This work proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.
problem Proving the asymptotic freeness of layerwise Jacobians in multilayer perceptrons (MLPs).
method Replacing each layer's parameter matrix with itself multiplied by a Haar orthogonal matrix, and using the invariance of the MLP.
result Proves the asymptotic freeness of layerwise Jacobians in MLPs with Haar orthogonal matrices.
New method μP2 improves neural network training by scaling perturbations layerwise.
problem Improving neural network performance as models scale up.
method Layerwise perturbation scaling in the infinite-width limit of neural networks.
result Layerwise perturbation scaling ensures all layers are effectively perturbed in the limit.
Proposes efficient training method for deep thin networks.
problem Deploying deep learning models with accuracy and compactness.
method Three-stage method: widen, warm up, fine tune.
result Deep thin networks trained with method outperform standard deep networks.
Training large deep neural networks on massive datasets is computationally very challenging. There has been recent surge in interest in using large batch stochastic optimization methods to tackle this issue. The most prominent algorithm in this line of research is LARS, which by employing layerwise adaptive learning ra…
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.
A new method for learning Bayesian neural networks using layerwise inference.
problem Learning Bayesian neural networks efficiently and accurately.
method Bayesian layerwise inference, treating neural networks as stacked Bayesian linear models, with pseudo-targets defined by backpropagated gradients.
result The method converges quickly and performs well on various benchmarks.
Training avoids edge of stability by aligning Jacobian matrices.
problem Training neural networks on the edge of stability causes inaccuracies.
method Used an exponential Euler solver to prevent entering the edge of stability.
result Alignment of Jacobian matrices causes sharpness increase in Hessian.
Deep Gaussian Processes (DGP) are hierarchical generalizations of Gaussian Processes (GP) that have proven to work effectively on a multiple supervised regression tasks. They combine the well calibrated uncertainty estimates of GPs with the great flexibility of multilayer models. In DGPs, given the inputs, the outputs …
Deep learning is also known as hierarchical learning, where the learner _learns_ to represent a complicated target function by decomposing it into a sequence of simpler functions to reduce sample and time complexity. This paper formally analyzes how multi-layer neural networks can perform such hierarchical learning _ef…
Proves deep networks can learn hierarchical structures efficiently.
problem Understanding how deep networks learn hierarchical structures in data.
method Random Hierarchy Models, gradient-based methods, layerwise training.
result Proves deep networks can efficiently learn hierarchical structures.
AlphaPruning optimizes LLM pruning using HT-SR theory for better performance.
problem Improving pruning of large language models to reduce size without sacrificing performance.
method AlphaPruning uses HT-SR theory to allocate layerwise sparsity ratios more theoretically.
result AlphaPruning prunes LLaMA-7B to 80% sparsity with reasonable perplexity.
New bounds adaptively control spectral complexity of trained Transformers.
problem Understanding why Transformers generalize well in machine learning.
method Spectrum-adaptive post hoc generalization bounds for multi-layer Transformers.
result Bounds adaptively trade off spectral complexity against dimension and depth factors.
Estimating machine learning performance 'in the wild' is both an important and unsolved problem. In this paper, we seek to examine, understand, and predict the pointwise competence of classification models. Our contributions are twofold: First, we establish a statistically rigorous definition of competence that general…
Efficient algorithm for CMDPs reduces to offline density estimation.
problem Offline learning for CMDPs with horizon H.
method Reduction to offline density estimation, layerwise exploration-exploitation tradeoff.
result First efficient and near-optimal reduction from CMDPs to offline density estimation.
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.
We improve neural network explainability by bypassing batch normalization.
problem Lack of transparency in neural networks.
method Layer-wise Relevance Propagation with a method to include normalization layers.
result Heatmaps are more accurate for convolutional layers with our method.
