Two novel approaches improve prediction with Clusterwise Linear Regression.
problem Predicting cluster labels for unseen test points in CLR.
method Two novel approaches: Predictive CLR and Constrained CLR.
result Both approaches significantly improve over known CLR-based regression methods.
Proposes CLRS-Text, a new benchmark for evaluating LM reasoning capabilities.
problem Lack of transferable benchmarks for evaluating reasoning capabilities of language models.
method Developed a textual version of the CLRS benchmark, generating diverse algorithmic tasks.
result Demonstrates a novel challenge for the LM reasoning community and validates prior work.
Proposes CLRS benchmark to evaluate algorithmic reasoning.
problem Difficulty in transferring results across publications due to targeted algorithmic data.
method Develops a comprehensive benchmark covering various algorithmic tasks.
result Demonstrates performance of algorithmic reasoning baselines on the CLRS benchmark.
Cluster-wise linear regression (CLR), a clustering problem intertwined with regression, is to find clusters of entities such that the overall sum of squared errors from regressions performed over these clusters is minimized, where each cluster may have different variances. We generalize the CLR problem by allowing each…
Donor-aware scRNA-seq benchmarks improve classification accuracy in inflammatory bowel disease.
problem Influenza disease classification from scRNA-seq data is prone to donor-level confounding.
method Developed and evaluated three feature representations across two IBD cohorts.
result Compartment-stratified CLR composition and GatedStructuralCFN embeddings outperform linear models in classification accuracy.
Enhances neural architecture search efficiency and prevents performance collapse.
problem Improving memory efficiency and preventing performance collapse in neural architecture search.
method Employing continuous relaxation strategy and gradient-based optimization for over-parameterized BCNN construction, introducing Confident Learning Rate and partial channel connections.
result NAS-v2 delivers state-of-the-art search efficiency on CIFAR-10 and ImageNet.
Generalist neural learner can execute multiple algorithms.
problem Building models that can execute multiple algorithms.
method Single graph neural network processor, incorporating knowledge from specialist models.
result Generalist learner can execute multiple algorithms with improved performance.
Characterizes corridors in loss surfaces for gradient-based optimization.
problem Understanding and mitigating training instabilities in gradient-based optimization.
method Characterizes corridors as regions where gradient descent and gradient flow trajectories are linearly related.
result Corridors indicate regions without implicit regularization effects, leading to better learning rate adaptation schemes.
LibAUC optimizes X-risks for AI tasks like CID, LTR, and CLR.
problem Optimizing risk functions in AI for tasks like classification, ranking, and representation learning.
method Developed a new mini-batch pipeline for deep X-risk optimization (DXO) algorithms.
result Achieved great success in solving CID, LTR, and CLR tasks with faster convergence and scalable performance.
New algorithms improve sampling from complex distributions.
problem Sampling from distributions with convex outside and nonconvex inside.
method Overdamped and underdamped Langevin MCMC methods.
result Upper bounds on the number of steps for sampling accuracy.
Graph Neural Networks align with dynamic programming, improving algorithmic reasoning.
problem Demonstrate and quantify alignment between GNNs and dynamic programming.
method Category theory and abstract algebra methods to expose intricate connection.
result Showed GNNs align with dynamic programming beyond individual algorithms.
Researchers analyze and improve latent space in NAR models.
problem Latent space resolution and range issues in NAR models.
method Detailed analysis of GNN latent space structure, proposing and testing solutions.
result Improvements in majority of algorithms on CLRS-30 benchmark.
New algorithms for sampling in constrained domains without learning rates.
problem Sampling in constrained domains with fairness constraints and post-selection inference.
method Coin betting ideas from convex optimisation and a unifying framework for constrained sampling.
result Our algorithms achieve competitive performance without hyperparameter tuning.
Develops a theory to make learning solutions fair and safe.
problem Ensuring learning solutions are unbiased and safe in critical applications.
method Generates a generalization theory based on PAC learning framework, introduces constrained learning algorithm.
result Proves that constrained learning is as learnable as unconstrained learning, provides practical algorithm.
The paper classifies a special family of knots in lens spaces using knot Floer homology.
problem Classifying constrained knots in lens spaces.
method Parameterization by five integers, characterization via spinc structures, and knot Floer homology calculations. result Complete classification of constrained knots based on knot Floer homology.
