This paper studies the curious phenomenon for machine learning models with Transformer architectures that their activation maps are sparse. By activation map we refer to the intermediate output of the multi-layer perceptrons (MLPs) after a ReLU activation function, and by sparse we mean that on average very few entries (e.g., 3.0% for T5-Base and 6.3% for ViT-B16) are nonzero for each input to MLP. Moreover, larger Transformers with more layers and wider MLP hidden dimensions are sparser as measured by the percentage of nonzero entries. Through extensive experiments we demonstrate that the emergence of sparsity is a prevalent phenomenon that occurs for both natural language processing and vision tasks, on both training and evaluation data, for Transformers of various configurations, at layers of all depth levels, as well as for other architectures including MLP-mixers and 2-layer MLPs. We show that sparsity also emerges using training datasets with random labels, or with random inputs, or with infinite amount of data, demonstrating that sparsity is not a result of a specific family of datasets. We discuss how sparsity immediately implies a way to significantly reduce the FLOP count and improve efficiency for Transformers. Moreover, we demonstrate perhaps surprisingly that enforcing an even sparser activation via Top-k thresholding with a small value of k brings a collection of desired but missing properties for Transformers, namely less sensitivity to noisy training data, more robustness to input corruptions, and better calibration for their prediction confidence.
University of Sheffield（谢菲尔德大学）；The University of Sheffield（谢菲尔德大学）
"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparsity" is related to a penalty term that leads to some connecting weights becoming small or zero, in biological brains, sparsity is often created when high spiking thresholds prevent neuronal activity. Here we introduce sparsity into a reservoir computing network via neuron-specific learnable thresholds of activity, allowing neurons with low thresholds to contribute to decision-making but suppressing information from neurons…
Virginia Tech（弗吉尼亚理工学院）；Howard University（霍华德大学）；West Virginia University（西弗吉尼亚大学）
Network pruning is aimed at imposing sparsity in a neural network architecture by increasing the portion of zero-valued weights for reducing its size regarding energy-efficiency consideration and increasing evaluation speed. In most of the conducted research efforts, the sparsity is enforced for network pruning without any attention to the internal network characteristics such as unbalanced outputs of the neurons or more specifically the distribution of the weights and outputs of the neurons. That may cause severe accuracy drop due to uncontrolled sparsity. In this work, we propose an attentio…
The mushroom body is the key network for the representation of learned olfactory stimuli in Drosophila and insects. The sparse activity of Kenyon cells, the principal neurons in the mushroom body, plays a key role in the learned classification of different odours. In the specific case of the fruit fly, the sparseness of the network is enforced by an inhibitory feedback neuron called APL, and by an intrinsic high firing threshold of the Kenyon cells. In this work we took inspiration from the fruit fly brain to formulate a novel machine learning algorithm that is able to optimize the sparsity le…
Sequential learning, also called lifelong learning, studies the problem of learning tasks in a sequence with access restricted to only the data of the current task. In this paper we look at a scenario with fixed model capacity, and postulate that the learning process should not be selfish, i.e. it should account for future tasks to be added and thus leave enough capacity for them. To achieve Selfless Sequential Learning we study different regularization strategies and activation functions. We find that imposing sparsity at the level of the representation (i.e.~neuron activations) is more benef…
UCLA（加州大学洛杉矶分校）；Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）；Center for Data Science, New York University（纽约大学数据科学中心）；Institute for Advanced Study（普林斯顿高等研究院）
The analysis of neural network training beyond their linearization regime remains an outstanding open question, even in the simplest setup of a single hidden-layer. The limit of infinitely wide networks provides an appealing route forward through the mean-field perspective, but a key challenge is to bring learning guarantees back to the finite-neuron setting, where practical algorithms operate. Towards closing this gap, and focusing on shallow neural networks, in this work we study the ability of different regularisation strategies to capture solutions requiring only a finite amount of neurons…
Reservoir Computing (RC) is a well-known strategy for designing Recurrent Neural Networks featured by striking efficiency of training. The crucial aspect of RC is to properly instantiate the hidden recurrent layer that serves as dynamical memory to the system. In this respect, the common recipe is to create a pool of randomly and sparsely connected recurrent neurons. While the aspect of sparsity in the design of RC systems has been debated in the literature, it is nowadays understood mainly as a way to enhance the efficiency of computation, exploiting sparse matrix operations. In this paper, w…
ReLU$^2$ Wins: Discovering Efficient Activation Functions for Sparse LLMs
Tsinghua University（清华大学）；Shanghai Jiao Tong University（上海交通大学）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Renmin University of China（中国人民大学）
We study the supervised learning problem under either of the following two models: (1) Feature vectors ${\boldsymbol x}_i$ are $d$-dimensional Gaussians and responses are $y_i = f_*({\boldsymbol x}_i)$ for $f_*$ an unknown quadratic function; (2) Feature vectors ${\boldsymbol x}_i$ are distributed as a mixture of two $d$-dimensional centered Gaussians, and $y_i$'s are the corresponding class labels. We use two-layers neural networks with quadratic activations, and compare three different learning regimes: the random features (RF) regime in which we only train the second-layer weights; the neur…
