Study introduces a new investment strategy model using lazy factor and probability weights.
problem Optimizing investment strategies in volatile markets with transaction costs.
method Combines Price Portfolio Forecasting and Mean-Variance Models with Transaction Costs, using probability weights as laziness factor coefficients.
result Model demonstrates adaptability and generalizability in transforming investment strategies.
We explore how neural networks train to zero loss, focusing on initial scale.
problem Understanding neural network training dynamics and zero loss.
method Macroscopic limits analysis of gradient descent dynamics.
result Gradient descent can drive deep neural networks to zero loss regardless of initialization.
Study on adversarial robustness in neural networks across initialization and training phases.
problem Understanding adversarial robustness in neural networks during different learning stages.
method Analyzes adversarial robustness in various scenarios of over-parameterized networks with quadratic targets and infinite samples.
result Robustness can worsen when test error improves, and vice versa, revealing new tradeoffs.
Lazy Gradient Descent outperforms existing polytope algorithms in pseudo-regret.
problem Achieving optimal regret bounds on polytopes efficiently.
method Lazy Online Gradient Descent on polytopes.
result Proves O(1) pseudo-regret against i.i.d opponents. Gradient descent in tensor factorization favors low-rank solutions.
problem Tackling implicit regularization in tensor factorization problems.
method Gradient descent with small random initialization for overparametrized tensor factorization.
result Gradient descent leads to implicit regularization towards low tubal rank solutions.
Unified formula for training dynamics of linear networks combining lazy and balanced regimes.
problem Training dynamics of linear networks in two distinct setups: lazy and balanced/active.
method Unified formula for the evolution of the learned matrix, combining lazy and balanced regimes.
result Unified formula allows for rapid convergence and low rank bias, proving a complete phase diagram.
Counterfactual regret minimization (CFR) is the most popular algorithm on solving two-player zero-sum extensive games with imperfect information and achieves state-of-the-art performance in practice. However, the performance of CFR is not fully understood, since empirical results on the regret are much better than the …
Stochastic principal component analysis (SPCA) has become a popular dimensionality reduction strategy for large, high-dimensional datasets. We derive a simplified algorithm, called Lazy SPCA, which has reduced computational complexity and is better suited for large-scale distributed computation. We prove that SPCA and …
Lazy neural networks are vulnerable to adversarial attacks.
problem Adversarial robustness issues in lazy training models.
method Extending recent work on adversarial examples to lazy training models.
result Over-parametrized neural networks that generalize well remain vulnerable to single-step gradient ascent attacks.
A new method simulates a lazy version of a Markov chain for empirical inference.
problem Estimating and testing unknown Markov chains with limited data.
method Simulates an α-lazy version of an unknown Markov chain, making it ergodic.
result The pseudo spectral gap can be applied to non-ergodic Markov chains.
Gradient descent can find better tensor decompositions than lazy training in over-parameterized settings.
problem Finding better tensor decompositions in over-parameterized settings.
method Gradient descent on over-parameterized tensor decomposition problems.
result Gradient descent can find an approximate tensor decomposition with rank m=O∗(r2.5llogd), while lazy training requires m=Ω(dl−1). Lazy, perfectly informed investors trade infrequently due to costs.
problem The paradox of an omniscient yet lazy investor trading infrequently.
method Formalized the paradox using geometric and fractional Brownian motion models, derived closed-form profit functions, and proved existence and uniqueness of the optimal trading frequency.
result The optimal trading frequency can be interpreted through the fractal dimension of the price path.
New private algorithms for online learning improve regret in high privacy regimes.
problem Private online learning from experts and convex optimization.
method Transformed lazy algorithms for differential privacy.
result Improved regret bounds for DP-OPE and DP-OCO.
Quantum machine learning faces 'laziness' and 'barren plateaus', but noise can mitigate the latter.
problem Quantum machine learning's loss function landscape issues.
method Theoretical analysis of quantum variational circuits, neural tangent kernels, and noise effects.
result Noise can mitigate barren plateaus in quantum machine learning.
Deep networks prioritize easier examples over harder ones, leading to faster training.
problem Understanding how deep networks prioritize examples of varying difficulty.
method Investigated the effect of linear vs non-linear learning modes on example difficulty.
result Non-linear dynamics tend to sequentialize the learning of examples of increasing difficulty.
