Unified spectral framework for μP under joint width-depth scaling.
problem Challenges in stable feature learning and HP transfer for width-depth scaled models.
method Developed a simple and unified spectral framework for μP under joint width-depth scaling.
result Unified and generalized μP formulation for practical architectures with multi-transformation branches.
This paper studies activation sparsity in large language models, finding key trends and implications.
problem Activation sparsity in large language models (LLMs) can be improved for efficiency and interpretability.
method Proposes PPL-p% sparsity, analyzes trends with training data, width-depth ratio, and parameter scale. result ReLU is more efficient for sparsity than SiLU, and deeper architectures can improve sparsity.
The dependency of the generalization error of neural networks on model and dataset size is of critical importance both in practice and for understanding the theory of neural networks. Nevertheless, the functional form of this dependency remains elusive. In this work, we present a functional form which approximates well…
Pruned neural networks' error scales predictably with architecture and task.
problem Understanding the predictability of pruning across different scales and architectures.
method Functionally approximated the error of pruned networks, showing it is predictable in terms of invariant tying width, depth, and pruning level.
result The error of pruned networks follows a scaling law with interpretable coefficients that depend on architecture and task.
nGPT learns to transfer learning rates across model dimensions and token horizons.
problem nGPT does not transfer learning rates across model size and token horizon.
method Combining numerical experiments with alignment exponents, a novel nGPT parameterization νGPT is developed.
result νGPT exhibits learning rate transfer across width, depth, and token horizon.
Extends hyperparameter transfer across model sizes and modules, improving training speed.
problem Training stability and performance of large-scale models with optimal hyperparameters.
method Complete(d) Parameterisation, per-module hyperparameter optimisation and transfer. result Hyperparameter transfer holds even in the per-module hyperparameter regime, improving training speed.
New insights into how depth and width affect in-context learning in deep models.
problem Understanding how various resources impact in-context learning in deep models.
method Analyzed linear regression in a deep linear self-attention model, varying resources like depth, width, context length, and training steps.
result Increasing depth improves in-context learning even at infinite context length, contrary to previous findings.
Develops methods to measure and set function-space learning rates in neural networks.
problem Measuring and optimizing changes in neural network output functions.
method Efficient methods to measure and set function-space learning rates, requiring minimal computational overhead.
result Demonstrates FLeRM (Function-space Learning Rate Matching) for hyperparameter transfer across model scales.
New scaling framework for MoE architectures ensures stability and optimal performance at scale.
problem Lack of principled understanding of how hyperparameters should scale in MoE architectures.
method Developed a novel Dynamical Mean Field Theory (DMFT) for three scaling regimes of MoE architectures.
result Derived Maximally Scale-Stable Parameterization (MSSP) for SGD and Adam, providing robust learning rate transfer and monotonic improvement with scale.
Transformers show strengths and weaknesses in complexity analysis.
problem Understanding the strengths and limitations of attention layers in transformers.
method Analysis of representation power through complexity parameters and task-specific constructions.
result Transformers can solve sparse averaging tasks with logarithmic complexity, but triple detection tasks require linear complexity.
MPNNs over-squash distant node information, study shows.
problem Over-squashing in MPNNs where node features ignore distant nodes.
method Theoretical analysis of MPNNs' over-squashing, focusing on width, depth, and graph topology.
result Width mitigates over-squashing but makes network more sensitive, depth doesn't help, graph topology is key.
The study analyzes deep linear networks from random initialization, capturing dynamics and hyperparameter effects.
problem Understanding training dynamics in deep linear networks from random initialization.
method Theoretical analysis of gradient descent dynamics in deep linear networks with random initialization and large data.
result Captures the 'wider is better' effect and hyperparameter transfer effects, contrasting with neural-tangent parameterization.
The Fisher information matrix (FIM) plays an essential role in statistics and machine learning as a Riemannian metric tensor or a component of the Hessian matrix of loss functions. Focusing on the FIM and its variants in deep neural networks (DNNs), we reveal their characteristic scale dependence on the network width, …
Deep networks can approximate various activation functions with modest adjustments.
problem Expressive power of deep neural networks with diverse activation functions.
method Approximation of any activation function in set A by ReLU networks with specific scaling factors.
result Approximation of any activation function in a specific subset of A by ReLU networks with (1,1) scaling factors.
