ResNets and DenseNets converge to NTK with depth and width, offering advantages for kernel regression.
problem Understanding convergence of ResNets and DenseNets to Neural Tangent Kernel (NTK).
method Analysis of finite width and depth corrections for NTK of ResNets and DenseNets.
result ResNets and DenseNets can converge to NTK with depth and width, unlike vanilla networks.
Quantum advantage in derivative pricing requires 8k qubits and 54M T-depth.
problem Quantum advantage in pricing derivatives.
method Re-parameterization method combining pre-trained variational circuits and fault-tolerant quantum computing.
result Benchmark use cases require 8k logical qubits and a T-depth of 54 million.
Data depth aids in identifying anomalies in multivariate data.
problem Detecting abnormal observations in multivariate datasets.
method Using data depth to assign abnormality labels to observations with lower depth values.
result Data depth effectively identifies anomalies in multivariate settings.
Deep RNNs excel at capturing long-term dependencies in sequential data.
problem Lack of a formal measure for RNNs' long-term memory capacity.
method Introduced a measure called Start-End separation rank to quantify RNNs' ability to model long-term dependencies.
result Deep RNNs support Start-End separation ranks that are combinatorially higher than shallow ones.
Researchers quantify the relationship between feature depth and performance in deep neural networks.
problem Understanding how depth affects feature extraction and generalization in deep neural networks.
method Adaptive analysis of feature-depth trade-offs in deep nets, proving optimal generalization performance.
result Optimal generalization performance achieved through empirical risk minimization on deep nets.
Paper uses statistical depth to create DP estimators for regression.
problem Creating differentially private estimators in high dimensions.
method Uses halfspace and regression depth to analyze maximum influence and construct DP estimators.
result New DP estimators for location and regression show favorable performance.
AdaEnsemble learns adaptive feature interactions for CTR prediction.
problem Learning feature interactions for CTR prediction in recommender systems and Ads ranking.
method AdaEnsemble is a Sparsely-Gated Mixture-of-Experts (SparseMoE) architecture that dynamically selects feature interaction depth.
result AdaEnsemble achieves better prediction accuracy and inference efficiency compared to state-of-the-art models.
Smooth activations enable optimal error rates in neural networks for Sobolev function classes.
problem Achieving optimal approximation and estimation error rates for neural networks in Sobolev function classes.
method Study of neural networks with smooth activations, proving optimal rates via approximation and statistical properties.
result Constant-depth networks with smooth activations achieve optimal rates of approximation and estimation, demonstrating smoothness adaptivity.
Single T-gate makes distribution learning hard for deep circuits.
problem Learning probability distributions from quantum circuits.
method Characterization of learnability and simulatability of quantum circuit outputs.
result Injection of a single T-gate into depth n^Ω(1) circuits makes distribution learning hard.
AR-GANs learn depth and DoF from unlabeled images using aperture rendering and focus cues.
problem Learning depth and DoF from unlabeled natural images with diverse viewpoints and shapes.
method Aperture rendering and focus cues to learn depth and DoF from unlabeled images.
result AR-GANs effectively learn depth and DoF from various datasets, including flower, bird, and face images.
Deeper networks are better for local labels, but shallower for global labels.
problem Understanding the effect of depth in overparameterized neural networks.
method Introduced local and global labels to investigate the advantage of depth.
result Deeper networks are better for local labels, shallower for global labels.
In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a …
New model separates objects in scenes, enabling novel arrangements and depth.
problem Lack of modular, compositional scene modeling in generative models.
method Ensemble of generative models (experts) compete for explaining different parts of a scene.
result Model generates scenes with novel object arrangement and depth ordering.
Autonomous construction of deep neural network (DNNs) is desired for data streams because it potentially offers two advantages: proper model's capacity and quick reaction to drift and shift. While the self-organizing mechanism of DNNs remains an open issue, this task is even more challenging to be developed for standar…
Quantum circuits reveal pathways to dequantization in machine learning models.
problem Navigating the complex landscape of quantum machine learning models and algorithms.
method Introducing a framework connecting quantum circuit structure to function representability.
result Fundamental properties of quantum circuits determine classical simulability of models.
VQAs use classical optimization to train quantum circuits, promising quantum advantage.
problem High computational cost of quantum simulations and solving large-scale problems.
method Variational Quantum Algorithms (VQAs) use classical optimizers to train parametrized quantum circuits.
result VQAs are a promising strategy for obtaining quantum advantage.