This article reviews and explains HMC-based methods for sampling constrained continuous distributions.
problem Sampling from continuous distributions with constraints.
method HMC and related methods for constrained sampling.
result HMC and related methods are more efficient for constrained sampling.
A deep learning framework improves constrained clustering with new types of side information.
problem Limitations of existing constrained clustering formulations.
method Developed a deep learning framework to extend constrained clustering.
result Framework handles various types of constraints, including continuous values and high-level domain knowledge.
Optimizes PDE-constrained LDDMM for efficient non-rigid registration.
problem Inexact Newton-Krylov optimization in PDE-constrained LDDMM leads to poor geodesic paths.
method Band-limited vector field parameterization to optimize computational complexity.
result Optimized method shows competitive performance with reduced memory load and computational time.
Exploring conjectures in constrained Willmore problem.
problem Understanding the Willmore functional over compact surfaces.
method Analyzing conjectures from partial results and numerical experiments.
result Ramifications for deeper understanding of the Willmore functional.
New adaptive filtering algorithm CMCC improves performance in impulsive noises.
problem Adaptive filtering in non-Gaussian impulsive noises.
method CMCC incorporates a linear constraint into MCC filter to solve a constrained optimization problem.
result CMCC significantly outperforms MSE based constrained adaptive algorithms in impulsive noises.
Tensor networks constrain kernel machines to Gaussian processes.
problem Speeding up kernel machines with reduced model complexity.
method Proving CPD and TT-constrained models recover Gaussian processes with i.i.d. priors.
result TT-constrained models exhibit more Gaussian process behavior than CPD for the same parameters.
Extends GENO framework for GPU optimization of constrained ML problems.
problem Constrained optimization in classical machine learning.
method Extends GENO framework to GPU optimization, specifying problems in a modeling language.
result Solvers on GPU outperform state-of-the-art approaches by several orders of magnitude.
New method solves portfolio optimization with cardinality constraints efficiently.
problem Real-world portfolio constraints like transaction costs and client preferences.
method Continuous relaxation method for NP-hard problems, extending Markowitz and CVaR models.
result Efficient algorithms find near-optimal portfolios for cardinality-constrained problems.
Deep learning improves decoding of constrained sequence codes, reducing errors and increasing throughput.
problem Errors during transmission of constrained sequence codes.
method Deep learning, specifically MLP and CNN networks.
result Achieved low bit error rates close to MAP decoding and improved system throughput.
Paper proves unique energy-minimizing curves in constrained spaces.
problem Uniqueness of energy-minimizing curves in constrained spaces.
method Investigated energy-minimizing curves with fixed endpoints in a constrained space.
result Proved that the set of points for which the energy-minimizing curve is not unique has no interior points.
Researchers identify only two types of tori with specific energy constraints.
problem Finding constrained Willmore tori in 3-space with specific energy limits.
method Analyzing isothermic constrained Willmore tori in the 3-sphere.
result Homogeneous and 2-lobe Delaunay tori are the only isothermic constrained Willmore tori with Willmore energy below 8π.
Algorithm tackles constrained reinforcement learning with concave-convex and knapsack constraints.
problem Constrained episodic reinforcement learning with concave rewards and convex constraints.
method Modular analysis with strong theoretical guarantees for concave-convex and knapsack settings.
result Significantly outperforms existing approaches in constrained episodic environments.
Balls are the only volume-constrained critical points of perimeter.
problem Finding volume-constrained critical points of perimeter.
method Analyzing sets of finite perimeter and using Alexandrov's theorem.
result Balls are the only volume-constrained critical points of perimeter.
Energy quantization for surfaces with area, volume, and mean curvature constraints.
problem Energy quantization for constrained Willmore surfaces.
method Established through strong compactness under energy thresholds.
result Strong compactness of constrained Willmore surfaces, including minimizers.
This study improves numeric data generation using constrained WGAN structures.
problem Overfitting and ill-conditioning in numeric data generation with GANs.
method Designs and evaluates constrained network structures (isomorphic, mirror, self-symmetric) in WGANs for numeric data generation.
result Constrained structures significantly improve numeric data generation in 17/20 experiments.
