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.
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.
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have several limitations. A fundamental strength of deep learning is its flexibility, a…
Some recent studies have suggested using GANs for numeric data generation such as to generate data for completing the imbalanced numeric data. Considering the significant difference between the dimensions of the numeric data and images, as well as the strong correlations between features of numeric data, the convention…
New model generates data on constrained sets without losing tractability.
problem Generating data on constrained sets without losing tractability.
method Mirror Diffusion Models (MDM) learn diffusion processes in a dual space constructed from a mirror map.
result MDM generates data on convex constrained sets without losing tractability.
Generalizes momentum map to Courant algebroid for constrained mechanics.
problem Generalizing momentum map to new geometric structures.
method Generalized momentum section on Lie algebroid to Courant algebroid, constructed cohomological formulations.
result Identified momentum section in constrained Hamiltonian mechanics with Courant algebroid symmetry.
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.
Proposes a new method for constrained generative modeling using Langevin dynamics.
problem Challenges in satisfying underlying constraints with score-based generative models.
method Uses kinetic Langevin dynamics with specular reflection to model constraints.
result Demonstrates efficient numerical samplers with optimal convergence rates.
The paper studies surfaces with spherical curvature lines and their generation by constrained elastic curves.
problem Understanding surfaces with spherical curvature lines and their generation mechanisms.
method The approach involves Lie sphere transformations, Legendre curves, and polynomial conserved quantities of connections.
result Lie applicable surfaces with exactly one family of spherical curvature lines are generated by the lift of constrained elastic curves.
Unified framework for aligning and composing diffusion models to satisfy multiple constraints.
problem Improving quality and compliance of generated samples from diffusion models.
method Constrained optimization framework that unifies alignment and composition of diffusion models.
result Proposed framework effectively satisfies multiple constraints in image generation.
The Hawking energy is nonnegative and rigid on area-constrained surfaces in general relativity.
problem The rigidity and positivity of the Hawking energy on specific surfaces in general relativity.
method Evaluation of the Hawking energy on area-constrained critical surfaces under the dominant energy condition.
result The Hawking energy is nonnegative and rigid on area-constrained surfaces, including charged and cosmological constant variants.
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…
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.
CoMPNetX uses neural networks to efficiently solve constrained motion planning problems.
problem Finding collision-free paths on constraint manifolds efficiently.
method Neural generator and discriminator with neural gradients-based projection operator.
result CoMPNetX finds path solutions with high success rates and lower computation times.
Oracle-efficient algorithm for offline RL with partial data coverage.
problem Offline reinforcement learning with partial data coverage and constraints.
method PDOCRL, a primal-dual algorithm with decomposed linear-programming formulation.
result Near-optimal, near-feasible policy with \(\widetilde{\mathcal O}(ε^{-2})\) sample guarantee.
We call a Morse function f on a closed manifold k-constrained if neither f nor −f has critical points of indefinite Morse index <k. In this paper we study bordism groups of k-constrained Morse functions, and thus interpolate between the case k=1 of bordism groups of Morse functions (computed by Ikegami…
Novel methods generate diverse policies in reinforcement learning.
problem Generating diverse policies in reinforcement learning.
method Constrained optimization perspective, introducing new metrics, and novel policy generation methods.
result Improved novelty and performance of generated policies.
Paper uses RL to solve constrained combinatorial optimization problems.
problem Constrained combinatorial optimization problems.
method Extending NCO theory to CMDPs, using RL with penalty signals.
result Proposes a superior method for solving constrained problems.
Unified framework for constrained diffusion models on nonconvex sets with efficient landing mechanism.
problem Efficiently modeling generative models under nonconvex constraints.
method Unified framework with overdamped and underdamped dynamics, landing mechanism.
result Significantly reduces computational cost while maintaining sample quality.
Develops G-MLKM for better data-target association in constrained spaces.
problem Data-target association problem in constrained spaces with limited sensor information.
method Graph-based multi-layer k-means++ (G-MLKM) method, including MLKM for local space and G-MLKM for general constrained space.
result Improves data-target association accuracy through error correction mechanisms.
We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior information into the model. In addition to quadratic programming, we employ the alterna…
New method for constrained sampling using gradient flows.
problem Sampling from constrained domains.
method Introducing a boundary condition for gradient flow to confine particles within the domain.
result Provable continuous-time convergence in total variation for constrained sampling.
Chance-constrained ActInf allows for small violations of constraints to drive goal-directed behavior.
problem Goal-directed behavior constrained by prior beliefs.
method Introducing chance constraints to ActInf, allowing for small violations of constraints.
result Chance-constrained ActInf allows for a trade-off between robust control and chance constraint violation.
Physics-constrained neural nets solve EM fields of charged particle beams.
problem Solving Maxwell's equations for intense charged particle beams.
method 3D Convolutional Neural Networks (CNNs) constrained by physics.
result 3D CNNs generate electromagnetic fields from current and charge densities.