DiffEnc improves diffusion models by adding flexibility and achieving better likelihood on CIFAR-10.
problem Improving the likelihood of diffusion models on image datasets.
method Introducing a data- and depth-dependent mean function and a free weight parameter for noise variance.
result Achieved statistically significant improvement in likelihood on CIFAR-10.
Theory explains why DARTS favors deep architectures over shallow ones.
problem DARTS selects architectures with dominated skip connections, leading to performance degradation.
method Theoretical analysis of operations' effects on network optimization; introduces sparse binary gates and path-depth-wise regularization.
result Theoretical proof that architectures with more skip connections converge faster.
New neural network architecture with height adds expressive power.
problem Expressiveness of neural networks limited by width and depth.
method Introduces height as a new hyper-parameter in neural network architecture.
result Neural networks with height achieve significantly better approximation of functions.
The great success of deep learning poses urgent challenges for understanding its working mechanism and rationality. The depth, structure, and massive size of the data are recognized to be three key ingredients for deep learning. Most of the recent theoretical studies for deep learning focus on the necessity and advanta…
Many deep learning algorithms can be easily fooled with simple adversarial examples. To address the limitations of existing defenses, we devised a probabilistic framework that can generate an exponentially large ensemble of models from a single model with just a linear cost. This framework takes advantage of neural net…
We study the complexity of functions computable by deep feedforward neural networks with piecewise linear activations in terms of the symmetries and the number of linear regions that they have. Deep networks are able to sequentially map portions of each layer's input-space to the same output. In this way, deep models c…
We introduce the framework of continuous--depth graph neural networks (GNNs). Graph neural ordinary differential equations (GDEs) are formalized as the counterpart to GNNs where the input-output relationship is determined by a continuum of GNN layers, blending discrete topological structures and differential equations.…
Enhanced ODT with Feature Concatenation boosts learning efficiency.
problem Insufficient learning efficiency of ODT due to linear projections not being transmitted to child nodes.
method Feature Concatenation ( exttt{FC-ODT}) to transmit linear projections along decision paths.
result Experiments show exttt{FC-ODT} outperforms state-of-the-art decision trees with a limited tree depth.
Quantum networks offer exponential communication savings for large machine learning models.
problem Training and inference of large models require efficient communication.
method Quantum encoding and gradient descent for distributed computation.
result Exponential reduction in communication for gradient descent on quantum networks.
Deep networks learn hierarchical functions more efficiently than shallow ones.
problem Understanding the advantage of deep neural networks over shallow models.
method Analytical study of learning dynamics and generalization performance of deep networks compared to shallow ones.
result Deep networks reduce effective dimensionality, enabling learning with fewer samples.
We present a new approach to modeling sequential data: the deep equilibrium model (DEQ). Motivated by an observation that the hidden layers of many existing deep sequence models converge towards some fixed point, we propose the DEQ approach that directly finds these equilibrium points via root-finding. Such a method is…
A new depth measure for non-convex data supports, faster than halfspace depth.
problem Non-convex data supports in multivariate statistics.
method Extending halfspace depth to Reproducing Kernel Hilbert Space (RKHS).
result The new depth measure is consistent and can be computed faster.
The paper studies randomized approximations of Tukey's depth for log-concave isotropic data.
problem The challenge of approximating Tukey's depth in high dimensions.
method The study examines randomized algorithms for approximating Tukey's depth for log-concave isotropic data.
result Randomized algorithms correctly approximate maximal depth and close to zero depths but not intermediate depths.
This paper connects functional data analysis with machine learning techniques.
problem Lack of theoretical analysis for functional depths.
method Viewing functional depths as kernel mean embeddings in machine learning.
result Facilitates answers to open questions about functional depths.
Self-attention models benefit equally from width and depth, but beyond a certain point, depth becomes less efficient.
problem Understanding the optimal balance between depth and width in self-attention models.
method Theoretical predictions and empirical ablations on networks of varying depths and widths.
result An optimal width of 30K is recommended for a 1-Trillion parameter network, marking a significant width for self-attention models.
Study identifies three quantization regimes for ReLU networks.
problem Approximation of Lipschitz functions by ReLU networks with finite-precision weights.
method Established through nonasymptotic tight lower and upper bounds on minimax approximation error.
result Memory-optimality achieved in proper quantization regime for deep networks.
