Adaptive Rational Activations to Boost Deep Reinforcement Learning
TU Darmstadt（达姆施塔特工业大学）；German Center for Artificial Intelligence（德国人工智能研究中心）；Hessian Center for Artifical Intelligence（黑森人工智能中心）；Centre for Cognitive Science（认知科学中心）
Quentin Delfosse, Patrick Schramowski, Martin Mundt, Alejandro Molina, Kristian Kersting
Latest insights from biology show that intelligence not only emerges from the connections between neurons but that individual neurons shoulder more computational responsibility than previously anticipated. This perspective should be critical in the context of constantly changing distinct reinforcement learning environments, yet current approaches still primarily employ static activation functions. In this work, we motivate why rationals are suitable for adaptable activation functions and why their inclusion into neural networks is crucial. Inspired by recurrence in residual networks, we derive a condition under which rational units are closed under residual connections and formulate a naturally regularised version: the recurrent-rational. We demonstrate that equipping popular algorithms with (recurrent-)rational activations leads to consistent improvements on Atari games, especially turning simple DQN into a solid approach, competitive to DDQN and Rainbow.
Entropy Regularizing Activation: Boosting Continuous Control, Large Language Models, and Image Classification with Activation as Entropy Constraints
Shanghai Qi Zhi Institute（上海启智研究所）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）
Rational Neural Networks have Expressivity Advantages
Center for Applied Mathematics, Cornell University, United States（应用数学中心，康奈尔大学，美国）；Department of Mathematics, Cornell University, United States（数学系，康奈尔大学，美国）
University of Oxford（牛津大学）；Cornell University（康奈尔大学）
We consider neural networks with rational activation functions. The choice of the nonlinear activation function in deep learning architectures is crucial and heavily impacts the performance of a neural network. We establish optimal bounds in terms of network complexity and prove that rational neural networks approximate smooth functions more efficiently than ReLU networks with exponentially smaller depth. The flexibility and smoothness of rational activation functions make them an attractive alternative to ReLU, as we demonstrate with numerical experiments.
TU Darmstadt（达姆施塔特工业大学）；Centre for Cognitive Science, TU Darmstadt（达姆施塔特工业大学认知科学中心）
The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture, hyper-parameters, and even on the dataset. Typically these activations are fixed by hand before training. Here, we demonstrate how to eliminate the reliance on first picking fixed activation functions by using flexible parametric rational functions instead. The resulting Padé Activation Units (PAUs) can both approximate common activation functions and also l…
Deep learning researchers have a keen interest in proposing two new novel activation functions which can boost network performance. A good choice of activation function can have significant consequences in improving network performance. A handcrafted activation is the most common choice in neural network models. ReLU is the most common choice in the deep learning community due to its simplicity though ReLU has some serious drawbacks. In this paper, we have proposed a new novel activation function based on approximation of known activation functions like Leaky ReLU, and we call this function Sm…
In recent years novel activation functions have been proposed to improve the performance of neural networks, and they show superior performance compared to the ReLU counterpart. However, there are environments, where the availability of complex activations is limited, and usually only the ReLU is supported. In this paper we propose methods that can be used to improve the performance of ReLU networks by using these efficient novel activations during model training. More specifically, we propose ensemble activations that are composed of the ReLU and one of these novel activations. Furthermore, t…
Model compression becomes a recent trend due to the requirement of deploying neural networks on embedded and mobile devices. Hence, both accuracy and efficiency are of critical importance. To explore a balance between them, a knowledge distillation strategy is proposed for general visual representation learning. It utilizes our well-designed activation map adaptive module to replace some blocks of the teacher network, exploring the most appropriate supervisory features adaptively during the training process. Using the teacher's hidden layer output to prompt the student network to train so as t…
Sberbank AI Lab（俄罗斯联邦储蓄银行人工智能实验室）；Samsung AI Center in Moscow（三星莫斯科人工智能中心）；Stern School of Business, NYU（纽约大学斯特恩商学院）
We introduce a novel approach to feed-forward neural network interpretation based on partitioning the space of sequences of neuron activations. In line with this approach, we propose a model-specific interpretation method, called YASENN. Our method inherits many advantages of model-agnostic distillation, such as an ability to focus on the particular input region and to express an explanation in terms of features different from those observed by a neural network. Moreover, examination of distillation error makes the method applicable to the problems with low tolerance to interpretation mistakes…
Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis. This doctoral thesis introduces theoretical results and deep learning algorithms to learn Green's functions associated with linear partial differential equations and rigorously justify PDE learning techniques. A theoretically rigorous algorithm is derived to obtain a learning rate, which characterizes the amount of training data needed to approximately learn Green's functions associated with elliptic PDEs. The construction conne…
One of the key challenges of deep learning based image retrieval remains in aggregating convolutional activations into one highly representative feature vector. Ideally, this descriptor should encode semantic, spatial and low level information. Even though off-the-shelf pre-trained neural networks can already produce good representations in combination with aggregation methods, appropriate fine tuning for the task of image retrieval has shown to significantly boost retrieval performance. In this paper, we present a simple yet effective supervised aggregation method built on top of existing reg…
TU Delft（代尔夫特理工大学）；Shell Global Solutions International B.V.（壳牌全球解决方案国际有限公司）
