Residual flows are shown to approximate MMD well.
problem Lack of theoretical understanding of normalizing flows' expressiveness.
method Proved residual flows are universal approximators in MMD.
result Residual flows can approximate MMD with a bounded number of blocks.
Simplifies residual flows to make flow-based modeling more practical.
problem Extremely high computational cost of residual flows limits their applicability.
method Introduces Quasi-Autoregressive (QuAR) approach to residual flows.
result Significantly reduces compute time and memory requirements for flow-based modeling.
Extends VAEs to handle complex Bayesian network structures.
problem Handling complex dependency structures in Bayesian networks.
method Extends VAEs with graphical residual flows to model arbitrary dependency structures.
result Demonstrates improved performance on synthetic datasets.
Researchers relax the CVF's smoothness requirement to create more flexible flow models.
problem Challenges in constructing flexible density models due to the CVF's smoothness requirement.
method Introduce L-diffeomorphisms as generalized transformations that may violate smoothness on zero Lebesgue-measure sets. result The relaxation allows for the use of non-smooth activation functions like ReLU in residual flows.
Invertible DenseNets improve model efficiency and performance.
problem Improving model efficiency and performance in neural networks.
method Enforcing invertibility in DenseNets by satisfying the Lipschitz constraint and proposing a learnable concatenation.
result i-DenseNets outperform Residual Flows in negative log-likelihood on various datasets.
Statistical generative models for molecular graphs attract attention from many researchers from the fields of bio- and chemo-informatics. Among these models, invertible flow-based approaches are not fully explored yet. In this paper, we propose a powerful invertible flow for molecular graphs, called graph residual flow…
Flow-based generative models parameterize probability distributions through an invertible transformation and can be trained by maximum likelihood. Invertible residual networks provide a flexible family of transformations where only Lipschitz conditions rather than strict architectural constraints are needed for enforci…
JKO-iFlow uses neural ODEs to improve generative models with reduced memory and training complexity.
problem Efficiently training deep generative models in high dimensions with reduced memory and training complexity.
method JKO scheme inspired neural ODE flow network with adaptive time reparameterization.
result JKO-iFlow achieves competitive performance compared to existing models at reduced computational and memory cost.
This paper improves bond market making by adjusting hit-ratios for client flow quality.
problem Economic misleading of raw hit-ratios in corporate bond market making.
method Stochastic-control framework with residual-quality-adjusted hit-ratio.
result Optimal quotes decompose into various components, improving service/economics frontier.
i-DenseNets improve parameter efficiency and performance in density estimation.
problem Improving parameter efficiency and performance in density estimation models.
method Invertible Dense Networks (i-DenseNets) with learnable weighted concatenation and Concatenated LipSwish activation function.
result i-DenseNets outperform Residual Flows and other flow-based models in bits per dimension.
Deep residual networks implicitly converge to neural ODEs.
problem Link between discrete and continuous deep learning models.
method Establishing implicit regularization for residual networks towards neural ODEs.
result Deep residual networks initialized as discretizations of neural ODEs converge to such ODEs during training.
A GPU-based workflow for building physics emulators of hypersonic flows
problem Resolving complex physical phenomena in hypersonic flows
method Fully GPU-based workflow integrating accelerated data generation and neural emulators
result Physics emulators remain reliable beyond their training distribution
A new method for learning gradient flows from population dynamics.
problem Reconstructing population dynamics from limited data.
method Residual approach to enforce continuity equations, combining with data-fitting divergence.
result Demonstrated state-of-the-art performance across trajectory inference benchmarks.
ELF simplifies normalizing flows, making them more efficient and universal.
problem Computational inefficiency of normalizing flows.
method ELF introduces a simple, one-layer network with closed-form Lipschitz constants, combining the ease of residual flows with the performance of autoregressive flows.
result ELF is a provably universal density approximator, more efficient computationally and parameter-wise.
New method learns PDE solutions from low-fidelity data.
problem Challenges in learning PDE surrogates with scarce data.
method Flow matching in infinite-dimensional space with conditional neural operators.
result Accurately learns PDE solutions across different resolutions and fidelities.