This paper considers the power of deep neural networks (deep nets for short) in realizing data features. Based on refined covering number estimates, we find that, to realize some complex data features, deep nets can improve the performances of shallow neural networks (shallow nets for short) without requiring additiona…
Capsule Networks improve autonomous navigation in sparse environments.
problem Challenges in reinforcement learning for sparse reward environments.
method Caps-EM pairs CapsNets with Advantage Actor Critic, using fewer parameters.
result Caps-EM achieves significant time improvements and fewer parameters compared to competing methods.
A new depth measure based on optimal control theory captures multi-modal data.
problem Statistical depths for high-dimensional data.
method Eikonal equations and optimal control theory.
result The new depth measure is robust under adversarial models.
A new depth measure and median defined on Hadamard manifolds.
problem Statistical depth and median on Hadamard manifolds.
method Horospherical depth and Busemann median defined using renormalized distance functions.
result The Busemann median exists for every Borel probability measure on Hadamard manifolds.
New approach uses loss functions to extend data depth for anomaly detection.
problem Anomaly detection in high-dimensional data.
method Introducing loss depths to generalize halfspace depth.
result New loss depths improve anomaly detection efficiency and interpretability.
Proves depth 2 neural networks can't approximate certain functions as well as depth 3 networks.
problem Approximating functions with depth 2 networks in high dimensions.
method Lower bound proof using worst-to-average-case random self-reducibility.
result Proves depth 2 networks can't approximate certain functions as well as depth 3 networks, resolving an open problem.
New findings on depth vs. width in neural networks, showing depth can improve learnability.
problem Understanding the role of depth in neural networks, especially when width is unbounded.
method Analyzing sample complexity for learnability in norm-controlled depth-2 and depth-3 ReLU networks.
result Depth can improve learnability of functions that are otherwise unlearnable with depth-2 networks.
Learning based methods have shown very promising results for the task of depth estimation in single images. However, most existing approaches treat depth prediction as a supervised regression problem and as a result, require vast quantities of corresponding ground truth depth data for training. Just recording quality d…
Introduces Polar Depth for analyzing multivariate heavy-tailed data extremes.
problem Analyzing the behavior of extremes from multivariate heavy-tailed distributions.
method Introduces Polar Depth, a novel statistical depth function expressed in polar coordinates.
result The polar depth of the largest observations converges to the polar depth of the limiting distribution as the threshold increases.
Study on feature learning dynamics in infinite-depth neural networks, focusing on ResNets.
problem Understanding how features evolve during training in deep neural networks, especially in the large-depth limit.
method Conditional Gaussian representations and SDE system with decoupled backward weights.
result Depth-induced suppression of forward-backward coupling in infinite-depth networks, leading to a decoupled forward-backward SDE system.
Quantum algorithm reduces CVA risk-neutral expectation estimation costs.
problem Reducing Monte Carlo sampling cost for CVA on real quantum hardware.
method Noise-aware quantum workflow combining market calibration, discretisation, and oracle construction.
result CABIQAE achieves lower classical post-processing runtime and more effective error exploitation.
Following the seminal idea of Tukey, data depth is a function that measures how close an arbitrary point of the space is located to an implicitly defined center of a data cloud. Having undergone theoretical and computational developments, it is now employed in numerous applications with classification being the most po…
Enhances SSL methods with depth cues for better image understanding.
problem Lack of depth cues in 2D image pixel maps limits SSL performance.
method Integrates depth signals from a pretrained monocular RGB-to-depth model into contrastive learning frameworks.
result Improves SSL methods' robustness and generalization with depth signals.
The paper proves barriers to approximating functions with small weights and depth in neural networks.
problem Proving barriers to approximating functions with constant depth neural networks.
method Reduction to open problems and natural-proof barriers in circuit complexity, and a new approach to polynomially-bounded functions.
result There are fundamental barriers to proving results beyond depth 4 for constant-depth neural networks.
Proposes a new method to estimate Bayesian neural network depth.
problem Estimating the depth of Bayesian neural networks.
method Uses a discrete truncated normal distribution to learn depth mean and variance, inferring posterior distributions by minimizing variational free energy.
result Improves test accuracy and reduces posterior depth variance on the spiral dataset.
seMCD computes depth functions with statistical guarantees using sequential Monte Carlo.
problem Computing depth functions is computationally challenging, especially in high dimensions.
method Sequential Monte Carlo methodology with theoretical and empirical guarantees.
result The seMCD method provides accurate depth approximations with fewer samples than traditional methods.