Untrained neural networks can unfairly assign predictions to the same class.
problem Biasing effects in neural networks during initial training phases.
method Theoretical analysis of deep neural networks, focusing on Initial Guessing Bias (IGB).
result Model structure and preprocessing methods influence IGB.
New proof links initial class bias to DNN trainability, challenging traditional understanding.
problem Understanding the initial class bias in DNNs and its impact on trainability.
method Theoretical proof linking initial class bias to mean field theories of DNNs.
result Efficient learning is connected to a network's prejudice towards a specific class, contradicting traditional understanding.
The paper analyzes how good initial guesses affect the amount of data needed for low-rank matrix recovery.
problem Theoretical guarantee of local optimization algorithms requires excessive data to prevent spurious local minima.
method Quantifies the relationship between initial guess quality and sample complexity using restricted isometry constant.
result A linear improvement in initial guess quality leads to a constant factor improvement in sample complexity.
Counterfactual data augmentations may not ensure OOD robustness if performed by a context-guessing machine.
problem Deep learning models lack out-of-distribution robustness due to reliance on spurious features.
method Theoretical analysis and demonstration of counterfactual data augmentations performed by a context-guessing machine.
result Counterfactual data augmentations by a context-guessing machine do not lead to robust OOD classifiers.
Forward gradients improve neural network training without backpropagation issues.
problem Training neural networks without backpropagation's locking and memorization problems.
method Using directional derivatives in forward differentiation mode, with biased guesses based on feedback from small auxiliary networks.
result Using gradients from a local loss as a candidate direction improves Forward Gradient methods.
Bias and flexibility trade off in learning algorithms.
problem Understanding the trade-off between bias and expressivity in learning algorithms.
method Measuring expressivity using entropy on algorithm outcome distributions, and deriving bounds on bias and expressivity.
result There is a necessary trade-off between bias and expressivity in learning algorithms.
Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network parameters, leading to substantially better optimization results.
New methods improve accuracy in detecting concentric objects.
problem Detecting concentric geometric objects in noisy data.
method Developed new estimators and compared performance of existing methods.
result New methods outperform existing non-iterative methods and are robust to noise.
We give convergence guarantees for estimating the coefficients of a symmetric mixture of two linear regressions by expectation maximization (EM). In particular, we show that the empirical EM iterates converge to the target parameter vector at the parametric rate, provided the algorithm is initialized in an unbounded co…
In this article we provide a formulation of empirical bayes described by Atchade (2011) to tune the hyperparameters of priors used in bayesian set up of collaborative filter. We implement the same in MovieLens small dataset. We see that it can be used to get a good initial choice for the parameters. It can also be used…
PINNs solve neuronal parameter and state estimation problems with limited data.
problem Estimating parameters and hidden state variables from noisy partial data in multiscale neuronal models.
method Physics-informed neural networks (PINNs) for joint state and parameter estimation.
result PINNs deliver robust and accurate parameter inference and state reconstruction, even with limited data.
Next generation deep neural networks for classification hosted on embedded platforms will rely on fast, efficient, and accurate learning algorithms. Initialization of weights in learning networks has a great impact on the classification accuracy. In this paper we focus on deriving good initial weights by modeling the e…
Study reveals how initialization scale affects training accuracy in linear networks.
problem Understanding implicit bias in linear classification models.
method Asymptotic analysis of gradient flow trajectories and training loss minimization.
result Implicit bias is more complex at reasonable initialization scales and training accuracies.
In this article we select the unknown dimension of the feature by re- versible jump MCMC inside a simulated annealing in bayesian set up of collaborative filter. We implement the same in MovieLens small dataset. We also tune the hyper parameter by using a modified empirical bayes. It can also be used to guess an initia…
Deep networks retain initial bias after training, affecting generalization.
problem Understanding how much initial bias in neural networks survives training.
method Introduced initialization memory to measure initial bias's survival.
result SGD can preserve initial bias, while Adam-family methods erase it.
Randomly guessing weights helps analyze RL benchmarks objectively.
problem Understanding the complexity of reinforcement learning benchmarks.
method Generate policy networks by randomly guessing their parameters, evaluate on benchmarks, and analyze results.
result Small untrained networks can provide a robust baseline for various RL tasks.