PDCA algorithm learns policies for RL with constraints using a primal-dual approach.
problem Offline constrained reinforcement learning with general function approximation.
method Primal-Dual-Critic Algorithm (PDCA) using a primal-dual approach.
result PDCA finds a near saddle point of the Lagrangian, nearly optimal for constrained RL.
We present a novel approach for constrained Bayesian inference. Unlike current methods, our approach does not require convexity of the constraint set. We reduce the constrained variational inference to a parametric optimization over the feasible set of densities and propose a general recipe for such problems. We apply …
Unified framework for constrained online decision-making.
problem Sequential decisions under stage-wise feasibility constraints.
method Upper counterfactual confidence bounds and generalized eluder dimension.
result Principled foundation for constrained sequential decision-making.
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.
Let (M,g) be a 3-dimensional Riemannian manifold. The goal of the paper it to show that if P0∈M is a non-degenerate critical point of the scalar curvature, then a neighborhood of P0 is foliated by area-constrained Willmore spheres. Such a foliation is unique among foliations by area-constrained Willmore …
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA). Bayesian inference involving probability distributions confined to constrained d…
This work compares regularization and constrained inference for label constraints in machine learning.
problem Improving model performance with label constraints in machine learning.
method Comparison of regularization and constrained inference strategies.
result Constrained inference reduces population risk by correcting model violations, while regularization narrows the generalization gap but introduces bias.
Develops an online method for solving constrained optimization problems with debiasing techniques.
problem Online inference of solutions to constrained optimization problems with equality and inequality constraints.
method Stochastic Sequential Quadratic Programming (SSQP) with momentum debiasing.
result Achieves global almost-sure convergence and local asymptotic normality with optimal primal-dual limiting covariance.
Adaptive sampling method solves constrained and composite optimization problems.
problem Solving constrained optimization problems with stochastic objectives and deterministic constraints.
method Proximal gradient method with adaptive sampling to improve gradient approximation quality.
result Convergence results established for both strongly convex and general convex objectives.
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.
Koopman Regularization learns governing equations from sparse data.
problem Learning governing equations from sparse and corrupted data.
method Constrained optimization using Koopman Eigenfunctions.
result Restores dynamics precisely with minimal assumptions.
AskewSGD optimizes quantized neural networks with interval-constrained optimization.
problem Training deep neural networks with quantized weights.
method Formulates QNN training as smoothed interval-constrained optimization, proposes AskewSGD for solving each subproblem.
result AskewSGD avoids projections and allows infeasible iterates, performs better than state-of-the-art methods.
Paper proves linear convergence of SCMS algorithm for directional data.
problem Identifying density ridges in directional data.
method Generalized SCMS algorithm to directional data, derived from SCGA with adaptive step size.
result Linear convergence of the proposed directional SCMS algorithm.
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.
Paper tackles constrained learning with non-convex losses, overcoming challenges with new approach.
problem Challenges in learning with non-convex losses and statistical constraints.
method Learning in the empirical dual domain, bounding empirical duality gap.
result Established a constrained counterpart to classical learning theory.
A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new appro…
CPS solves inverse problems using forward passes and constrained particle seeking.
problem Solving inverse problems with limited forward observation information.
method Gradient-free approach that reformulates inverse problem as constrained optimization.
result CPS achieves results comparable to gradient-based methods while outperforming alternatives.
Develops methods for estimating constrained function-valued parameters in infinite-dimensional models.
problem Estimating function-valued parameters with structural constraints in complex models.
method Characterizes constrained solutions as minimizers of penalized population risk, using a Lagrange-type formulation and path through unconstrained space.
result Proposes estimators that achieve optimal risk and constraint satisfaction, applicable across various statistical learning approaches.
Physics-constrained deep learning predicts geophysical dynamics with boundedness.
problem Forecasting geophysical systems with hidden variables and incomplete observations.
method Physics-constrained neural ordinary differential equation (NODE) representations with boundedness constraints.
result The approach generalizes learned dynamics to arbitrary initial conditions.
Automatic Chemical Design is a framework for generating novel molecules with optimized properties. The original scheme, featuring Bayesian optimization over the latent space of a variational autoencoder, suffers from the pathology that it tends to produce invalid molecular structures. First, we demonstrate empirically …
This paper introduces resilient constrained learning to adapt learning constraints while solving machine learning tasks.
problem Adapting machine learning solutions to satisfy multiple requirements beyond accuracy.
method Adapts learning constraints during training by balancing performance gains against a user-defined cost of relaxation.
result Shows conditions and introduces a practical algorithm to compute the balance, with approximation and generalization guarantees.
DGNet solves complex dynamical systems with neural networks and constraints.
problem Real-time accurate solutions for large-scale complex systems.
method Model-constrained discontinuous Galerkin Network (DGNet) for compressible Euler equations.
result DGNet achieves out-of-distribution generalization and improved stability.
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine learning applications and theoretical approximation algorithms for graph cluste…
We study configuration spaces of linkages whose underlying graph are polygons with diagonal constrains, or more general, partial two-trees. We show that (with an appropriate definition) the oriented area is a Bott-Morse function on the configuration space. Its critical points are described and Bott-Morse indices are co…