In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate O(ε21) improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan an…
Grokking occurs when neural networks transition from lazy to rich training dynamics, fitting initial features before generalizing.
problem Understanding why neural networks exhibit early train loss decrease without corresponding test loss improvement.
method Analyzing vanilla gradient descent on polynomial regression with a two-layer neural network, identifying sufficient statistics for test loss.
result Grokking arises when a network first attempts to fit a kernel regression solution with initial features, followed by late-time feature learning.
Study shows optimal model performance at critical level of feature learning.
problem Catastrophic forgetting in neural networks, especially in non-stationary environments.
method Systematic study on model scale and feature learning, using dynamical mean field theory.
result Optimal performance achieved at a critical level of feature learning, dependent on task non-stationarity and model scale.
New metric measures dynamical richness without relying on accuracy.
problem Lack of a reliable metric for measuring dynamical richness.
method Developed a computationally efficient, performance-independent metric based on low-rank bias.
result Metric recovers neural collapse as a special case and captures known transitions without accuracy.
We discuss the approximation of the value function for infinite-horizon discounted Markov Reward Processes (MRP) with nonlinear functions trained with the Temporal-Difference (TD) learning algorithm. We first consider this problem under a certain scaling of the approximating function, leading to a regime called lazy tr…
Study on network-valued processes with asynchronous updates, proving consistency in community and changepoint estimation.
problem Understanding the behavior of network-valued stochastic processes with asynchronous updates.
method Analysis of concentration properties of aggregated adjacency and Laplacian matrices for lazy network-valued stochastic processes.
result Demonstrates consistency of estimators in community and changepoint estimation problems.
Most machine learning methods require careful selection of hyper-parameters in order to train a high performing model with good generalization abilities. Hence, several automatic selection algorithms have been introduced to overcome tedious manual (try and error) tuning of these parameters. Due to its very high sample …
Neural networks compress uninformative input directions, improving test error.
problem Data lie in a high-dimensional space but labels vary along a lower-dimensional manifold.
method One-hidden layer network trained with gradient descent, analyzing weight evolution and compression.
result Compression factor λ ∼ √p improves test error, with β Feature > β Lazy.
New method converts and optimizes sampling schedules for generative models.
problem Optimizing sampling schedules for generative models like flows and diffusions.
method Unified framework for stochastic interpolants, including point mass schedules.
result Demonstrated efficient generation of images with fewer steps.
Unintended effects from scaling neural network outputs with adaptive learning rates.
problem Adaptive learning rate optimization's behavior is altered by output scaling, leading to misinterpretation.
method Presented a modified optimization algorithm to mitigate unintended effects.
result Adaptive learning rate's effectiveness is significantly impacted by output scaling, especially for small scaling factors.
Clapping reduces memory usage in distributed optimization by reusing data samples.
problem Significant communication overhead and impractical memory overhead in pipeline-parallel distributed optimization.
method Lazy sampling strategy to reuse data samples across steps, supporting convergence without unbiased gradient assumptions.
result Clapping achieves convergence in few-epoch or online training regimes without sample-size memory overhead.
We propose a framework for solving high-dimensional Bayesian inference problems using \emph{structure-exploiting} low-dimensional transport maps or flows. These maps are confined to a low-dimensional subspace (hence, lazy), and the subspace is identified by minimizing an upper bound on the Kullback--Leibler divergence …
ABC algorithms involve a large number of simulations from the model of interest, which can be very computationally costly. This paper summarises the lazy ABC algorithm of Prangle (2015), which reduces the computational demand by abandoning many unpromising simulations before completion. By using a random stopping decis…
A method learns common bias for multiple low-variance tasks without hyper-parameter tuning.
problem Learning common bias for multiple low-variance tasks without manual tuning.
method Two variants of online learning methods (aggressive and lazy) that update bias after each datapoint or at the end of each task.
result Across-tasks regret bound derived for the method, showing faster rates for aggressive variant and standard rates for lazy variant.
Transformers learn rich in-context dependencies efficiently.
problem Understanding how transformers learn long-range dependencies efficiently.
method Approximation and dynamics analysis of induction head mechanisms.
result Abrupt transition from lazy to rich mechanisms during training.
Improved privacy and efficiency in online convex optimization.
problem Differentially private online convex optimization in high dimensions.
method Improves upon Agarwal et al. [2023] by reducing dimension factors and removing smoothness requirement.
result Best known rates for (ε,δ)-differentially private online convex optimization in the regime of ε not being very small. We study Bayesian optimal control of a general class of smoothly parameterized Markov decision problems. Since computing the optimal control is computationally expensive, we design an algorithm that trades off performance for computational efficiency. The algorithm is a lazy posterior sampling method that maintains a d…
Analyzes neural networks using linear models to understand their behavior.
problem Understanding multi-layer neural networks through linear models.
method Recalls and reviews four models: linear regression with concentrated features, kernel ridge regression, random feature model, and neural tangent model.
result Highlights limitations of linear theory and discusses approaches to overcome them.
