Improves ordinal classification by avoiding ambiguous class predictions.
problem Ambiguity in class predictions for ordinal data.
method Proposes a noncrossing ordinal classification method with noncrossing constraints.
result Improves classification performance for ordinal data without ambiguous class predictions.
Researchers prove conjecture about contractible subcomplexes in noncrossing partition link.
problem Understanding contractibility of subcomplexes in the noncrossing partition link.
method Combining contractibility of flag complexes' stars with noncrossing hypertrees theory.
result Proved conjecture about contractible subcomplexes in the noncrossing partition link.
The study explores continuous noncrossing partitions and their relation to weighted circular factorizations.
problem Understanding the structure of continuous noncrossing partitions on the unit circle.
method Analyzes degree-d continuous noncrossing partitions and their equivalence classes of weighted linear factorizations.
result Maximal elements in the poset of continuous noncrossing partitions form a subspace homeomorphic to the dual Garside classifying space for the d-strand braid group.
New combinatorial method connects knot invariants to reflection groups.
problem Computing knot invariants using combinatorial techniques.
method Relating dual braid group generators, Hecke images of pure braids, and reflection groups.
result The ( a , z = 0 ) (a,z=0) ( a , z = 0 ) -HOMFLYPT polynomial can be computed as a solution to factorization problems. Characterizes elements in braid conjugacy classes using noncrossing partitions.
problem Conjugacy problem for periodic braids.
method Characterization of elements in super summit set via noncrossing partitions.
result Directly provides a conjugating element and determines the size of the super summit set.
Proof of K ( π , 1 ) K(π, 1) K ( π , 1 ) conjecture for affine Artin groups.
problem Asphericality of complements of affine hyperplane arrangements.
method Combinatorics of noncrossing partition posets, dual Artin groups, and topological models.
result Affine Artin groups are aspherical.
A meander of order n is a simple closed curve in the plane which intersects a horizontal line transversely at 2n points. (Meanders which differ by an isotopy of the line and plane are considered equivalent.) Let Gamma_n be the Cayley graph of the symmetric group S_n as generated by all (n choose 2) transpositions. Let …
Extended dual Coxeter and Artin groups theory to rank-three systems.
problem Extend dual Coxeter and Artin groups theory to rank-three systems.
method Geometric, combinatorial, and topological techniques.
result Proved the K ( π , 1 ) K(π, 1) K ( π , 1 ) conjecture, triviality of the center, and solubility of the word problem for rank-three Artin groups. We prove a long-standing conjecture about complex reflection arrangements.
problem The K ( π , 1 ) K(π,1) K ( π , 1 ) conjecture for affine Artin groups. method Recent advancements in dual Coxeter and Artin groups theory, new constructions, and poset shellability.
result The complexified complement of an affine reflection arrangement is a classifying space.
Triangulates permutahedra for Coxeter groups, revealing braid group connections.
problem Triangulating permutahedra for Coxeter groups.
method Constructs triangulations using total linear stability and height functions.
result Explicitly relates two braid group presentations.
The paper proves conditions for the isomorphism between standard and dual Artin groups.
problem Conditions for the isomorphism between standard and dual Artin groups.
method Analyzes Coxeter systems and their actions on reduced words to prove isomorphisms.
result Proves conditions for the isomorphism between standard and dual Artin groups.
Affine Artin groups have a finite classifying space.
problem Proving the K ( π , 1 ) K(π,1) K ( π , 1 ) conjecture for affine Artin groups. method Dual Garside structures, Euclidean isometries, and shellability of noncrossing partitions.
result Affine Artin groups have a finite classifying space.
New geometric object for polynomials simplifies complex data.
problem Understanding the combinatorial and geometric properties of polynomials.
method Introducing a compact planar 2-complex for polynomials with distinct roots.
result Extracts combinatorial data from a geometric structure of polynomials.
We consider two systems of curves ( α 1 , . . . , α m ) (α_1,...,α_m) ( α 1 , ... , α m ) and ( β 1 , . . . , β n ) (β_1,...,β_n) ( β 1 , ... , β n ) drawn on a compact two-dimensional surface M M M with boundary. Each α i α_i α i and each β j β_j β j is either an arc meeting the boundary of M M M at its two endpoints, or a closed curve. The α i α_i α i are pairwise disjoint except for possibly sharing endpoints, and s…
The paper studies geometric structures of polynomial spaces.
problem Understanding the geometric and combinatorial structures of polynomial spaces.
method Introducing and analyzing finite piecewise Euclidean cell complexes.
result The branched rectangle and annulus complexes are homeomorphic to specific polynomial spaces.
