AutoGrow automatically discovers optimal depth in DNNs.
problem Designing optimal depth in deep neural networks is difficult and time-consuming.
method AutoGrow grows new layers in a seed architecture if it improves accuracy; stops if no improvement. Robust policies generalize to different architectures and datasets.
result AutoGrow discovers near-optimal depth on various datasets, improving accuracy-computation trade-off in ResNets.
This paper shows that scientific discovery can be efficiently learned via compositional function trees, reducing the sample complexity.
problem Statistical and computational intractability of scientific discovery via symbolic regression.
method PAC learning approach focusing on compositional function trees built from a finite vocabulary of smooth operators.
result The Rademacher complexity and excess risk are controlled by depth and Lipschitz constants of the base operators, leading to finite-union bounds and high-probability risk bounds.
Robust scatter estimation is a fundamental task in statistics. The recent discovery on the connection between robust estimation and generative adversarial nets (GANs) by Gao et al. (2018) suggests that it is possible to compute depth-like robust estimators using similar techniques that optimize GANs. In this paper, we …
Flexible deep learning framework controls FDR for feature selection.
problem Controlling Type-I error in feature selection for deep neural networks.
method Approximates FDR control for a wide range of deep architectures using gradient-based feature-importance vectors.
result Theoretical guarantee of FDR control for feature selection in deep learning models.
Enhances KANs for accuracy and interpretability with multi-exit architecture.
problem Unclear optimal depth for KANs and difficulty in optimization and interpretation.
method Introduces multi-exit KANs with each layer having its own prediction branch.
result Multi-exit KANs outperform single-exit versions on various datasets.
Derives token price process for AMM tokens, finds leverage effect and pricing discrepancies.
problem Derives token price process for AMM tokens.
method Derives CEV process for token price, derives closed-form option prices, introduces liquidity-adjusted Greeks.
result Token price process is CEV, with leverage effect and pricing discrepancies.
Derandomization reveals structure in neural networks, reducing sample complexity.
problem Understanding feature learning dynamics in neural networks.
method Derandomization lemma applied to arbitrary NNs with any smooth loss function.
result Optimizing function converges to zero weight matrix, revealing structure.
This paper reviews causal inference methods for time series data.
problem Estimating treatment effects and identifying causal relations from time series data.
method Comprehensive review of approaches for treatment effect estimation and causal discovery.
result Provides a list of evaluation metrics and datasets for time series causal inference.
Efficiently discovers causal DAG permutations without additional assumptions.
problem Learning a DAG up to Markov equivalence.
method Utilizing DAG-specific problem structure, introduces an efficient algorithm for sparse permutations.
result Significant improvement in permutation discovery compared to existing algorithms.
In this paper we study the adaptive learnability of decision trees of depth at most d from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman solves the problem in a randomized polynomial time algorithm that asks $\tilde O(2^…
In this paper, we introduce a novel framework for combining scientific knowledge within physics-based models and recurrent neural networks to advance scientific discovery in many dynamical systems. We will first describe the use of outputs from physics-based models in learning a hybrid-physics-data model. Then, we furt…
IRNet improves material property prediction from composition and crystal structure.
problem Predicting material properties from composition and crystal structure.
method Deep residual regression network with individual residual learning.
result IRNet outperforms state-of-the-art machine learning approaches in predicting material properties.
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.
Data-driven approach discovers molecular photoswitches with separated electronic absorption bands.
problem Engineering photoswitchable molecules with specific electronic absorption bands remains challenging.
method Data-driven discovery pipeline using Gaussian processes for multitask learning.
result Multioutput Gaussian process (MOGP) trained on four photoswitch transition wavelengths outperforms single-task models and TD-DFT.
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.
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.
New algorithm proves deep networks can learn better than shallow ones.
problem Understanding the power difference between shallow and deep neural networks.
method Identifying a class of Boolean functions and proving that logarithmic-depth networks can learn them efficiently using hierarchical reconstruction.
result First algorithmic separation between constant-depth and logarithmic-depth neural networks.