Method for conditional sampling with pre-trained normalizing flows.
problem Conditional sampling for incomplete observations.
method Variational Schur conditional sampling with normalizing flows.
result Successfully applied to invertible residual networks for inference and classification.
ImpFlows generalize normalizing flows by implicitly defining transformations.
problem Creating flexible and tractable probability distributions.
method Implicitly defined invertible transformations using roots of equations.
result ImpFlows can represent functions that ResFlows cannot, with comparable parameters.
Framework calculates positional influence in causal residual Transformers.
problem Understanding positional influence in causal residual Transformers.
method Adjoint-sensitivity framework for positional influence in causal residual Transformers.
result Exact evolution of adjoint-energy influence density and decomposition into residual transmission, nonlocal Volterra, and local channels.
Study Transformer layers under cross-entropy training using mean field control.
problem Understanding the behavior of Transformer layers in cross-entropy training.
method Continuous-depth mean field control analysis, treating depth as time and layer parameters as controls.
result Derivation of a Pontryagin condition for the limiting population problem, involving the softmax residual.
The effective application of neural networks in the real-world relies on proficiently detecting out-of-distribution examples. Contemporary methods seek to model the distribution of feature activations in the training data for adequately distinguishing abnormalities, and the state-of-the-art method uses Gaussian distrib…
We present an approach to market-consistent multi-period valuation of insurance liability cash flows based on a two-stage valuation procedure. First, a portfolio of traded financial instrument aimed at replicating the liability cash flow is fixed. Then the residual cash flow is managed by repeated one-period replicatio…
We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for universal approximation using continuous-time deep residual networks, which can …
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
Let M be an even-dimensional, oriented closed manifold. We show that the restriction of a singular Riemannian flow on M to a small tubular neighborhood of each connected component of its singular stratum is foliated-diffeomorphic to an isometric flow on the same neighborhood. We then prove a formula that computes c…
MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution.
problem Understanding the coarse-graining procedure in MLP residual networks
method Analyzing a pure MLP residual stack on synthetic Markov chain sequences
result MLP residual networks implement a selective coarse-graining procedure governed by the spectral structure of the input distribution
This paper begins to explore the determinants of the topological properties of the international - trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a "residual" ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and …
Convolutional neural networks (CNNs) with residual links (ResNets) and causal dilated convolutional units have been the network of choice for deep learning approaches to speech enhancement. While residual links improve gradient flow during training, feature diminution of shallow layer outputs can occur due to repetitiv…
A major contributing factor to the recent advances in deep neural networks is structural units that let sensory information and gradients to propagate easily. Gating is one such structure that acts as a flow control. Gates are employed in many recent state-of-the-art recurrent models such as LSTM and GRU, and feedforwa…
Deep linear networks minimize sharpness, avoiding large eigenvalues.
problem Understanding optimization dynamics in deep linear networks for regression.
method Analyzing sharpness (largest eigenvalue of Hessian) of minimizers and gradient flow solutions.
result Gradient flow implicitly regularizes towards flat minima, with sharpness bounded by a constant.
New diagnostic method detects misspecified models in inverse PDE problems.
problem Misleading residual-norm diagnostics in inverse PDE problems.
method Structure-sensitive sequential diagnostic using e-processes.
result Rejects fitted models that produce biased predictions.
CCVFM uses coreset to improve generative models by refining residual flows.
problem Generating multimodal distributions from scratch is challenging.
method Augments hierarchical rectified flow with a data-informed source distribution using a coreset.
result CCVFM achieves competitive few-step generation without a learned noise-to-data map.
New framework learns nonlinear cyclic causal models from data.
problem Challenges in learning causal relationships from real-world, cyclic systems.
method NODAGS-Flow: a novel framework using residual normalizing flows for likelihood estimation.
result Significant performance improvements in structure recovery and predictive performance compared to state-of-the-art methods.