Unified clustering model handles both pairwise and cardinality constraints for better performance.
problem Clustering with specific constraints (pairwise and cardinality) to improve clustering quality.
method Unified integer programming formulation, binary and quadratic constraints, reformulated as continuous constraints, solved using ADMM.
result Unified model outperforms single category constraints and achieves better clustering performance.
Paper analyzes minimal investment risk with budget and concentration constraints.
problem Minimal investment risk in portfolio optimization with budget and concentration constraints.
method Replica analysis to consider the minimal investment risk.
result Minimal investment risk with concentration constraint is larger than without.
This work proposes an online learning approach to tighten constraints in stochastic control problems.
problem Solving chance-constrained stochastic optimal control problems is computationally challenging.
method Reformulate chance constraints as a binary regression problem and use a GP model to learn constraint-tightening parameters online.
result The approach tightens constraints more effectively, leading to lower costs in numerical experiments.
A new algorithm tackles submodular bandit problems with multiple constraints.
problem Addressing diversified retrieval and online learning with budget constraints.
method Non-greedy algorithm focusing on upper-confidence bounds.
result High-probability upper bound of an approximation regret matching fast offline algorithm's ratio.
Improved online convex optimization with long-term constraints achieving low regret and constraint violations.
problem Online convex optimization with long-term constraints over complicated sets.
method A new simple algorithm achieving O ( T ) O(\sqrt{T}) O ( T ) regret and O ( 1 ) O(1) O ( 1 ) constraint violations. result Improved performance with O ( T ) O(\sqrt{T}) O ( T ) regret and O ( 1 ) O(1) O ( 1 ) constraint violations. Simplifies neural network constraints with computationally efficient method.
problem Implementing hard output constraints in neural networks.
method Additional neural network layer for output constraints.
result Computational simplicity with complexity O(n*m) for linear constraints.
Reduces Lie (bi-)algebroids and Dirac manifolds using constraint vector bundles.
problem Reduction of Lie (bi-)algebroids and Dirac manifolds.
method Introduces constraint manifolds and constraint vector bundles; proves constraint Serre-Swan theorem; introduces Cartan calculus for constraint forms and multivector fields; shows compatibility with reduction.
result Reduction procedure for Lie (bi-)algebroids and Dirac manifolds.
Optimistic algorithm reduces regret and constraint violations in online convex optimization with adversarial constraints.
problem Online convex optimization with adversarial constraints.
method Improved algorithm using accurate predictions of loss and constraint functions.
result Improved bounds on regret and cumulative constraint violations.
Holistic GLMs add constraints for better model quality.
problem Improving classical linear regression models.
method Sparsity-inducing, sign-coherence, and linear constraints.
result Holistic GLMs reliably solve GLMs for various responses.
A new ML method teaches constraints directly to models.
problem Addressing safety and fairness in AI systems.
method Directly teaching constraint satisfaction to ML models using a constraint solver.
result Empirically, our approach performs well on fairness and synthetic constraints.
Paper tackles constrained bandit problems with a new learning framework.
problem Optimizing a black-box reward function subject to a black-box constraint function over a continuous space.
method Rectified Pessimistic-Optimistic Learning (RPOL) framework, incorporating optimistic and pessimistic GP bandit learning.
result RPOL achieves sublinear regret and minimal cumulative constraint violation.
Survey of Gaussian process constraints for modeling expensive data.
problem Modeling expensive data with physical constraints.
method Overview of various Gaussian process constraints and their implementation.
result Discussion of computational challenges introduced by constraints.
A new method LIF for equality constraints in GCNN models is proposed.
problem Embedding and selecting imposing schemes for prior information in GCNN models.
method Locally Imposing Function (LIF) for equality constraints.
result LIF enables local and explicit constraint implementation in the domain.
Iterative method learns unknown constraints for MPC control.
problem Learning to satisfy unknown polyhedral state constraints in iterative MPC.
method Collects and improves estimates of unknown constraints using collected data, designs an MPC controller to satisfy the estimated constraints.
result Robust and probabilistic guarantees of constraint satisfaction as a function of task iterations.
We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a measurable selection but still implies the Hamilton-Jacobi-Bellman equation in the …
We reformulate data-dependent constraints to ensure they are always met with high probability.
problem Ensuring fairness and stability in machine learning models with data-dependent constraints.
method Calibrated reformulation of constraints to guarantee satisfaction with a specified probability.
result Our method guarantees that fairness constraints are met at test time with high probability.
Physics-constrained GANs generate samples that meet deterministic constraints.
problem Ensuring GAN-generated samples comply with physical constraints.
method Enforce deterministic constraints via modified loss function.
result Physics-constrained GANs produce samples that accurately meet underlying constraints.