LAZO reduces query complexity and variance in ZO methods.
problem High query complexity and variance in zeroth-order optimization.
method LAZO uses adaptive lazy queries to reduce variance and save queries.
result LAZO achieves lower regret and query complexity compared to existing methods.
Study highlights how lazy data practices in fair ML research can unfairly impact minority groups.
problem Lazy data practices in fair ML research can unfairly impact minority groups.
method Systematic study of 280 experiments across 142 publications on 142 datasets.
result Unreflective data practices lead to biased findings and unfair treatment of minorities.
LazyDINO efficiently solves high-dimensional Bayesian inverse problems with fast and scalable solutions.
problem High-dimensional nonlinear Bayesian inverse problems with expensive parameter-to-observable maps.
method LazyDINO combines derivative-informed neural surrogates and lazy map variational inference for efficient posterior approximation.
result Significant cost reduction in amortized Bayesian inversion, achieving one to two orders of magnitude improvement.
Two distinct limits for deep learning have been derived as the network width h→∞, depending on how the weights of the last layer scale with h. In the Neural Tangent Kernel (NTK) limit, the dynamics becomes linear in the weights and is described by a frozen kernel Θ. By contrast, in the Mean-Field …
Study on rich regime training in deep learning, finding active parameters in bottom layers.
problem Understanding the practical success of deep learning models.
method Empirical study on rich regime training with benchmark datasets, re-initialization analysis, and probabilistic Layer-Wise Sparse SGD.
result Probabilistic Layer-Wise Sparse SGD matches vanilla SGD's generalization performance with improved efficiency.
Auto-CEI improves LLM reasoning by balancing assertiveness and conservativeness.
problem Hallucinations and laziness in LLM reasoning tasks.
method Expert Iteration explores reasoning trajectories, guiding incorrect paths back on track and promoting appropriate 'I don't know' responses.
result Auto-CEI achieves superior alignment in logical reasoning, mathematics, and planning tasks.
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.
A recent line of work studies overparametrized neural networks in the "kernel regime," i.e. when the network behaves during training as a kernelized linear predictor, and thus training with gradient descent has the effect of finding the minimum RKHS norm solution. This stands in contrast to other studies which demonstr…
Use simplified layerwise linear models to understand neural dynamics.
problem Complex neural network dynamics are hard to grasp.
method Apply simplified layerwise linear models to explain neural phenomena.
result Simplified models explain neural collapse, emergence, etc.
New algorithm reduces regret and constraint violation in online convex optimization with predictions.
problem Online convex optimization with time-varying constraints and predictions.
method Primal-dual algorithm combining Follow-The-Regularized-Leader with adaptive steps.
result Achieves O(T43−β) regret and O(T21+β) constraint violation bounds. Exact solutions reveal how unbalanced initializations promote rapid feature learning in neural networks.
problem Understanding how neural networks efficiently extract features from data.
method Deriving exact solutions to a minimal model of neural networks transitioning between lazy and rich learning regimes.
result Unbalanced layer-specific initialization variances and learning rates determine the degree of feature learning.
Transformers capture combinatorial tasks with bounded error and logarithmic sample dependence.
problem Capturing complex combinatorial tasks with bounded error and sample efficiency.
method Formal definition of algorithmic capture, empirical analysis of infinite-width transformers, upper bounds on computational complexity.
result Transformers exhibit an inductive bias favoring simpler algorithmic procedures over higher complexity ones.
Deep networks generalize well even when they fit training data perfectly, thanks to overparametrization.
problem Understanding generalization in overparametrized deep networks.
method Random features regression, asymptotic analysis, ensemble averaging.
result Bias remains constant beyond the interpolation threshold, while variance components decay with overparametrization.
Study on how adversarial training affects neural network kernels and robustness.
problem Understanding and improving adversarial robustness in neural networks.
method Empirical study of the evolution of the empirical Neural Tangent Kernel (NTK) under standard and adversarial training.
result Adversarial training leads to a new kernel that provides robustness, even when non-robust training is performed on top of it.
Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors algorithm is based on averaging the target values of the spatial neighbors. The selecti…