Fast nonparametric conditional independence testing via two-stage regression
problem Fast nonparametric conditional independence testing
method BLITZ (Broad-to-Local Independence Testing via residualiZation)
result Better null calibration than fast kernel, random-feature, and regression-based competitors
We show that normalising flows become pathological when used to model targets whose supports have complicated topologies. In this scenario, we prove that a flow must become arbitrarily numerically noninvertible in order to approximate the target closely. This result has implications for all flow-based models, and espec…
Study geodesic flows on hyperbolic manifolds without conjugate points, proving unique measure of maximal entropy.
problem Proving uniqueness of measure of maximal entropy for geodesic flows on specific manifolds.
method Analyzing geodesic flows on closed Riemannian manifolds without conjugate points, using properties of Gromov hyperbolic and residually finite groups.
result Proves geodesic flow has a unique measure of maximal entropy under appropriate assumptions.
We prove that there exists a residual set of (non-rational) polygons such the billiard flow is weakly mixing with respect to the Liouville measure (on the unit tangent bundle to the billiard). This follows, via a Baire category argument, from showing that for any translation surface the product of the flows in almost e…
Paper uses optimal transport for low-dimensional representation of leukemia flow cytometry data.
problem Detecting minimal residual disease in leukemia patients using flow cytometry data.
method Optimal transport for dimensionality reduction and visualization of multi-patient flow cytometry datasets.
result OT-based approach provides a more informative two-dimensional representation of leukemia MRD.
Boosted GFlowNets improve exploration by sequentially training GFlowNets with residual rewards.
problem GFlowNets struggle to evenly explore reward landscapes, leading to poor coverage of high-reward areas.
method Sequential training of an ensemble of GFlowNets, each optimizing a residual reward.
result Boosted GFlowNets achieve better exploration and sample diversity on multimodal benchmarks and peptide design tasks.
One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approximation and estimation errors by a particular machine learning model. In this paper, we address this iss…
ESS-Flow guides flow models without retraining, using Bayesian inference in source space.
problem Training flow models on paired data for conditional generation or sample production.
method Gradient-free Bayesian inference in source space using Elliptical Slice Sampling.
result Effective in diverse tasks including material design and protein structure prediction.
Generative model designs highly designable proteins using geometric algebra.
problem Creating proteins with diverse and statistically accurate secondary structures.
method Introduced a geometric algebra flow matching model (FrameFlow) with Clifford Frame Attention (CFA) for protein backbone design.
result Achieved high designability, diversity, and novelty in protein backbone sampling.
The paper analyzes how open-end fund sales affect prices and returns.
problem How open-end fund sales impact prices and returns.
method Continuous-time market-clearing model to derive expected-return restrictions.
result Forced-sale pressure predicts actual fund selling and positive returns.
Gradient oversmoothing and expansion hinder deep GNN training, solved with normalization.
problem Gradient oversmoothing and expansion prevent deep GNN training.
method Proposed normalization method to constrain the Lipschitz bound of each layer.
result Residual GNNs with hundreds of layers can be efficiently trained with the proposed normalization.
Any traversally generic vector flow on a compact manifold X with boundary leaves some residual structure on its boundary $\d X$. A part of this structure is the flow-generated causality map Cv, which takes a region of $\d X$ to the complementary region. By the Holography Theorem from \cite{K4}, the map Cv allow…
We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting network architectures. In contrast, our approach only requires adding a simple …
CPFM integrates dimensionality reduction and reconstruction with flow networks.
problem Learning coupled continuous flows for data and embeddings.
method Coupled flow matching framework with Gromov-Wasserstein objective and dual-conditional flow network.
result CPFM preserves and recovers residual information in latent space.
Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the fact that many repeated evaluations of the forward model are often required. In…
New linear flows using exponential of linear transformations improve generative models.
problem Improving generative models in machine learning.
method Developed convolution exponentials and generalized Sylvester Flows using the exponential of linear transformations.
result Convolution exponentials and Convolutional Sylvester Flows outperform other models in log-likelihood.