University of Turin（都灵大学）；Télécom Paris, Institut Polytechnique de Paris（巴黎理工学院巴黎电信学院）
Deep neural networks include millions of learnable parameters, making their deployment over resource-constrained devices problematic. SeReNe (Sensitivity-based Regularization of Neurons) is a method for learning sparse topologies with a structure, exploiting neural sensitivity as a regularizer. We define the sensitivity of a neuron as the variation of the network output with respect to the variation of the activity of the neuron. The lower the sensitivity of a neuron, the less the network output is perturbed if the neuron output changes. By including the neuron sensitivity in the cost function…
Eindhoven University of Technology（埃因霍温理工大学）；University of Twente（特文特大学）；Iowa State University（爱荷华州立大学）
Artificial Neural Networks (ANNs) have emerged as hot topics in the research community. Despite the success of ANNs, it is challenging to train and deploy modern ANNs on commodity hardware due to the ever-increasing model size and the unprecedented growth in the data volumes. Particularly for microarray data, the very-high dimensionality and the small number of samples make it difficult for machine learning techniques to handle. Furthermore, specialized hardware such as Graphics Processing Unit (GPU) is expensive. Sparse neural networks are the leading approaches to address these challenges. H…
Adaptive Rank Allocation: Speeding Up Modern Transformers with RaNA Adapters
Institute of Computational and Mathematical Engineering, Stanford University（计算与数学工程研究所，斯坦福大学）；Department of Computer Science, Stanford University（计算机科学系，斯坦福大学）
University of Michigan（密歇根大学）；University of Western Australia（西澳大利亚大学）
Spiking neural networks can compensate for quantization error by encoding information either in the temporal domain, or by processing discretized quantities in hidden states of higher precision. In theory, a wide dynamic range state-space enables multiple binarized inputs to be accumulated together, thus improving the representational capacity of individual neurons. This may be achieved by increasing the firing threshold, but make it too high and sparse spike activity turns into no spike emission. In this paper, we propose the use of `threshold annealing' as a warm-up method for firing thresho…
Resting Neurons, Active Insights: Robustifying Activation Sparsity in LLMs via Spontaneity
IBM Thomas J. Watson Research Center, Yorktown Heights, USA（IBM 托马斯·J·沃森研究中心，美国Yorktown Heights）；Halıcıoğlu Data Science Institute, UC San Diego, La Jolla, USA（哈利奇欧数据科学研究所，美国UC圣地亚哥La Jolla）；Stony Brook University, Stony Brook, USA（史泰文·布鲁克大学，美国Stony Brook）
Two distinct limits for deep learning have been derived as the network width $h\rightarrow \infty$, 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 limit, the dynamics can be expressed in terms of the distribution of the parameters associated with a neuron, that follows a partial differential equation. In this work we consider deep networks where the weights in the last layer scale as $αh^{-1/2}$ at initialization. By varyin…
Nowadays, the number of layers and of neurons in each layer of a deep network are typically set manually. While very deep and wide networks have proven effective in general, they come at a high memory and computation cost, thus making them impractical for constrained platforms. These networks, however, are known to have many redundant parameters, and could thus, in principle, be replaced by more compact architectures. In this paper, we introduce an approach to automatically determining the number of neurons in each layer of a deep network during learning. To this end, we propose to make use of…
While variational dropout approaches have been shown to be effective for network sparsification, they are still suboptimal in the sense that they set the dropout rate for each neuron without consideration of the input data. With such input-independent dropout, each neuron is evolved to be generic across inputs, which makes it difficult to sparsify networks without accuracy loss. To overcome this limitation, we propose adaptive variational dropout whose probabilities are drawn from sparsity-inducing beta Bernoulli prior. It allows each neuron to be evolved either to be generic or specific for c…
Courant Institute of Mathematical Sciences（库朗数学科学研究所）；New York University（纽约大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Institut de Science Financière et d’Assurances（金融与保险科学研究所）；Université Lyon 1（里昂第一大学）
We study the loss surface of DNNs with $L_{2}$ regularization. We show that the loss in terms of the parameters can be reformulated into a loss in terms of the layerwise activations $Z_{\ell}$ of the training set. This reformulation reveals the dynamics behind feature learning: each hidden representations $Z_{\ell}$ are optimal w.r.t. to an attraction/repulsion problem and interpolate between the input and output representations, keeping as little information from the input as necessary to construct the activation of the next layer. For positively homogeneous non-linearities, the loss can be f…
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Academy for Advanced Interdisciplinary Studies, Peking University（北京大学前沿交叉学科研究院）
In this paper, we follow Eftekhari's work to give a non-local convergence analysis of deep linear networks. Specifically, we consider optimizing deep linear networks which have a layer with one neuron under quadratic loss. We describe the convergent point of trajectories with arbitrary starting point under gradient flow, including the paths which converge to one of the saddle points or the original point. We also show specific convergence rates of trajectories that converge to the global minimizer by stages. To achieve these results, this paper mainly extends the machinery in Eftekhari's work …
