This work explains scaling laws as redundancy laws in deep learning.
problem The mathematical origins of scaling laws in deep learning models remain unclear.
method Kernel regression and analysis of data covariance spectra.
result Scaling laws can be explained as redundancy laws, revealing the learning curve's slope depends on data redundancy.
A new scaling law predicts optimal batch size for training models.
problem Finding the optimal batch size for training models efficiently.
method Proposed a three-term scaling law that considers model size, training data, training steps, and batch size.
result The three-term law accurately recovers the optimal batch size and can be robustly fit with fewer training runs.
Large models follow power laws in performance with dataset size or parameters.
problem Understanding neural scaling laws in large language models.
method Joint generative data model and random feature model.
result Modeling and solving the dual limit reveals insights into scaling laws.
This work extends the scaling law to multiple and kernel regression, challenging traditional machine learning principles.
problem Challenging traditional machine learning wisdom with scaling law in large practical models.
method Demonstrates the scaling law in multiple and kernel regression settings.
result The scaling law extends to multiple and kernel regression, providing deeper insights into LLMs.
Study reveals neural scaling laws in random graphs and natural language models.
problem Understanding the origin of neural scaling laws in complex systems.
method Examined scaling laws in transformers trained on random walks and simplified natural language models.
result Neural scaling laws emerge in the absence of power law structure in data correlations.
This work analyzes neural scaling laws using power-law data spectra and derives analytical expressions for generalization error.
problem Understanding how neural network performance scales with key factors like data size and model complexity.
method Statistical mechanics techniques applied to one-pass stochastic gradient descent in a student-teacher framework.
result Derivation of analytical expressions for generalization error under power-law data spectra and identification of conditions for power-law scaling.
Unified theory for neural scaling laws in hierarchically compositional data.
problem Understanding neural scaling laws in hierarchically compositional data.
method Probabilistic context-free grammars and power-law distributed production rules.
result Unified learning curve behavior for classification and next-token prediction tasks.
New scaling laws explain deep learning performance growth.
problem Understanding neural network performance growth.
method Analyzed entire training dynamics of various architectures.
result Identified two dynamical scaling laws.
Scaling laws in linear regression explain model performance improvements with size and data.
problem Disagreement between empirical neural scaling laws and conventional wisdom on variance error.
method Infinite dimensional linear regression setup, one-pass SGD, Gaussian prior, power-law spectrum.
result Variance error is dominated by other errors, disappearing from the bound due to SGD's implicit regularization.
Employing profits data of Japanese companies in 2002 and 2003, we confirm that Pareto's law and the Pareto index are derived from the law of detailed balance and Gibrat's law. The last two laws are observed beyond the region where Pareto's law holds. By classifying companies into job categories, we find that companies …
New pruning method breaks power law scaling, potentially reducing error to exponential.
problem Improving neural network performance through scaling alone is costly.
method Developed a new data pruning metric to break power law scaling.
result Pruned datasets show better than power law scaling on various image datasets.
We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence of the double scaling law is demonstrated empirically for the sales and the lab…
The study explains transformer scaling laws using statistical and approximation theories.
problem Understanding why transformer scaling laws exist for large models trained on low-dimensional data.
method Established statistical estimation and mathematical approximation theories for transformers on low-dimensional manifolds.
result Predicted a power law between generalization error and model and data sizes, with power depending on intrinsic data dimension.
Scaling laws govern predictive uncertainties in deep learning models.
problem Understanding predictive uncertainties in deep learning models.
method Empirical analysis and approximate Bayesian inference on vision and language tasks.
result Scaling laws exist for various measures of predictive uncertainty in deep learning models.
New neural scaling law found for simple quadratic function.
problem Neural scaling laws and their predictions for model performance.
method Analysis of neural networks, lottery ticket ensembling, statistical interpretation.
result Found a new scaling law (α=1) for a simple quadratic function, contradicting previous theories. Improved scaling laws in linear regression using data reuse.
problem Sustainability of neural scaling laws when running out of new data.
method Data reuse in multi-pass stochastic gradient descent (multi-pass SGD) for M-dimensional linear models trained on N data with sketched features. result Multi-pass SGD achieves a test error of Θ(M1−b+L(1−b)/a) with L>N, improving scaling laws in data-constrained regimes. Non-Markovian point process shows power-law scaling, similar to nonlinear Markovian process.
problem Understanding the scaling behavior of non-Markovian point processes.
method Analyzed a confined fractional Brownian motion-driven point process and compared it to a nonlinear Markovian process.
result A nonlinear Markovian process can reproduce the power-law scaling behavior of a non-Markovian point process.
