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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Stochastic Gradient Descent shows directional bias with moderate learning rates, impacting optimization outcomes.
problem Understanding the bias of SGD with moderate learning rates in practical scenarios.
method Analyzing SGD and GD on an overparameterized linear regression problem.
result SGD converges along large eigenvalue directions, GD along small ones, affecting early stopping outcomes.
Analyzes how bias evolves in SGD training across different data sub-populations.
problem Understanding bias formation during machine learning training.
method Analytical description of SGD dynamics in a teacher-student setup with Gaussian-mixture model.
result Different sub-populations influence bias at different timescales, revealing shifting classifier preferences.
The paper connects neural collapse and low-rank bias in networks with L2 regularization.
problem Understanding the emergence of low-rank bias and neural collapse in L2-regularized networks.
method Unified theoretical framework linking TCV and rank of weight matrices, proving global optimality of DNC1, and establishing a benign landscape property.
result Zero TCV across intermediate layers minimizes representation cost under natural architectural constraints, and DNC1 is globally optimal.
Matrix SMD converges to unique solution minimizing Bregman divergence.
problem High-dimensional multi-output classification and matrix completion problems.
method Stochastic Mirror Descent with matrix parameters and matrix mirror functions.
result Matrix SMD converges exponentially to the unique solution minimizing Bregman divergence.
Study data biases to predict algorithmic discrimination, developing a Data Bias Profile.
problem Data biases contribute to algorithmic discrimination, but their impact is understudied.
method Analyzed three common data biases across various datasets and models, developing a Data Bias Profile.
result Combination of proxies and label bias can lead to more significant discrimination than underrepresentation alone.
A leading hypothesis for the surprising generalization of neural networks is that the dynamics of gradient descent bias the model towards simple solutions, by searching through the solution space in an incremental order of complexity. We formally define the notion of incremental learning dynamics and derive the conditi…
Deep neural networks can achieve remarkable generalization performances while interpolating the training data perfectly. Rather than the U-curve emblematic of the bias-variance trade-off, their test error often follows a "double descent" - a mark of the beneficial role of overparametrization. In this work, we develop a…
FreSh shifts model's initial frequency spectrum to match target signal, improving neural representation performance.
problem MLPs' low-frequency bias limits capturing high-frequency details accurately.
method FreSh selects embedding hyperparameters to align model's initial output spectrum with target signal's spectrum.
result FreSh improves performance across various neural representation methods and tasks with minimal computational overhead.
LLMs show biases in investment analysis, leading to unreliable recommendations.
problem LLMs face conflicts between pre-trained knowledge and real-time market data, leading to biases in investment analysis.
method Experimental framework to investigate emergent behaviors in LLMs, analyzing sector, size, and momentum biases.
result Distinct, model-specific biases observed, including a tendency to prefer technology stocks, large-cap stocks, and contrarian strategies.
The paper uses a graph autoencoder to learn unbiased plant-pollinator interaction embeddings.
problem Sampling bias in citizen science data affects ecological network analysis.
method Bipartite graph variational autoencoder with HSIC for fairness.
result The method mitigates sampling bias and provides unbiased embeddings.
New method stabilizes deep neural networks by setting Lyapunov exponent to zero.
problem Stability issues in deep neural networks with low width.
method Lyapunov initialization method to set Lyapunov exponent to zero.
result Lyapunov exponent governs stability of deep networks; standard methods fail for low width.
Deep ReLU networks escape from the origin via saddle points with a low-rank bias.
problem Understanding the dynamics of gradient descent in deep ReLU networks.
method Analysis of escape directions and singular values of weight matrices.
result The first singular value of the ℓ \ell ℓ -th layer weight matrix is at least ℓ 1 4 \ell^{\frac{1}{4}} ℓ 4 1 larger than any other singular value. Two-layer networks favor simple features, especially in complex datasets.
problem Simplicity bias in neural networks over-reliing on simple features.
method Characterization of two-layer neural networks with small weights and gradient flow.
result Features learned in middle training stages are more useful for out-of-distribution transfer.
We reparametrize ReLU NNs as splines to understand their learning dynamics.
problem Understanding the learning dynamics and inductive bias of neural networks.
method Reparametrize ReLU NNs as continuous piecewise linear splines to study learning dynamics.
result Standard weight initializations yield very flat functions, leading to strength and type of implicit regularization.
The paper analyzes the implicit bias of SGD near loss manifold and provides new insights.
problem Understanding the implicit bias of SGD near loss manifolds in overparametrized models.
method Adapting ideas from Katzenberger (1991) to analyze SGD dynamics using a stochastic differential equation (SDE).
result SGD with label noise locally decreases the sharpness of loss, leading to a global analysis of implicit bias.