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good generalization performance. Moreover, when we measure generalization as a function of pa…
We consider networks, trained via stochastic gradient descent to minimize ℓ2 loss, with the training labels perturbed by independent noise at each iteration. We characterize the behavior of the training dynamics near any parameter vector that achieves zero training error, in terms of an implicit regularization te…
This work analyzes the statistical properties of neural ODEs for distribution learning.
problem Statistical properties of neural ODEs for distribution learning.
method General nonparametric statistical convergence analysis for distribution learning via neural ODE models.
result Established nearly minimax-optimal convergence rates for neural ODEs.
DNArch learns CNN architectures by backpropagation.
problem Discovering optimal CNN architectures.
method Differentiable Neural Architectures (DNArch) learns CNN architectures by backpropagation, controlling kernel sizes, channels, downsampling positions, and depth.
result DNArch finds performant CNN architectures across various tasks.
Deep neural nets estimate operators between infinite-dimensional spaces with fast rates.
problem Estimating operators between infinite-dimensional spaces.
method Deep neural networks for nonparametric estimation of Lipschitz operators.
result Error bounds decay with fast rates depending on intrinsic dimension.
New findings show depth is more important than width in neural networks.
problem Understanding the role of width and depth in neural networks.
method Constructed networks with bounded weights and width at most d+2, showing depth plays a more significant role.
result Depth is more important than width in the expressive power of neural networks.
A major goal of unsupervised learning is to discover data representations that are useful for subsequent tasks, without access to supervised labels during training. Typically, this involves minimizing a surrogate objective, such as the negative log likelihood of a generative model, with the hope that representations us…
Analyzes the structure and rank of neural network Hessians.
problem Understanding redundancy in overparameterized neural networks.
method Theoretical tools to analyze Hessian map range and rank deficiency.
result Exact formulas and tight upper bounds for Hessian rank of deep linear networks.
This work explores feature learning tradeoffs in neural networks.
problem Resource tradeoffs in neural feature learning.
method Theoretical and experimental investigation of offline sparse parity learning.
result Width improves sample efficiency in sparse feature learning.
New method trains deep vanilla networks as fast as ResNets without shortcut connections.
problem Training very deep neural networks is challenging.
method Developed a new type of transformation compatible with Leaky ReLUs.
result Validation accuracies with deep vanilla networks are competitive with ResNets and significantly higher.
Study compares random and learned features in deep Bayesian linear models.
problem Understanding how feature learning affects generalization in deep learning.
method Comparing deep random feature models to deep networks with trained layers.
result Random feature models can display double-descent behavior, while deep networks do not.
Complex-valued neural networks can approximate any continuous function with bounded widths and depths.
problem Approximating continuous functions with complex-valued neural networks of bounded widths and depths.
method Analyzing activation functions and proving universality for complex-valued networks.
result Deep narrow complex-valued networks are universal if and only if their activation function is neither holomorphic, nor antiholomorphic, nor R-affine. New proof shows incremental flow models are essential for universal generation.
problem Understanding the universality of flow-based models in generating natural maps.
method Topological-dynamical argument and algebraic properties of flows.
result Incremental generation is necessary and sufficient for universal flow-based generation.
Paper introduces new neural network models and theories.
problem Understanding neural networks beyond over-parameterized regime.
method Develops two exact models and a novel representor theory.
result Provides insights into neural network training and kernel evolution.
Deep learning (DL) is transforming industry as decision-making processes are being automated by deep neural networks (DNNs) trained on real-world data. Driven partly by rapidly-expanding literature on DNN approximation theory showing they can approximate a rich variety of functions, such tools are increasingly being co…
Physics-informed neural networks improve by measuring effective dimensionality of constraints.
problem Task interference in physics-informed neural networks due to shared parameter space.
method Introduce effective dimensionality (deff) as an operator invariant to quantify constraints. result Effective dimensionality measures unconstrained parameter directions, independent of network architecture.
This work explains neural collapse in shallow neural networks and its impact on generalization.
problem Understanding neural collapse in shallow neural networks and its effect on generalization.
method Analysis of two and three-layer ReLU neural networks, focusing on data dimension, sample size, and signal-to-noise ratio.
result Neural collapse occurs in shallow ReLU networks under certain conditions related to data properties and network architecture.