With the development of cloud computing and big data, the reliability of data storage systems becomes increasingly important. Previous researchers have shown that machine learning algorithms based on SMART attributes are effective methods to predict hard drive failures. In this paper, we use SMART attributes to predict…
Deep neural networks (DNNs) depend on the storage of a large number of parameters, which consumes an important portion of the energy used during inference. This paper considers the case where the energy usage of memory elements can be reduced at the cost of reduced reliability. A training algorithm is proposed to optim…
New optimizers control network width scaling, improving stability and transfer across different model sizes.
problem Designing stable optimizers for networks of varying widths.
method Interpreting optimizers as steepest descent under mean-normalized operator norms, enabling layerwise composability and width-independent bounds.
result New optimizers like row normalization and column normalization provide stable learning-rate transfer across different model widths.
New view: Deep GCNs learn to anti-oversmooth during training.
problem Performance drop in deep GCNs due to oversmoothing.
method Interpreted GCN as MLP + graph regularization, analyzed training process.
result Deep GCNs learn to anti-oversmooth during training, not over-smooth.
We propose a distributed approach to train deep neural networks (DNNs), which has guaranteed convergence theoretically and great scalability empirically: close to 6 times faster on instance of ImageNet data set when run with 6 machines. The proposed scheme is close to optimally scalable in terms of number of machines, …
A new robust prefix-tuning framework improves model robustness against adversarial attacks.
problem Lack of robustness in prefix-tuning for adversarial attacks.
method Leveraging layerwise activations of pretrained models for additional prefix finetuning during the test phase.
result Framework substantially improves robustness over strong baselines while maintaining comparable accuracy on clean texts.
Adversarial training has been shown to regularize deep neural networks in addition to increasing their robustness to adversarial examples. However, its impact on very deep state of the art networks has not been fully investigated. In this paper, we present an efficient approach to perform adversarial training by pertur…
A new measure predicts deep learning model performance.
problem Predicting the generalization error of deep learning models.
method 2sED measure based on effective dimension, layerwise iterative approximation.
result 2sED correlates well with training error and generalization error.
In this note we present a generative model of natural images consisting of a deep hierarchy of layers of latent random variables, each of which follows a new type of distribution that we call rectified Gaussian. These rectified Gaussian units allow spike-and-slab type sparsity, while retaining the differentiability nec…
MTL-NAS combines NAS with GP-MTL for task-agnostic multi-task learning.
problem Designing architectures for diverse tasks with varying priors.
method Disentangled GP-MTL networks, hierarchical feature sharing, and gradient-based search.
result General-purpose model trained once can adapt to multiple tasks.
Low complexity decentralized neural net with centralized performance.
problem Training large neural networks in distributed nodes without data sharing.
method Layer-wise learning using ADMM for low complexity and centralized performance.
result Equivalent learning performance to centralized training in distributed nodes.
While the backpropagation of error algorithm enables deep neural network training, it implies (i) bidirectional synaptic weight transport and (ii) update locking until the forward and backward passes are completed. Not only do these constraints preclude biological plausibility, but they also hinder the development of l…
Large learning rates work surprisingly well in standard parameterization, contrary to theory.
problem Theoretical limits of large learning rates do not match practical network behavior.
method Fine-grained analysis of learning rates and network behavior under cross-entropy loss.
result There are two distinct sub-regimes of unstable learning rates, with a controlled divergence regime where features continue to evolve.
TSSM splits neural networks for parallel training with minimal accuracy loss.
problem Accuracy degradation in parallel training of deep neural networks.
method TSSM reformulates alternating minimization to achieve parallelism with minimal accuracy loss.
result TSSM achieves significant speedup without accuracy loss on multiple datasets.
Multitask learning has shown promising performance in many applications and many multitask models have been proposed. In order to identify an effective multitask model for a given multitask problem, we propose a learning framework called learning to multitask (L2MT). To achieve the goal, L2MT exploits historical multit…
SAEs struggle with curved activation manifolds, revealing layer-dependent scaling laws.
problem Sparse autoencoders' reconstruction error varies across layers, not fitting existing scaling laws.
method Cross-layer study of 844 SAE checkpoints, fitting and regressing on manifold geometry.
result Manifold geometry predicts layer-dependent width exponents in SAEs, with transferable coefficients.