A simple model explains inference scaling in neural models.
problem Understanding how model performance improves with repeated inference attempts.
method A statistical ansatz based on memorization to study inference scaling laws.
result Inference loss exhibits a power law decay with increasing trials.
Study uncovers scaling laws and spectral properties of shallow neural networks.
problem Understanding scaling laws and spectral properties of shallow neural networks.
method Leveraging connections with matrix compressed sensing and LASSO, derived a phase diagram for excess risk.
result Uncovered crossovers between scaling regimes and plateau behaviors, validated empirical observations.
The paper explores neural scaling laws for deep operator networks, offering a theoretical foundation.
problem Understanding neural scaling laws in deep operator networks.
method Theoretical analysis of approximation and generalization errors.
result Established a theoretical framework to quantify neural scaling laws for deep operator networks.
Develops a simple model to understand learning curves for arbitrary power laws.
problem Lack of theoretical understanding of scaling laws in machine learning.
method Analyzes a toy model to determine if learning curves are universal or depend on data distribution.
result Determines that learning curves can exhibit n−β for arbitrary power β>0. Sloth predicts LLM performance using latent skills across families.
problem Variations in benchmark performance due to differences in training configurations and data processing across model families.
method Sloth uses publicly available benchmark data and assumes LLM performance is driven by latent skills influenced by model size and training tokens. It exploits correlations across benchmarks to provide accurate predictions.
result Sloth predicts LLM performance accurately and offers insights into scaling behaviors for complex tasks.
Sharp theory of neural network scaling laws for hierarchical targets.
problem Learning hierarchical multi-index models in neural networks.
method Sharp information-theoretic scaling laws derived for two-layer neural networks.
result Optimal rates achieved by a simple spectral estimator.
Model shows feature learning can improve neural scaling laws for hard tasks.
problem Understanding and improving neural network scaling laws for various task difficulties.
method Developed a solvable model of neural scaling laws, identified three scaling regimes, and demonstrated feature learning's impact on scaling exponents.
result Feature learning can improve scaling with training time and compute for hard tasks, nearly doubling the exponent.
By using numerical simulation, we confirm that Takayasu--Sato--Takayasu (TST) model which leads Pareto's law satisfies the detailed balance under Gibrat's law. In the simulation, we take an exponential tent-shaped function as the growth rate distribution. We also numerically confirm the reflection law equivalent to the…
A hierarchical model shows how scaling laws emerge from sequential feature recovery.
problem Emergence of scaling laws from feature learning in multi-layer networks.
method Layer-wise spectral algorithm adapted to compositional structure, sequential feature detection.
result Sequential detection of latent features, leading to explicit power-law decay of prediction error.
Scaling laws found for reinforcement learning performance with model size and compute.
problem Challenges in extending generative modeling scaling laws to reinforcement learning.
method Introduced intrinsic performance as a monotonic function of mean episode return.
result Intrinsic performance scales as a power law in model size and environment interactions.
Neural networks' performance scales with data size, explained by data manifold dimensionality.
problem Understanding the scaling of neural network performance with the number of parameters.
method Explained by the intrinsic dimension of the data manifold, confirmed through teacher/student framework and various datasets.
result The scaling exponent α is approximately 4 divided by the intrinsic dimension d of the data manifold.
Theory predicts neural scaling exponents from language statistics.
problem No existing theory could quantitatively predict neural scaling exponents.
method Isolated two key statistical properties of language.
result Derives a simple formula predicting neural scaling exponents.
New phases identified in neural scaling laws with compute limits.
problem Understanding neural scaling laws under compute constraints.
method Solved neural scaling model with stochastic gradient descent, derived loss curves, analyzed model-parameter-count phases.
result Identified 4 phases (+3 subphases) in data-complexity/target-complexity phase-plane, derived exponents.
Model predicts neural network performance scaling laws across various factors.
problem Understanding the performance of neural networks across different training factors.
method Random feature model trained with gradient descent, analyzing compute-optimal scaling laws.
result Predicts asymmetric compute-optimal scaling rule and behavior of training and test loss gap.
We discover scaling laws for kernel regression loss under various learning rate schedules.
problem Understanding loss dynamics and learning rate schedules in kernel regression.
method Theoretical analysis of stochastic gradient descent on a power-law kernel regression model.
result Established a Functional Scaling Law (FSL) capturing the full loss trajectory under arbitrary learning rate schedules.
Predicts language model performance from public models without training.
problem Understanding how language model performance varies with scale.
method Observational approach building scaling laws from publicly available models.
result Smooth, sigmoidal behavior of emergent phenomena is predictable from small models.