SIP corrects model bias in Bayesian ML.
problem Model selection biases predictions in Bayesian ML.
method Sparse Implicit Processes (SIP) for flexible, trainable predictions.
result SIP provides better predictive distributions than initial models.
New attention model removes softmax, improving sequence length bias.
problem Softmax attention's limitations and sequence length bias.
method Replaces softmax with normalization in self-attention.
result Normalization leads to more robust and bias-free attention.
Machine Learning (ML) is increasingly applied in real-life scenarios, raising concerns about bias in automatic decision making. We focus on bias as a notion of opinion exclusion, that stems from the direct application of traditional ML pipelines to infer subjective properties. We argue that such ML systems should be ev…
Mirror flow in shallow neural networks shows similar implicit bias to gradient flow, with key differences in curvature penalties.
problem Analyzing implicit bias in shallow neural networks with mirror flow.
method Characterization through variational problems and scaled potentials.
result Mirror flow with scaled potentials induces a rich class of biases not captured by RKHS norms.
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.
Optimizes wide low-rank neural networks for reduced parameters and cost.
problem Reducing the number of learnable parameters in wide neural networks.
method Analyzed edge-of-chaos dynamics and derived formulae for optimal weight and bias variances.
result Optimal weight and bias variances for low-rank networks follow from multiplicative scaling.
Anonymizing company names in financial news improves trading performance, contrary to initial expectations.
problem Look-ahead and distraction biases in sentiment analysis of financial news.
method Investigated trading strategies based on original and anonymized headlines, comparing performance.
result Anonymized headlines outperform original in-sample, suggesting distraction effect is stronger.
Gradient descent with small random init mimics spectral methods for low-rank matrix recovery.
problem Reconstructing a low-rank matrix from few measurements.
method Gradient descent with small random initialization followed by a few iterations.
result Gradient descent from small random init converges to a well-generalizing solution.
From scientific experiments to online A/B testing, the previously observed data often affects how future experiments are performed, which in turn affects which data will be collected. Such adaptivity introduces complex correlations between the data and the collection procedure. In this paper, we prove that when the dat…
Neural networks learn incrementally from orthogonal data, interpolating with minimal complexity.
problem Understanding the learning dynamics and implicit bias in ReLU networks with orthogonal data.
method Gradient flow analysis of two-layer ReLU networks from small initialization with orthogonal training data.
result The learned interpolator has a squared ℓ 2 \ell_2 ℓ 2 -norm scaling as n \sqrt{n} n , close to the minimal interpolator's complexity. Lectures on deep learning from a learning theory perspective.
problem Understanding how deep learning architectures lead to inductive bias.
method Statistical learning theory and stochastic optimization.
result Gradient descent on linear diagonal networks can lead to various forms of implicit bias.
New method debiases selection bias in PU classification with exposure data.
problem Binary classification from positive and unlabeled data with selection bias.
method Automatic Debiased PUE (ADPUE) learning method.
result ADPUE outperforms traditional PU learning methods on various datasets.
State-of-the-art neural networks are heavily over-parameterized, making the optimization algorithm a crucial ingredient for learning predictive models with good generalization properties. A recent line of work has shown that in a certain over-parameterized regime, the learning dynamics of gradient descent are governed …
New method for initializing RBM weights without datasets.
problem No dataset-free weight-initialization for RBMs.
method Statistical mechanical analysis to derive Gaussian distribution with optimized standard deviation.
result Optimal weight initialization improves learning efficiency in RBMs.
Gradient flow on ReLU networks converges to a simple model with few regions.
problem Understanding the dynamics of gradient flow in shallow ReLU networks.
method Analysis of gradient flow dynamics on univariate ReLU neural networks.
result Gradient flow converges to a network with at most O(r) linear regions.
The paper explores how linear neural networks can overfit without bias when data is well-behaved.
problem Understanding why linear neural networks can generalize well despite fitting noisy data.
method Analyzing two-layer linear neural networks trained with gradient flow, deriving bounds on excess risk.
result The excess risk depends on initialization quality and data covariance matrix properties.
New initialization methods speed up Sinkhorn algorithm for OT problems.
problem Improving runtime of the Sinkhorn algorithm for optimal transport problems.
method Data-dependent initializers for Sinkhorn algorithm, based on closed-form solutions for specific settings.
result Data-dependent initializers result in dramatic speed-ups without affecting differentiability.
Noise in SGD affects overparameterized models, favoring sparse solutions.
problem Understanding and mitigating implicit bias in SGD with parameter-dependent noise.
method Theoretical analysis of a quadratically-parameterized model with label noise and Gaussian noise.
result SGD with label noise recovers sparse ground-truth solutions, while SGD with Gaussian noise overfits dense solutions.