowledge.
problem Finding cause-effect relationships from high-dimensional data.
method Cluster-DAGs as prior knowledge framework, modified constraint-based algorithms Cluster-PC and Cluster-FCI.
result Cluster-PC and Cluster-FCI outperform baselines without prior knowledge.
The paper examines how timing of observations affects causal discovery methods.
problem The sensitivity of causal discovery methods to mismatched observation timing.
method Empirical and theoretical analysis of classical and recent causal discovery methods.
result Causal discovery methods are sensitive to sampling rate and window length.
New algorithm improves materials discovery using max K-Armed Bandit.
problem Maximizing material breakthroughs in materials discovery.
method Proposed a search algorithm based on max K-Armed Bandit (MKB) for materials discovery.
result Stable performance in late search stages, outperforming other bandit algorithms.
This work integrates domain knowledge into A*-based causal discovery methods.
problem Efficiently incorporating domain knowledge into A*-based causal discovery methods.
method Integrates various types of domain knowledge into A*-based causal discovery methods, reducing the graph search space and improving computational gains.
result Small amounts of domain knowledge can dramatically speed up A*-based causal discovery and improve its performance and practicality.
New methods control false discoveries near the boundary in conformal novelty detection.
problem Over-optimistic assessments near the rejection threshold in conformal novelty detection.
method Support line (SL) correction and alternative procedures to control boundary false discovery rate (bFDR).
result New procedures control the boundary false discovery rate (bFDR) in the conformal setting.