The Poisson equation is commonly encountered in engineering, for instance in computational fluid dynamics (CFD) where it is needed to compute corrections to the pressure field to ensure the incompressibility of the velocity field. In the present work, we propose a novel fully convolutional neural network (CNN) architec…
Deep learning models can have low bias and variance, contrary to classical theory.
problem Understanding the performance of deep learning models at high complexity.
method Developed a fine-grained bias-variance decomposition for random feature kernel regression, analyzing the effects of sampling, initialization, and labels.
result The variance terms exhibit non-monotonic behavior and can diverge at the interpolation boundary, even in the absence of label noise.
The paper introduces negative controls to evaluate causal discovery algorithms, improving their reliability.
problem Lack of a general guideline for evaluating causal discovery algorithms.
method Derive exact distributional results under random guessing for evaluation metrics and propose a pipeline for using negative controls.
result Evaluation metrics can achieve very favorable values under random guessing, highlighting the need for negative control results.
This paper studies how gradient descent in control systems can perform well on unseen data.
problem The extent of a learned controller's ability to extrapolate to unseen initial states.
method Theoretical study of policy gradient in Linear Quadratic Regulator (LQR) problems, focusing on the role of exploration.
result The performance of a learned controller on unseen initial states depends on the degree of exploration induced by the system.
Linear RNNs exhibit a bias towards shorter memory due to initialization variance.
problem Understanding the performance limitations of RNNs, especially linear ones.
method Kernel regime analysis to show equivalence to 1D-convolutional networks and analyze weightings.
result Linear RNNs with random initialization have a bias towards shorter memory periods.
Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the…
SSMs have a built-in bias towards low-frequency components, which can be adjusted.
problem Frequency bias in SSMs affects their performance on long-range sequences.
method Proposed two mechanisms to tune frequency bias: scaling initialization or applying a Sobolev-norm-based filter.
result Tuning frequency bias improves SSMs' performance on long-range sequence learning tasks.
We consider the fundamental problem of solving quadratic systems of equations in n variables, where yi=∣⟨ai,x⟩∣2, i=1,…,m and x∈Rn is unknown. We propose a novel method, which starting with an initial guess computed by means of a …
Understanding deep neural networks is a major research objective with notable experimental and theoretical attention in recent years. The practical success of excessively large networks underscores the need for better theoretical analyses and justifications. In this paper we focus on layer-wise functional structure and…
Gradient descent training of neural networks leads to solutions close to natural cubic splines.
problem Understanding the implicit bias of gradient descent in neural networks.
method Analysis of gradient descent training for wide neural networks, focusing on the curvature penalty and initialization schemes.
result The solutions of gradient descent training are polyharmonic splines for certain initialization schemes.
Improved bounds for Black-Scholes volatility lead to faster root-finding.
problem Finding accurate implied volatility for Black-Scholes model.
method Systematic use of option delta to derive tighter bounds, proposing a Newton-Raphson algorithm.
result Proposed algorithm converges rapidly for all price ranges, especially useful for extreme option prices.
This paper analyzes implicit bias in Deep Linear Discriminant Analysis.
problem The implicit bias of Deep Linear Discriminant Analysis.
method Analyzing gradient flow on a L-layer diagonal linear network.
result Under balanced initialization, the network transforms additive updates into multiplicative updates, conserving the (2/L) quasi-norm.
Paper analyzes biases in video QA datasets, showing models can answer 37-48% questions correctly without multimodal context.
problem Question answering biases in video QA datasets can lead to model overfitting and poor generalization.
method Analyzed popular video question answering datasets, conducted ablation studies on biases from annotators and question types.
result Pretrained language models can answer 37-48% questions correctly without multimodal context, far exceeding random guess baseline.
Anderson acceleration (or Anderson mixing) is an efficient acceleration method for fixed point iterations xt+1=G(xt), e.g., gradient descent can be viewed as iteratively applying the operation G(x)≜x−α∇f(x). It is known that Anderson acceleration is quite efficient in practice and can be viewed…
Using a bondholder who seeks to determine when to sell his bond as our motivating example, we revisit one of Larry Shepp's classical theorems on optimal stopping. We offer a novel proof of Theorem 1 from from \cite{Shepp}. Our approach is that of guessing the optimal control function and proving its optimality with mar…
Research shows bias in machine learning can be due to algorithmic flaws, not just data.
problem Underestimation bias in machine learning algorithms.
method Initial research to understand factors contributing to bias in classification algorithms.
result Regularization methods to address overfitting can also accentuate bias.