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.
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.
A new depth function improves multivariate data analysis by considering variability directions.
problem Developing a depth function that respects quantile properties and is affine-invariant.
method Integrating rank-weighted depth with affine-invariance and covariance matrices.
result The AI-IRW depth function provides accurate quantile estimates and is robust to data variability.
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.
Over-parameterized CNNs show U-shaped test risk with depth increase.
problem Understanding the impact of depth on test risk in over-parameterized CNNs.
method Empirical image classification experiments and linear regression framework.
result Test risk is U-shaped with increasing depth in over-parameterized CNNs.
New depth function for partial orders helps compare machine learning algorithms.
problem Comparing machine learning algorithms using non-standard data types.
method Adapted simplicial depth to partial orders, using ufg depth for comparison.
result Demonstrates promising variety of analysis approaches based on ufg methods.
Study infinite-depth limits of neural networks with fixed width.
problem Understanding the behavior of neural networks as depth increases with fixed width.
method Analyzing finite-width residual networks with random Gaussian weights, focusing on the infinite-depth limit.
result The pre-activations converge to a zero-drift diffusion process, differing from the infinite-width limit.
Inverse depth scaling found in LLMs due to similar layers averaging error.
problem Understanding how depth affects loss in large language models.
method Analysis of LLMs and toy residual networks.
result Loss scales inversely proportional to depth in LLMs.
Extends partitioned local depth concept with probabilistic considerations.
problem Uncertain, variable, and conflicting information in data.
method Partitioned local depth with probabilistic concepts of local relevance and support division.
result Extends original ideas to handle uncertain data.
One-shot neural architecture search limits depth search space and prunes networks for better performance and uncertainty.
problem Finding optimal depth in residual networks for efficient training and inference.
method Formulated a variational objective to approximate the depth distribution and pruned networks based on this distribution.
result Pruned networks achieve competitive accuracy with unpruned networks and better uncertainty calibration.
Defines slice depth for 2-knots and sets upper bounds for specific knots.
problem Determining the minimum dimension for a 2-knot to be slice.
method Introduces slice depth, defines it for 2-knots, and provides upper bounds for specific knot types.
result Upper bounds for slice depth of certain 2-knots.
Theoretical limits of deep residual networks show consistent covariance structures.
problem Understanding the limits of deep residual networks.
method Analyzing the behavior of deep residual networks with skip connections as width and depth approach infinity.
result Theoretical analysis confirms that the covariance structure remains consistent regardless of the order of width and depth.
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.
We describe a method to infer dense depth from camera motion and sparse depth as estimated using a visual-inertial odometry system. Unlike other scenarios using point clouds from lidar or structured light sensors, we have few hundreds to few thousand points, insufficient to inform the topology of the scene. Our method …
Bayesian linear networks reveal optimal depth and width trade-offs.
problem Understanding how depth, width, and dataset size affect model quality in linear networks.
method Zero noise Bayesian inference with Gaussian weight priors and mean squared error.
result Optimal predictions at infinite depth and maximized Bayesian model evidence at infinite depth.
Gradient descent with early stopping achieves optimal sparse recovery.
problem Sparse regression with gradient descent and early stopping.
method Gradient descent on depth-N networks with early stopping.
result Implicit sparse regularization occurs with early stopping for general depth N.
A new procedure, called DDa-procedure, is developed to solve the problem of classifying d-dimensional objects into q >= 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0,1]^q. Specifically, the depth i…
Differentiable causal discovery methods perform robustly under model violations.
problem Causal discovery algorithms struggle with real-world data due to unverifiable causal assumptions.
method Benchmarked differentiable causal discovery methods under eight model assumption violations.
result Differentiable causal discovery methods exhibit robust performance under Structural Hamming Distance and Structural Intervention Distance metrics.
New framework uses background knowledge to speed up causal discovery.
problem Scalable causal discovery for large datasets.
method Utilizes background knowledge during causal discovery process.
result Background knowledge reduces computational requirements and improves structure quality.