Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science

Graph Structure of Neural Networks

View recent discussion. Abstract: Neural networks are often represented as graphs of connections between neurons. However, despite their wide use, there is currently little understanding of the relationship between the graph structure of the neural network and its predictive performance. Here we systematically investigate how does the graph structure of neural networks affect their predictive performance. To this end, we develop a novel graph-based representation of neural networks called relational graph, where layers of neural network computation correspond to rounds of message exchange along the graph structure. Using this representation we show that: (1) a "sweet spot" of relational graphs leads to neural networks with significantly improved predictive performance; (2) neural network's performance is approximately a smooth function of the clustering coefficient and average path length of its relational graph; (3) our findings are consistent across many different tasks and datasets; (4) the sweet spot can be identified efficiently; (5) top-performing neural networks have graph structure surprisingly similar to those of real biological neural networks. Our work opens new directions for the design of neural architectures and the understanding on neural networks in general.

Beyond neural scaling laws: beating power law scaling via data pruning

Widely observed neural scaling laws, in which error falls off as a power of the training set size, model size, or both, have driven substantial performance improvements in deep learning. However, these improvements through scaling alone require considerable costs in compute and energy. Here we focus on the scaling of error with dataset size and show how in theory we can break beyond power law scaling and potentially even reduce it to exponential scaling instead if we have access to a high-quality data pruning metric that ranks the order in which training examples should be discarded to achieve any pruned dataset size. We then test this improved scaling prediction with pruned dataset size empirically, and indeed observe better than power law scaling in practice on ResNets trained on CIFAR-10, SVHN, and ImageNet. Next, given the importance of finding high-quality pruning metrics, we perform the first large-scale benchmarking study of ten different data pruning metrics on ImageNet. We find most existing high performing metrics scale poorly to ImageNet, while the best are computationally intensive and require labels for every image. We therefore developed a new simple, cheap and scalable self-supervised pruning metric that demonstrates comparable performance to the best supervised metrics. Overall, our work suggests that the discovery of good data-pruning metrics may provide a viable path forward to substantially improved neural scaling laws, thereby reducing the resource costs of modern deep learning.

LayerMerge: Neural Network Depth Compression through Layer Pruning and Merging

Recent works show that reducing the number of layers in a convolutional neural network can enhance efficiency while maintaining the performance of the network. Existing depth compression methods remove redundant non-linear activation functions and merge the consecutive convolution layers into a single layer. However, these methods suffer from a critical drawback; the kernel size of the merged layers becomes larger, significantly undermining the latency reduction gained from reducing the depth of the network. We show that this problem can be addressed by jointly pruning convolution layers and activation functions. To this end, we propose LayerMerge, a novel depth compression method that selects which activation layers and convolution layers to remove, to achieve a desired inference speed-up while minimizing performance loss. Since the corresponding selection problem involves an exponential search space, we formulate a novel surrogate optimization problem and efficiently solve it via dynamic programming. Empirical results demonstrate that our method consistently outperforms existing depth compression and layer pruning methods on various network architectures, both on image classification and generation tasks. We release the code at https://github.com/snu-mllab/LayerMerge.

Eternal Sunshine of the Spotless Net: Selective Forgetting in Deep Networks

We explore the problem of selectively forgetting a particular subset of the data used for training a deep neural network. While the effects of the data to be forgotten can be hidden from the output of the network, insights may still be gleaned by probing deep into its weights. We propose a method for "scrubbing" the weights clean of information about a particular set of training data. The method does not require retraining from scratch, nor access to the data originally used for training. Instead, the weights are modified so that any probing function of the weights is indistinguishable from the same function applied to the weights of a network trained without the data to be forgotten. This condition is a generalized and weaker form of Differential Privacy. Exploiting ideas related to the stability of stochastic gradient descent, we introduce an upper-bound on the amount of information remaining in the weights, which can be estimated efficiently even for deep neural networks.

Coresets for Data-efficient Training of Machine Learning Models

Incremental gradient (IG) methods, such as stochastic gradient descent and its variants are commonly used for large scale optimization in machine learning. Despite the sustained effort to make IG methods more data-efficient, it remains an open question how to select a training data subset that can theoretically and practically perform on par with the full dataset. Here we develop CRAIG, a method to select a weighted subset (or coreset) of training data that closely estimates the full gradient by maximizing a submodular function. We prove that applying IG to this subset is guaranteed to converge to the (near)optimal solution with the same convergence rate as that of IG for convex optimization. As a result, CRAIG achieves a speedup that is inversely proportional to the size of the subset. To our knowledge, this is the first rigorous method for data-efficient training of general machine learning models. Our extensive set of experiments show that CRAIG, while achieving practically the same solution, speeds up various IG methods by up to 6x for logistic regression and 3x for training deep neural networks.

