SOC-ICNN expands neural network representational capacity by using conic optimization.
problem Restrictive representational capacity of ReLU-based ICNNs.
method Proposes SOC-ICNN architecture that uses Second-Order Cone Programming.
result SOC-ICNN strictly expands representational space without increasing complexity.
New weight initialisation for ICNNs accelerates learning and improves generalization.
problem Lack of effective initialisation strategies for ICNNs due to their unique weight and activation properties.
method Derived a principled weight initialisation by generalizing signal propagation theory for ICNNs with non-negative weights.
result Principled initialisation effectively accelerates learning and leads to better generalization in ICNNs.
Proposes a differentiable LSE-ICNN for modeling multi-well potentials.
problem Modeling multi-well potentials in various scientific domains.
method Log-sum-exponential (LSE) mixture of input convex neural network (ICNN) modes.
result Smooth surrogate that retains convexity within basins and allows gradient-based learning.
HyCNNs improve convex function learning and optimal transport.
problem Learning and optimizing convex functions efficiently.
method Combining Maxout networks and ICNNs to create a new neural architecture.
result HyCNNs require fewer parameters and outperform existing methods in convex tasks.
Optimizes functionals on probability space using ICNNs.
problem Optimizing functionals on the space of probabilities with high-dimensional convex functions.
method Proposes an approach using input-convex neural networks (ICNNs) to approximate the JKO scheme.
result Demonstrates feasibility and validity in approximating solutions of PDEs and molecular discovery.
Presented are two neural network architectures for convex functions, demonstrating competitive performance.
problem Approximating convex functions efficiently and accurately.
method Developed two neural network architectures: one based on linear-by-part representation and the other on cubic splines.
result Cubic ICKAN networks produce results similar to classical ICNNs in solving convex approximation problems.
Algorithm classifies point clouds using deep set linearized optimal transport.
problem Classifying point clouds efficiently and accurately.
method Deep Set Linearized Optimal Transport, ICNNs, and a discriminator network.
result Efficiently distinguishes between various classes of point clouds.
Paper introduces ICGNs to model convex gradients.
problem Modeling convex gradients efficiently.
method Integrates Jacobian-vector product in a neural network.
result Single layer ICGN outperforms single layer ICNN in fitting.
A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.
problem Training input-convex neural networks with non-negative weights.
method Introduces a hypernetwork that emits non-negative weights from a summary of the input batch, adding stochasticity to soften the loss landscape.
result The lift method achieves lower test loss than projected gradient descent and direct softplus reparametrization.
A neural network learns a convex regularizer for better image reconstruction.
problem Improving image reconstruction in inverse problems.
method Adversarial training of a data-adaptive ICNN as a convex regularizer.
result The convex regularizer leads to better convergence and error reduction in image reconstruction.
This paper proposes a new method to solve functional minimization problems in probability distributions using sliced-Wasserstein gradient flows.
problem Solving functional minimization problems in high-dimensional probability distributions is computationally challenging.
method The paper introduces a new approach using sliced-Wasserstein gradient flows to approximate the Jordan-Kinderlehrer-Otto (JKO) scheme, parameterizing densities with generative models.
result The proposed method is more flexible and computationally tractable compared to existing methods like JKO-ICNN.
Proposes a new neural head for asymmetric representation learning.
problem Asymmetric representation learning in directed relations.
method Role-aware neural convex divergence head.
result Role-aware projections improve directional accuracy over plain ICNN-Bregman heads.
A new method to estimate optimal transport maps without constraints.
problem Challenges in fitting optimal transport maps with neural networks.
method Introducing a Monge gap regularizer to estimate OT maps without architectural constraints.
result The proposed method significantly outperforms other baselines in practice.