Modern neural networks are often operated in a strongly overparametrized regime: they comprise so many parameters that they can interpolate the training set, even if actual labels are replaced by purely random ones. Despite this, they achieve good prediction error on unseen data: interpolating the training set does not lead to a large generalization error. Further, overparametrization appears to be beneficial in that it simplifies the optimization landscape. Here we study these phenomena in the context of two-layers neural networks in the neural tangent (NT) regime. We consider a simple data m…
EECS University of Michigan（密歇根大学EECS学院）；CSE University of Maine（缅因大学计算机科学与工程学院）
Most approaches to deep neural network compression via pruning either evaluate a filter's importance using its weights or optimize an alternative objective function with sparsity constraints. While these methods offer a useful way to approximate contributions from similar filters, they often either ignore the dependency between layers or solve a more difficult optimization objective than standard cross-entropy. Our method, Mutual Information-based Neuron Trimming (MINT), approaches deep compression via pruning by enforcing sparsity based on the strength of the relationship between filters of a…
Recurrent Neural Networks (RNNs), more specifically their Long Short-Term Memory (LSTM) variants, have been widely used as a deep learning tool for tackling sequence-based learning tasks in text and speech. Training of such LSTM applications is computationally intensive due to the recurrent nature of hidden state computation that repeats for each time step. While sparsity in Deep Neural Nets has been widely seen as an opportunity for reducing computation time in both training and inference phases, the usage of non-ReLU activation in LSTM RNNs renders the opportunities for such dynamic sparsity…
Institute for Neural Computation, Ruhr University Bochum（波鸿鲁尔大学神经计算研究所）；Royal Holloway, University of London（伦敦大学皇家霍洛威学院）；Faculty of Electrical and Computer Engineering, Technische Universität Dresden（德累斯顿工业大学电气与计算机工程学院）
Recurrent neural networks (RNNs) are well suited for solving sequence tasks in resource-constrained systems due to their expressivity and low computational requirements. However, there is still a need to bridge the gap between what RNNs are capable of in terms of efficiency and performance and real-world application requirements. The memory and computational requirements arising from propagating the activations of all the neurons at every time step to every connected neuron, together with the sequential dependence of activations, contribute to the inefficiency of training and using RNNs. We pr…
With the motive of training all the parameters of a neural network, we study why and when one can achieve this by iteratively creating, training, and combining randomly selected subnetworks. Such scenarios have either implicitly or explicitly emerged in the recent literature: see e.g., the Dropout family of regularization techniques, or some distributed ML training protocols that reduce communication/computation complexities, such as the Independent Subnet Training protocol. While these methods are studied empirically and utilized in practice, they often enjoy partial or no theoretical support…
Norwegian University of Science and Technology（挪威科技大学）
Despite the recent success of artificial neural networks, more biologically plausible learning methods may be needed to resolve the weaknesses of backpropagation trained models such as catastrophic forgetting and adversarial attacks. Although these weaknesses are not specifically addressed, a novel local learning rule is presented that performs online clustering with an upper limit on the number of clusters to be found rather than a fixed cluster count. Instead of using orthogonal weight or output activation constraints, activation sparsity is achieved by mutual repulsion of lateral Gaussian n…
Click-through rate (CTR) and post-click conversion rate (CVR) predictions are two fundamental modules in industrial ranking systems such as recommender systems, advertising, and search engines. Since CVR involves much fewer samples than CTR (known as the CVR data sparsity problem), most of the existing works try to leverage CTR&CVR multi-task learning to improve CVR performance. However, typical coarse-grained sub-network/layer sharing methods may introduce conflicts and lead to performance degradation, since not every neuron or neuron connection in one layer should be shared between CVR and C…
Feature selection is one of the most decisive tools in understanding data and machine learning models. Among other methods, sparsity induced by $L^{1}$ penalty is one of the simplest and best studied approaches to this problem. Although such regularization is frequently used in neural networks to achieve sparsity of weights or unit activations, it is unclear how it can be employed in the feature selection problem. This work aims at extending the neural network with ability to automatically select features by rethinking how the sparsity regularization can be used, namely, by stochastically pena…
In principle, sparse neural networks should be significantly more efficient than traditional dense networks. Neurons in the brain exhibit two types of sparsity; they are sparsely interconnected and sparsely active. These two types of sparsity, called weight sparsity and activation sparsity, when combined, offer the potential to reduce the computational cost of neural networks by two orders of magnitude. Despite this potential, today's neural networks deliver only modest performance benefits using just weight sparsity, because traditional computing hardware cannot efficiently process sparse net…