Unified scaling laws reveal how model size and training time impact neural network performance.
problem Understanding how much performance improvement can be expected from scaling model size or data volume.
method Established scale-time equivalence and combined it with a linear model analysis of double descent.
result Unified theoretical scaling laws explain previously unexplained phenomena and offer a more accessible path to training large models.
Bitcoin returns exhibit a distinct inverse cubic law scaling behavior.
problem Investigating the scaling properties of Bitcoin price returns.
method Analysis of recent Bitcoin data to determine tail index and autocorrelation of absolute returns.
result The tail index of Bitcoin returns changes to approximately 3, consistent with the inverse cubic law.
SignSGD outperforms SGD in linear regression with optimal scaling laws under PLRF model.
problem Improving linear regression performance with signSGD under power-law random features.
method Analysis of signSGD risk under PLRF model, comparison with SGD, identification of unique effects.
result SignSGD can have a steeper compute-optimal slope than SGD in noisy regimes, especially with WSD schedule.
The paper predicts loss scaling across different datasets and compute scales.
problem Predicting loss scaling across different datasets and compute scales.
method Derive shifted power law relationships between train and test losses.
result Shifted power law relationships hold for various datasets and tasks, improving prediction accuracy.
The paper studies scaling laws for associative memory mechanisms.
problem Understanding and optimizing learning and memorization processes.
method High-dimensional matrices of outer products of embeddings, relating to transformer models. Derived scaling laws with sample and parameter sizes. Extensive numerical experiments.
result Precise scaling laws and statistical efficiency of estimators.
Investigates ways to train larger models with fewer resources, finding that test loss depends only on the actual number of trainable parameters.
problem Training larger models for cheaper under hardware constraints.
method Emulates an increase in effective parameters using frozen random parameters or fast structured transforms.
result Scaling laws cannot be deceived by spurious parameters; test loss depends only on the actual number of trainable parameters.
We have discovered 12 independent new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The…
Study shows how anisotropic data affects learning dynamics in phase retrieval.
problem Understanding learning dynamics in phase retrieval with anisotropic Gaussian inputs.
method Developed a tractable reduction to reveal a three-phase trajectory and derived scaling laws.
result Found that anisotropy leads to a three-phase trajectory: fast escape, slow convergence, and spectral-tail learning.
Study how generalization scales with model size and data in quadratic neural networks.
problem Understanding how generalization scales with model size and data in quadratic neural networks.
method Analyzed ℓ2-regularized empirical test error minimization in a quadratic two-layer network with finite-sample setting and structured data. result Revealed a phase diagram with distinct scaling regimes as the number of parameters varies, showing data-dependent power laws controlled by spectral structure of the target.
Improved loss scaling for stochastic momentum algorithms in high dimensions.
problem Improving loss scaling for stochastic momentum algorithms in high dimensions.
method Dimension-adapted Nesterov acceleration (DANA) scales momentum hyperparameters based on model size and data complexity.
result DANA improves loss scaling exponents across various data and target complexities.
This study reveals statistical patterns in ERC20 token transactions on Ethereum blockchain.
problem Understanding transactional dynamics in decentralized systems.
method Examined over 44 million ERC20 token transfers, categorized by address type (EOA or SC), and analyzed using scaling laws.
result EOA-driven transactions exhibit consistent statistical behavior, while SC-driven activity displays sublinear scaling and bursty activity.
This work studies scaling laws for low-precision training in high-dimensional linear regression.
problem Optimizing trade-off between model quality and training costs in high-dimensional linear regression.
method Theoretical study of scaling laws for low-precision training within a high-dimensional sketched linear regression framework, analyzing multiplicative and additive quantization.
result Multiplicative quantization maintains full-precision model size, while additive quantization reduces effective model size.
We extend our previous study of scaling range properties done for detrended fluctuation analysis (DFA) \cite{former_paper} to other techniques of fluctuation analysis (FA). The new technique called Modified Detrended Moving Average Analysis (MDMA) is introduced and its scaling range properties are examined and compared…
New scaling laws optimize model size, training, and inference for better performance.
problem Trade-off between model size and inference cost in modern LLMs.
method Train-to-Test (T2) scaling laws that jointly optimize model size, training tokens, and inference samples. result Optimal pretraining decisions shift into overtraining regime, leading to stronger performance.
Taylor's law of temporal fluctuation scaling, variance ∼ a(mean)b, is ubiquitous in natural and social sciences. We report for the first time convincing evidence of a solid temporal fluctuation scaling law in stock illiquidity by investigating the mean-variance relationship of the high-frequency illiquidity o…