Introduces bounded scale measure and generalizes property A.
problem Defining property A for large scale spaces with bounded geometry.
method Introduces bounded scale measure, shows its coarse invariance, and generalizes property A.
result Definition of property A for large scale spaces with bounded scale measure is a coarse invariant.
Transformers can scale both context and task, but MLPs can only scale task.
problem Understanding and scaling In-Context Learning in transformers.
method Simplified transformer architecture, feature map, and MLP combination.
result Simplified transformer can perform ICL and context-scaling but not task-scaling.
New principles needed for scaling large language models, challenging traditional regularization methods.
problem The shift from generalization to scaling in machine learning requires new guiding principles.
method Examining the effectiveness of traditional regularization methods in the scaling-centric era.
result Traditional principles of regularization may not generalize to larger scales, highlighting new phenomena like scaling law crossover.
Improves U-Net for scale equivariance in semantic segmentation.
problem Improving generalization in semantic segmentation tasks with varying scales.
method Introduces Scale Equivariant U-Net (SEU-Net) with carefully applied subsampling and upsampling layers and scale-equivariant layers.
result Significantly improved generalization to different scales compared to U-Net and scale-equivariant architecture without upsampling.
Introduces resemblance structure for large scale geometry.
problem Defining similarity in large scale geometry.
method Axiomatizing the concept of resemblance for subsets of a set.
result Large scale resemblance structures can induce nearness and generalize large scale properties.
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.
Derives a family of hyperparameter scaling strategies for neural networks.
problem Optimizing hyperparameters for wide and deep neural networks.
method Introduces a one-parameter family of hyperparameter scaling strategies.
result Reveals proper scaling of depth with width for large-scale models.
To elucidate allometric scaling in complex systems, we investigated the underlying scaling relationships between typical three-scale indicators for approximately 500,000 Japanese firms; namely, annual sales, number of employees, and number of business partners. First, new scaling relations including the distributions o…
Study calculates tail risk for various mixture distributions.
problem Estimating tail risk for complex distribution mixtures.
method Analyzes tail conditional expectation for location-scale mixtures of elliptical distributions.
result Developed methods for calculating tail risk in various distributions.
A new robust scaling approach improves downstream metabolomics analysis.
problem Challenges in choosing scaling techniques for metabolomics data.
method Introduces a weighted scaling approach robust to outliers.
result The proposed method outperforms traditional scaling techniques in both outlier-free and outlier-present datasets.
Novel neural network solves PDEs with multi-scale resolution.
problem Solving time-dependent PDEs with varying spatial and temporal scales.
method Multi-scale message passing neural network with temporal and spatial gating modules.
result Outperforms baselines on PDEs with diverse scales.
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.
CrossAD detects anomalies in time series data by considering cross-scale associations and cross-window modeling.
problem Anomaly detection in time series data is challenging due to varying patterns at different scales and fixed window sizes.
method CrossAD incorporates cross-scale reconstruction and a query library to capture dynamic cross-scale associations and comprehensive context.
result CrossAD achieves state-of-the-art performance in anomaly detection across multiple real-world datasets.
Develops active learning for scale-bridging simulations.
problem Quantitative predictions in nanoporous media and inertial confinement fusion.
method Active learning approach to optimize fine-scale simulations for coarse-scale hydrodynamics.
result Optimizes use of fine-scale simulations for coarse-scale predictions.
Theory explains neural network scaling with dataset and model size.
problem Neural network scaling laws with dataset and model size.
method Identified variance-limited and resolution-limited scaling behaviors.
result Four scaling regimes explained: infinite data, infinite width, resolution-limited, and large width.
We define the intrinsic scale at which a network begins to reveal its identity as the scale at which subgraphs in the network (created by a random walk) are distinguishable from similar sized subgraphs in a perturbed copy of the network. We conduct an extensive study of intrinsic scale for several networks, ranging fro…
Study shows how non-uniform scaling affects persistence diagrams.
problem Stability of persistence diagrams under non-uniform scaling.
method Explicit bounds on bottleneck distance derived for Euclidean scaling.
result Explicit bounds on the stability of persistence diagrams under non-uniform scaling.