Binary Neural Networks (BNNs) are receiving an upsurge of attention for bringing power-hungry deep learning towards edge devices. The traditional wisdom in this space is to employ sign() for binarizing featuremaps. We argue and illustrate that sign() is a uniqueness bottleneck, limiting information propagation throughout the network. To alleviate this, we propose to dispense sign(), replacing it with a learnable activation binarizer (LAB), allowing the network to learn a fine-grained binarization kernel per layer - as opposed to global thresholding. LAB is a novel universal module that can sea…
Researchers have proposed various activation functions. These activation functions help the deep network to learn non-linear behavior with a significant effect on training dynamics and task performance. The performance of these activations also depends on the initial state of the weight parameters, i.e., different initial state leads to a difference in the performance of a network. In this paper, we have proposed a cooperative initialization for training the deep network using ReLU activation function to improve the network performance. Our approach uses multiple activation functions in the in…
Vanderbilt University（范德堡大学）；University of California, Davis（加州大学戴维斯分校）；Johns Hopkins University（约翰斯·霍普金斯大学）
Continual/lifelong learning from a non-stationary input data stream is a cornerstone of intelligence. Despite their phenomenal performance in a wide variety of applications, deep neural networks are prone to forgetting their previously learned information upon learning new ones. This phenomenon is called "catastrophic forgetting" and is deeply rooted in the stability-plasticity dilemma. Overcoming catastrophic forgetting in deep neural networks has become an active field of research in recent years. In particular, gradient projection-based methods have recently shown exceptional performance at…
Element-wise activation functions play a critical role in deep neural networks via affecting the expressivity power and the learning dynamics. Learning-based activation functions have recently gained increasing attention and success. We propose a new perspective of learnable activation function through formulating them with element-wise attention mechanism. In each network layer, we devise an attention module which learns an element-wise, sign-based attention map for the pre-activation feature map. The attention map scales an element based on its sign. Adding the attention module with a rectif…
We prove a negative result for the approximation of functions defined on compact subsets of $\mathbb{R}^d$ (where $d \geq 2$) using feedforward neural networks with one hidden layer and arbitrary continuous activation function. In a nutshell, this result claims the existence of target functions that are as difficult to approximate using these neural networks as one may want. We also demonstrate an analogous result (for general $d \in \mathbb{N}$) for neural networks with an \emph{arbitrary} number of hidden layers, for activation functions that are either rational functions or continuous splin…
Loom (LM), a hardware inference accelerator for Convolutional Neural Networks (CNNs) is presented. In LM every bit of data precision that can be saved translates to proportional performance gains. Specifically, for convolutional layers LM's execution time scales inversely proportionally with the precisions of both weights and activations. For fully-connected layers LM's performance scales inversely proportionally with the precision of the weights. LM targets area- and bandwidth-constrained System-on-a-Chip designs such as those found on mobile devices that cannot afford the multi-megabyte buff…
The University of British Columbia（不列颠哥伦比亚大学）；McGill University（麦吉尔大学）；Stanford University（斯坦福大学）
Multivariate techniques based on engineered features have found wide adoption in the identification of jets resulting from hadronic top decays at the Large Hadron Collider (LHC). Recent Deep Learning developments in this area include the treatment of the calorimeter activation as an image or supplying a list of jet constituent momenta to a fully connected network. This latter approach lends itself well to the use of Recurrent Neural Networks. In this work the applicability of architectures incorporating Long Short-Term Memory (LSTM) networks is explored. Several network architectures, methods …
We propose a simple change to existing neural network structures for better defending against gradient-based adversarial attacks. Instead of using popular activation functions (such as ReLU), we advocate the use of k-Winners-Take-All (k-WTA) activation, a C0 discontinuous function that purposely invalidates the neural network model's gradient at densely distributed input data points. The proposed k-WTA activation can be readily used in nearly all existing networks and training methods with no significant overhead. Our proposal is theoretically rationalized. We analyze why the discontinuities i…
Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院数学机械化重点实验室）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（北京雁栖湖应用数学研究院）；Yau Mathematical Sciences Center and Department of Mathematics, Tsinghua University（清华大学丘成桐数学科学中心与数学系）
In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schrödinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse problems of the (2+1)-dimensional KP-I equation and spin-NLS equation are studied via deep learning. The main idea of the data-driven forward and inverse problems is to use the deep neural networks with the activation function to approximate the solutions of the considered (2+1)-dimensional nonlinear wave equations by optimizing the chosen loss functions rela…
Turbo Sparse: Achieving LLM SOTA Performance with Minimal Activated Parameters
Institute of Parallel and Distributed Systems (IPADS), Shanghai Jiao Tong University（上海交通大学并行与分布式系统研究所（IPADS））；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）
We establish, for the first time, connections between feedforward neural networks with ReLU activation and tropical geometry --- we show that the family of such neural networks is equivalent to the family of tropical rational maps. Among other things, we deduce that feedforward ReLU neural networks with one hidden layer can be characterized by zonotopes, which serve as building blocks for deeper networks; we relate decision boundaries of such neural networks to tropical hypersurfaces, a major object of study in tropical geometry; and we prove that linear regions of such neural networks corresp…