Data Valuation Without Training of a Model

Many recent works on understanding deep learning try to quantify how much individual data instances influence the optimization and generalization of a model. Such attempts reveal characteristics and importance of individual instances, which may provide useful information in diagnosing and improving deep learning. However, most of the existing works on data valuation require actual training of a model, which often demands high-computational cost. In this paper, we provide a training-free data valuation score, called complexity-gap score, which is a data-centric score to quantify the influence of individual instances in generalization of two-layer overparameterized neural networks. The proposed score can quantify irregularity of the instances and measure how much each data instance contributes in the total movement of the network parameters during training. We theoretically analyze and empirically demonstrate the effectiveness of the complexity-gap score in finding `irregular or mislabeled' data instances, and also provide applications of the score in analyzing datasets and diagnosing training dynamics. Our code is publicly available at https://github.com/JJchy/CG_score.

Dataset Condensation with Distribution Matching

Computational cost to train state-of-the-art deep models in many learning problems is rapidly increasing due to more sophisticated models and larger datasets. A recent promising direction to reduce training time is dataset condensation that aims to replace the original large training set with a significantly smaller learned synthetic set while preserving its information. While training deep models on the small set of condensed images can be extremely fast, their synthesis remains computationally expensive due to the complex bi-level optimization and second-order derivative computation. In this work, we propose a simple yet effective dataset condensation technique that requires significantly lower training cost with comparable performance by matching feature distributions of the synthetic and original training images in sampled embedding spaces. Thanks to its efficiency, we apply our method to more realistic and larger datasets with sophisticated neural architectures and achieve a significant performance boost while using larger synthetic training set. We also show various practical benefits of our method in continual learning and neural architecture search.

Deep Learning on a Data Diet: Finding Important Examples Early in Training

Recent success in deep learning has partially been driven by training increasingly overparametrized networks on ever larger datasets. It is therefore natural to ask: how much of the data is superfluous, which examples are important for generalization, and how do we find them? In this work, we make the striking observation that, in standard vision datasets, simple scores averaged over several weight initializations can be used to identify important examples very early in training. We propose two such scores—the Gradient Normed (GraNd) and the Error L2-Norm (EL2N) scores—and demonstrate their efficacy on a range of architectures and datasets by pruning significant fractions of training data without sacrificing test accuracy. In fact, using EL2N scores calculated a few epochs into training, we can prune half of the CIFAR10 training set while slightly improving test accuracy. Furthermore, for a given dataset, EL2N scores from one architecture or hyperparameter configuration generalize to other configurations. Compared to recent work that prunes data by discarding examples that are rarely forgotten over the course of training, our scores use only local information early in training. We also use our scores to detect noisy examples and study training dynamics through the lens of important examples—we investigate how the data distribution shapes the loss surface and identify subspaces of the model’s data representation that are relatively stable over training.

Meta-Weight-Net: Learning an Explicit Mapping For Sample Weighting

Current deep neural networks(DNNs) can easily overfit to biased training data with corrupted labels or class imbalance. Sample re-weighting strategy is commonly used to alleviate this issue by designing a weighting function mapping from training loss to sample weight, and then iterating between weight recalculating and classifier updating. Current approaches, however, need manually pre-specify the weighting function as well as its additional hyper-parameters. It makes them fairly hard to be generally applied in practice due to the significant variation of proper weighting schemes relying on the investigated problem and training data. To address this issue, we propose a method capable of adaptively learning an explicit weighting function directly from data. The weighting function is an MLP with one hidden layer, constituting a universal approximator to almost any continuous functions, making the method able to fit a wide range of weighting function forms including those assumed in conventional research. Guided by a small amount of unbiased meta-data, the parameters of the weighting function can be finely updated simultaneously with the learning process of the classifiers. Synthetic and real experiments substantiate the capability of our method for achieving proper weighting functions in class imbalance and noisy label cases, fully complying with the common settings in traditional methods, and more complicated scenarios beyond conventional cases. This naturally leads to its better accuracy than other state-of-the-art methods.

Dataset Condensation with Gradient Matching

As the state-of-the-art machine learning methods in many fields rely on larger datasets, storing datasets and training models on them become significantly more expensive. This paper proposes a training set synthesis technique for data-efficient learning, called Dataset Condensation, that learns to condense large dataset into a small set of informative synthetic samples for training deep neural networks from scratch. We formulate this goal as a gradient matching problem between the gradients of deep neural network weights that are trained on the original and our synthetic data. We rigorously evaluate its performance in several computer vision benchmarks and demonstrate that it significantly outperforms the state-of-the-art methods. Finally we explore the use of our method in continual learning and neural architecture search and report promising gains when limited memory and computations are available.

Deep Learning Scaling is Predictable, Empirically

Deep learning (DL) creates impactful advances following a virtuous recipe: model architecture search, creating large training data sets, and scaling computation. It is widely believed that growing training sets and models should improve accuracy and result in better products. As DL application domains grow, we would like a deeper understanding of the relationships between training set size, computational scale, and model accuracy improvements to advance the state-of-the-art. This paper presents a large scale empirical characterization of generalization error and model size growth as training sets grow. We introduce a methodology for this measurement and test four machine learning domains: machine translation, language modeling, image processing, and speech recognition. Our empirical results show power-law generalization error scaling across a breadth of factors, resulting in power-law exponents---the "steepness" of the learning curve---yet to be explained by theoretical work. Further, model improvements only shift the error but do not appear to affect the power-law exponent. We also show that model size scales sublinearly with data size. These scaling relationships have significant implications on deep learning research, practice, and systems. They can assist model debugging, setting accuracy targets, and decisions about data set growth. They can also guide computing system design and underscore the importance of continued computational scaling.