While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- Internal Covariate Shift-- the current solution has certain drawbacks. Specifically, BN depends on batch statistics for layerwise input normalization during training which makes the estimates of …
While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- \textit{Internal Covariate Shift}-- the current solution has certain drawbacks. For instance, BN depends on batch statistics for layerwise input normalization during training which makes the esti…
New analysis shows how to balance privacy and accuracy in deep learning.
problem Balancing privacy and accuracy in deep learning models.
method Continuous time analysis through neural tangent kernel (NTK) for arbitrary architectures.
result Large clipping norm improves calibration without sacrificing accuracy.
Injectivity of ReLU networks is characterized for generative models and inverse problems.
problem Injectivity in ReLU networks for generative models and inverse problems.
method Layerwise analysis, worst-case Lipschitz constants, differential topology, random projections.
result Global injectivity of ReLU networks requires expansivity between 3.4 and 10.5 for Gaussian matrices.
Traditionally, when generative models of data are developed via deep architectures, greedy layer-wise pre-training is employed. In a well-trained model, the lower layer of the architecture models the data distribution conditional upon the hidden variables, while the higher layers model the hidden distribution prior. Bu…
Shallow supervised 1-hidden layer neural networks have a number of favorable properties that make them easier to interpret, analyze, and optimize than their deep counterparts, but lack their representational power. Here we use 1-hidden layer learning problems to sequentially build deep networks layer by layer, which ca…
New learning rules for wide neural networks without backpropagation.
problem Training wide neural networks efficiently and without backpropagation.
method Input-weight alignment driven by gradient descent in the NTK regime.
result Biologically-motivated learning rules equivalent to backpropagation in wide networks.
A method to automatically choose feature dimensions in linear attention for better approximation quality.
problem Choosing the feature dimension in linear attention to balance quality and efficiency.
method Statistical degrees of freedom for determining feature dimension, layer-wise training strategy.
result Our method achieves smaller approximation error compared to fixed dimensions and improves model performance.
New theory maps neural network weights to optimize faster and scale.
problem Optimizing neural networks for speed and scalability.
method Constructing a duality map using layer-wise operator norms.
result Derived GPU-friendly algorithms for various layers.
Dropout and RaM become equivalent in large ResNets as depth and width increase.
problem Improving performance in deep learning models.
method Comparing Dropout and Random Gradient Masking in ResNets.
result Dropout and RaM converge to the same large-scale limiting dynamics in ResNets.
Spectral gradient methods outperform Euclidean in certain deep learning scenarios.
problem When do spectral gradient updates outperform Euclidean in deep learning?
method Layerwise condition comparing squared nuclear-to-Frobenius ratio to stable rank of activations.
result Spectral updates can be more effective than Euclidean in deep networks and transformers.
Scalable method bounds Lipschitz constant of generative models.
problem Bounding the Lipschitz constant of generative models.
method Layerwise convex approximations using zonotopes.
result Efficient and tight bounds on generative models.
In this paper, we study two aspects of the variational autoencoder (VAE): the prior distribution over the latent variables and its corresponding posterior. First, we decompose the learning of VAEs into layerwise density estimation, and argue that having a flexible prior is beneficial to both sample generation and infer…
Looped transformers with LN converge to power method for principal component prediction.
problem Understanding how transformers learn algorithmic procedures.
method Study of principal component prediction with looped linear transformers and layer normalization.
result Gradient descent trains looped transformers with LN to implement the power method for principal component prediction.
The paper explores how invertibility affects the complexity of encoder models in VAEs.
problem The complexity of the encoder model in VAEs when the generative map is invertible.
method Formalizes the concept of strong invertibility and analyzes the complexity of the encoder model.
result Strongly invertible generative maps allow for simpler encoder models, while non-invertible maps require exponentially larger encoders.
DNNs with L2 regularization reveal feature learning dynamics and sparsity.
problem Understanding feature learning in DNNs with L2 regularization. method Reformulating loss in terms of layerwise activations and covariances.
result Proving sparsity of local minima in L2-regularized DNNs.