Gradient descent amplifies random features in neural networks to useful ones.
problem Generalization in neural networks trained on corrupted data.
method Characterization of feature-learning process in two-layer ReLU networks trained by gradient descent.
result Gradient descent amplifies random features to useful ones, achieving near optimal generalization error.
In this article we present a method by which we can reduce a time series into a single point in R13. We have chosen 13 dimensions so as to prevent too many points from being labeled as "noise." When using a Euclidean (or Mahalanobis) metric, a simple clustering algorithm will with near certainty label the…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and the natural and empirically most popular approach to its solution has been the E…
We describe a novel family of models of multi- layer feedforward neural networks in which the activation functions are encoded via penalties in the training problem. Our approach is based on representing a non-decreasing activation function as the argmin of an appropriate convex optimiza- tion problem. The new framewor…
GUESS improves surrogate model accuracy with adaptive sampling.
problem Creating accurate surrogate models with limited data.
method Gradient and Uncertainty Enhanced Sequential Sampling (GUESS) using predictive uncertainty and Taylor expansion.
result GUESS achieved highest sample efficiency compared to other strategies.
A new algorithm finds minimizers in dueling optimization with a monotone adversary.
problem Finding minimizers in dueling optimization with a monotone adversary.
method Introduces and studies dueling optimization with a monotone adversary, designs an efficient randomized algorithm.
result Efficient algorithm incurs cost O(d) and iteration complexity O(dlog(1/ε)2), asymptotically optimal. Novel probabilistic solver speeds up solving related linear systems.
problem Efficiently solving multiple related linear systems.
method Probabilistic linear solver over the parameter space, leveraging solved systems.
result Faster and more efficient solution of related linear systems.
This paper concerns the problem of matrix completion, which is to estimate a matrix from observations in a small subset of indices. We propose a calibrated spectrum elastic net method with a sum of the nuclear and Frobenius penalties and develop an iterative algorithm to solve the convex minimization problem. The itera…
Improved iterative methods for risk parity portfolio weights.
problem Solving for portfolio weights in risk parity allocation.
method Enhanced CCD and Newton methods, including a rescaling step and improved initial guess.
result Improved CCD method is the best, three times faster with 40% fewer iterations.
State-of-the-art password guessing tools, such as HashCat and John the Ripper, enable users to check billions of passwords per second against password hashes. In addition to performing straightforward dictionary attacks, these tools can expand password dictionaries using password generation rules, such as concatenation…
Study shows neural networks learn low frequencies first, proposing solutions.
problem Frequency bias in neural network learning process.
method Developed a PDE to unravel frequency dynamics, used Fourier Features model.
result Appropriate weight initialization can eliminate or control frequency bias.
Cold-start problems are long-standing challenges for practical recommendations. Most existing recommendation algorithms rely on extensive observed data and are brittle to recommendation scenarios with few interactions. This paper addresses such problems using few-shot learning and meta learning. Our approach is based o…
This study investigates how gradient-based methods bias neural networks trained on high-dimensional data.
problem The implicit biases of gradient-based optimization algorithms in neural networks trained on high-dimensional data.
method Investigation of gradient flow and gradient descent in two-layer fully-connected neural networks with leaky ReLU activations.
result Gradient flow and gradient descent lead to neural networks with low-rank solutions and linear decision boundaries.
Gradient descent learns ReLU functions with non-zero bias efficiently.
problem Learning ReLU functions with non-zero bias under Gaussian distributions.
method Gradient descent starting from random initialization.
result Gradient descent achieves near-optimal error with high probability.
Unhinged loss minimization fails to improve classifier accuracy for simple data.
problem Accuracy of classifiers minimizing the unhinged loss.
method Minimizing the unhinged loss function.
result Minimizing the unhinged loss yields classifiers with accuracy no better than random guessing for simple data.
Develops Austen plots for assessing bias from unobserved confounding in observational studies.
problem Bias in causal estimates due to unobserved confounding.
method Formalizes confounding strength, uses Austen plots to visualize and quantify bias.
result Allows domain experts to assess the plausibility of strong confounders.