A new method solves complex constrained minimax problems.
problem Solving constrained minimax optimization problems.
method First-order augmented Lagrangian method.
result Established an operation complexity of O(ε−4logε−1). Proposes r2SGLD for efficient constrained exploration in non-convex learning.
problem Stagnation in high-temperature chains of reSGLD in distribution tails.
method r2SGLD: replica exchange with reflection steps in a bounded domain.
result Reflection steps enhance mixing rates with quadratic improvement in domain diameter.
The paper optimizes policies constrained to Schur stabilizing controllers using a Newton-type algorithm.
problem Optimizing policies under linear constraints in control systems.
method Newton-type algorithm on a manifold of Schur stabilizing controllers with a Riemannian metric.
result Local convergence guarantees for the Newton-type algorithm without relying on exponential mapping or retractions.
Consistent estimation of constrained autoregressive processes.
problem Estimating autoregressive processes with coefficients constrained to an ellipsoid.
method Use of constrained and penalized estimators under different norms.
result Provide consistency results for estimation of constrained autoregressive processes.
We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…
Algorithm optimizes constrained reinforcement learning with dual variables.
problem Minimizing convex functional subject to convex constraint in large state spaces.
method VPDPO algorithm using Lagrangian and Fenchel duality.
result Achieves sublinear regret and constraint violation, globally optimal policy.
Study of Morse functions with constraints and their bordism groups.
problem Interpolating between Morse and generic functions' bordism groups.
method Elimination of cusps, Stein factorization, two-index theorem, handle extension theorem.
result Constrained bordism groups are related to connective bordism.
The paper compares methods for solving constrained lasso problems.
problem Handling linear constraints in lasso regression.
method Quadratic programming, ADMM, and solution path algorithm.
result Efficiency and accuracy recommendations for different data sizes.
Estimates Markov chains from data with a non-convex rank-constrained approach.
problem Estimating low-rank Markov chains from empirical data.
method Rank-constrained likelihood maximization and DC programming.
result The proposed estimator achieves better empirical performance than other methods.
This paper tackles constrained statistical learning problems by proposing a new approach.
problem Statistical learning problems with constraints are challenging and scarce.
method Directly tackling the constrained problem using finite dimensional parameterizations, sample averages, and duality theory.
result We bound the empirical duality gap, showing the effectiveness of the constrained formulation.
Constrained Willmore surfaces are critical points of the Willmore functional under conformal variations. As shown in [5] one can associate to any conformally immersed constrained Willmore torus f a compact Riemann surface Σ, such that f can be reconstructed in terms of algebraic data on Σ. Particularly interesting exam…
Study of large area-constrained Willmore surfaces in Schwarzschild-like manifolds.
problem Understanding Willmore surfaces in asymptotically Schwarzschild 3-manifolds.
method Application of Lyapunov-Schmidt reduction method.
result End of the manifold is foliated by area-constrained Willmore spheres.
New method solves constrained optimization problems efficiently.
problem Equality-constrained nonlinear, nonconvex optimization problems.
method Adaptive inexact Newton method with randomized iterative sketching.
result Global almost sure convergence and local linear/superlinear convergence.
This paper studies constrained polygonal linkages and their configuration spaces.
problem Understanding the configuration spaces of constrained polygonal linkages.
method The paper uses Bott-Morse functions and critical point analysis to study the configuration spaces.
result The oriented area is a Bott-Morse function with computed indices.
A new method for optimizing non-decomposable metrics with constraints.
problem Optimizing complex machine learning objectives with thresholded constraints.
method Formulate rate-constrained optimization using the Implicit Function theorem and solve with gradient-based methods.
result Demonstrated effectiveness over existing methods on benchmark datasets.
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy W=∫H2 under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the crit…
Self-distillation improves constrained language generation by aligning models with target distributions.
problem Sparse and uninformative reward signals in constrained generation settings.
method Iteratively refining the base model through self-distillation, incorporating learned twist functions and proposals.
result Substantial gains in generation quality through improved model alignment with target distributions.
In this paper we consider two special classes of constrained Willmore tori in the 3-sphere. The first class is given by the rotation of closed elastic curves in the upper half plane - viewed as the hyperbolic plane - around the x-axis. The second is given as the preimage of closed constrained elastic curves, i.e., elas…