DynaMoE: Dynamic Token-Level Expert Activation with Layer-Wise Adaptive Capacity for Mixture-of-Experts Neural Networks

Mixture-of-Experts (MoE) architectures have emerged as a powerful paradigm for scaling neural networks while maintaining computational efficiency. However, standard MoE implementations rely on two rigid design assumptions: (1) fixed Top-K routing where exactly K experts are activated per token, and (2) uniform expert allocation across all layers. This paper introduces DynaMoE, a novel MoE framework that relaxes both constraints through dynamic token-level expert activation and layer-wise adaptive capacity allocation. DynaMoE introduces a principled routing mechanism where the number of active experts per token varies based on input complexity. Concurrently, the framework implements six distinct scheduling strategies for distributing expert capacity across network depth, including descending, ascending, pyramid, and wave patterns. We theoretically analyze the expressivity gains of dynamic routing and derive bounds on computational efficiency. Through extensive experiments on MNIST, Fashion-MNIST, CIFAR-10 (image classification), and Recycling-the-Web (language modeling) across multiple model scales, we demonstrate that DynaMoE achieves superior parameter efficiency compared to static baselines. Our key finding is that optimal expert schedules are task- and scale-dependent: descending schedules (concentrating capacity in early layers) outperform uniform baselines on image classification. For language modeling, optimal schedules vary by model size, descending for Tiny, ascending for Small, and uniform for Medium. Furthermore, dynamic routing reduces gradient variance during training, leading to improved convergence stability. DynaMoE establishes a new framework for adaptive computation in neural networks, providing principled guidance for MoE architecture design.

Curriculum learning

Humans and animals learn much better when the examples are not randomly presented but organized in a meaningful order which illustrates gradually more concepts, and gradually more complex ones. Here, we formalize such training strategies in the context of machine learning, and call them "curriculum learning". In the context of recent research studying the difficulty of training in the presence of non-convex training criteria (for deep deterministic and stochastic neural networks), we explore curriculum learning in various set-ups. The experiments show that significant improvements in generalization can be achieved. We hypothesize that curriculum learning has both an effect on the speed of convergence of the training process to a minimum and, in the case of non-convex criteria, on the quality of the local minima obtained: curriculum learning can be seen as a particular form of continuation method (a general strategy for global optimization of non-convex functions).

Dataset Distillation

Model distillation aims to distill the knowledge of a complex model into a simpler one. In this paper, we consider an alternative formulation called {\em dataset distillation}: we keep the model fixed and instead attempt to distill the knowledge from a large training dataset into a small one. The idea is to {\em synthesize} a small number of data points that do not need to come from the correct data distribution, but will, when given to the learning algorithm as training data, approximate the model trained on the original data. For example, we show that it is possible to compress $60,000$ MNIST training images into just $10$ synthetic {\em distilled images} (one per class) and achieve close to original performance with only a few steps of gradient descent, given a particular fixed network initialization. We evaluate our method in a wide range of initialization settings and with different learning objectives. Experiments on multiple datasets show the advantage of our approach compared to alternative methods in most settings.

DAVINZ: Data Valuation using Deep Neural Networks at Initialization

Recent years have witnessed a surge of interest in developing trustworthy methods to evaluate the value of data in many real-world applications (e.g., collaborative machine learning, data marketplaces). Existing data valuation methods typically valuate data using the generalization performance of converged machine learning models after their long-term model training, hence making data valuation on large complex deep neural networks (DNNs) unaffordable. To this end, we theoretically derive a domain-aware generalization bound to estimate the generalization performance of DNNs without model training. We then exploit this theoretically derived generalization bound to develop a novel training-free data valuation method named data valuation at initialization (DAVINZ) on DNNs, which consistently achieves remarkable effectiveness and efficiency in practice. Moreover, our training-free DAVINZ, surprisingly, can even theoretically and empirically enjoy the desirable properties that training-based data valuation methods usually attain, thus making it more trustworthy in practice.

Distilling Dataset into Neural Field

Utilizing a large-scale dataset is essential for training high-performance deep learning models, but it also comes with substantial computation and storage costs. To overcome these challenges, dataset distillation has emerged as a promising solution by compressing the large-scale dataset into a smaller synthetic dataset that retains the essential information needed for training. This paper proposes a novel parameterization framework for dataset distillation, coined Distilling Dataset into Neural Field (DDiF), which leverages the neural field to store the necessary information of the large-scale dataset. Due to the unique nature of the neural field, which takes coordinates as input and output quantity, DDiF effectively preserves the information and easily generates various shapes of data. We theoretically confirm that DDiF exhibits greater expressiveness than some previous literature when the utilized budget for a single synthetic instance is the same. Through extensive experiments, we demonstrate that DDiF achieves superior performance on several benchmark datasets, extending beyond the image domain to include video, audio, and 3D voxel. We release the code at \url{https://github.com/aailab-kaist/DDiF}.