New algorithm reduces regret and constraint violation in online convex optimization with complex constraints.
problem Online convex optimization with multiple functional constraints and a simple constraint set.
method Instance-dependent bound using online primal-dual mirror-prox algorithm in general normed spaces.
result Achieves an O(√V*(T)) regret and O(1) constraint violation, improving over previous works.
The paper explores how to learn models that respect constraints in probabilistic learning.
problem Learning models that respect declared constraints in probabilistic learning.
method Mathematical inquiry on tractable probabilistic models like sum-product networks.
result Determines conditions under which constraints can be integrated with model learning.
Algorithm ensures privacy while strictly adhering to constraints.
problem Differential privacy with linear constraints that must be strictly followed.
method Developed an algorithm that releases a nearly-optimal solution satisfying constraints with probability 1.
result Achieved nearly optimal performance while preserving privacy and strictly adhering to constraints.
Proposes NUV priors for half-space and box constraints.
problem Adding constraints to linear Gaussian models without computational cost.
method Introduces NUV representations for half-space and box constraints.
result Adds constraints to linear Gaussian models without affecting computational tractability.
Meta-gradient D4PG optimizes performance and constraint adherence in RL.
problem Balancing performance and adherence to complex constraints in RL.
method Uses meta-gradients to find a balance between expected return and minimizing constraint violations.
result Meta-gradient D4PG consistently outperforms baselines across MuJoCo domains.
Geometrically characterizes virtual nonlinear nonholonomic constraints using symplectic methods.
problem Characterizing virtual nonlinear nonholonomic constraints geometrically.
method Geometric characterization using symplectic structures and Chetaev equations.
result A unique control law exists to satisfy virtual constraints, and closed-loop dynamics are projections of uncontrolled dynamics.
Develops a new method for optimizing with uncertain data.
problem Uncertainty in real-world optimization problems.
method Combines chance constraints and constraint learning for mixed-integer linear optimization.
result Data-driven solution for setting probabilistic bounds on learned constraints.
The paper improves Gaussian processes by adding sum constraints, enhancing prediction accuracy.
problem Improving Gaussian process predictions with background knowledge constraints.
method Conditioning the prior distribution on sum constraints to ensure fulfillment of linear and nonlinear constraints.
result The approach fulfills constraints with high precision and improves prediction accuracy.
Efficient algorithms decide algebraic constraints of causal graphs.
problem Distinguish causal graphs with latent confounders.
method Study algebraic constraints and propose efficient algorithms.
result Decide equivalence or subset of algebraic constraints.
The paper introduces MU for NMF with β β β -divergences and disjoint constraints.
problem Nonnegative matrix factorization with constraints.
method Design multiplicative updates for NMF based on β β β -divergences with disjoint constraints. result Multiplicative updates satisfy constraints and decrease the objective function.
FISAR uses neural networks to optimize safe reinforcement learning with forward-invariant constraints.
problem Safe reinforcement learning with constraints in safety-critical environments.
method Imposing linear constraints on policy parameters' updating dynamics, using a DNN-based optimizer to satisfy these constraints.
result The policy decreases constraint violation and maximizes cumulative reward monotonically.
We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The c…
Solves Einstein constraint equations on compact manifolds with specified boundaries.
problem Solving Einstein constraint equations with specified boundaries.
method Studies conformal constraint equations with low regularity assumptions.
result Solves Einstein constraint equations on compact manifolds with specified boundaries.
Algorithm finds real line mapping from points under ordinal constraints.
problem Finding a mapping from points to real line under ordinal constraints.
method Approximation algorithm for dense case in O ( n 7 ) + ( 1 / ε ) O ( 1 / ε 1 / 8 ) n O(n^7) + (1/\varepsilon)^{O(1/\varepsilon^{1/8})} n O ( n 7 ) + ( 1/ ε ) O ( 1/ ε 1/8 ) n time. result Computes a solution satisfying ( 1 − O ( ε 1 / 8 ) ) (1-O(\varepsilon^{1/8})) ( 1 − O ( ε 1/8 )) -fraction of all constraints. Formal constraints improve RL safety in complex environments.
problem Safety constraints in reinforcement learning for complex environments.
method Specify constraints in formal languages, instantiate as finite automata, augment MDP states, learn dense cost function.
result Improved safety in training RL algorithms over various constraints.
HardCoRe-NAS finds fitting neural networks adhering to hard resource constraints.
problem Finding fitting neural networks that adhere to hard resource constraints.
method Accurate formulation of resource requirement and scalable search method.
result HardCoRe-NAS generates state-of-the-art architectures strictly satisfying hard resource constraints.