اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPort-Hamiltonian Approach to Neural Network Training
105
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Neural networks are discrete entities: subdivided into discrete layers and parametrized by weights which are iteratively optimized via difference equations. Recent work proposes networks with layer outputs which are no longer quantized but are solutions of an ordinary differential equation (ODE); however, these networks are still optimized via discrete methods (e.g. gradient descent). In this paper, we explore a different direction: namely, we propose a novel framework for learning in which the parameters themselves are solutions of ODEs. By viewing the optimization process as the evolution of a port-Hamiltonian system, we can ensure convergence to a minimum of the objective function. Numerical experiments have been performed to show the validity and effectiveness of the proposed methods.
قيم البحث
اقرأ أيضاً
Each year a growing number of wind farms are being added to power grids to generate electricity. The power curve of a wind turbine, which exhibits the relationship between generated power and wind speed, plays a major role in assessing the performanc
e of a wind farm. Neural networks have been used for power curve estimation. However, they do not produce a confidence measure for their output, unless computationally prohibitive Bayesian methods are used. In this paper, a probabilistic neural network with Monte Carlo dropout is considered to quantify the model (epistemic) uncertainty of the power curve estimation. This approach offers a minimal increase in computational complexity over deterministic approaches. Furthermore, by incorporating a probabilistic loss function, the noise or aleatoric uncertainty in the data is estimated. The developed network captures both model and noise uncertainty which is found to be useful tools in assessing performance. Also, the developed network is compared with existing ones across a public domain dataset showing superior performance in terms of prediction accuracy.
Passivity-based control (PBC) for port-Hamiltonian systems provides an intuitive way of achieving stabilization by rendering a system passive with respect to a desired storage function. However, in most instances the control law is obtained without a
ny performance considerations and it has to be calculated by solving a complex partial differential equation (PDE). In order to address these issues we introduce a reinforcement learning approach into the energy-balancing passivity-based control (EB-PBC) method, which is a form of PBC in which the closed-loop energy is equal to the difference between the stored and supplied energies. We propose a technique to parameterize EB-PBC that preserves the systemss PDE matching conditions, does not require the specification of a global desired Hamiltonian, includes performance criteria, and is robust to extra non-linearities such as control input saturation. The parameters of the control law are found using actor-critic reinforcement learning, enabling learning near-optimal control policies satisfying a desired closed-loop energy landscape. The advantages are that near-optimal controllers can be generated using standard energy shaping techniques and that the solutions learned can be interpreted in terms of energy shaping and damping injection, which makes it possible to numerically assess stability using passivity theory. From the reinforcement learning perspective, our proposal allows for the class of port-Hamiltonian systems to be incorporated in the actor-critic framework, speeding up the learning thanks to the resulting parameterization of the policy. The method has been successfully applied to the pendulum swing-up problem in simulations and real-life experiments.
We introduce a method to train Quantized Neural Networks (QNNs) --- neural networks with extremely low precision (e.g., 1-bit) weights and activations, at run-time. At train-time the quantized weights and activations are used for computing the parame
ter gradients. During the forward pass, QNNs drastically reduce memory size and accesses, and replace most arithmetic operations with bit-wise operations. As a result, power consumption is expected to be drastically reduced. We trained QNNs over the MNIST, CIFAR-10, SVHN and ImageNet datasets. The resulting QNNs achieve prediction accuracy comparable to their 32-bit counterparts. For example, our quantized version of AlexNet with 1-bit weights and 2-bit activations achieves $51%$ top-1 accuracy. Moreover, we quantize the parameter gradients to 6-bits as well which enables gradients computation using only bit-wise operation. Quantized recurrent neural networks were tested over the Penn Treebank dataset, and achieved comparable accuracy as their 32-bit counterparts using only 4-bits. Last but not least, we programmed a binary matrix multiplication GPU kernel with which it is possible to run our MNIST QNN 7 times faster than with an unoptimized GPU kernel, without suffering any loss in classification accuracy. The QNN code is available online.
Binarized neural networks, or BNNs, show great promise in edge-side applications with resource limited hardware, but raise the concerns of reduced accuracy. Motivated by the complex neural networks, in this paper we introduce complex representation i
nto the BNNs and propose Binary complex neural network -- a novel network design that processes binary complex inputs and weights through complex convolution, but still can harvest the extraordinary computation efficiency of BNNs. To ensure fast convergence rate, we propose novel BCNN based batch normalization function and weight initialization function. Experimental results on Cifar10 and ImageNet using state-of-the-art network models (e.g., ResNet, ResNetE and NIN) show that BCNN can achieve better accuracy compared to the original BNN models. BCNN improves BNN by strengthening its learning capability through complex representation and extending its applicability to complex-valued input data. The source code of BCNN will be released on GitHub.
Normalization is known to help the optimization of deep neural networks. Curiously, different architectures require specialized normalization methods. In this paper, we study what normalization is effective for Graph Neural Networks (GNNs). First, we
adapt and evaluate the existing methods from other domains to GNNs. Faster convergence is achieved with InstanceNorm compared to BatchNorm and LayerNorm. We provide an explanation by showing that InstanceNorm serves as a preconditioner for GNNs, but such preconditioning effect is weaker with BatchNorm due to the heavy batch noise in graph datasets. Second, we show that the shift operation in InstanceNorm results in an expressiveness degradation of GNNs for highly regular graphs. We address this issue by proposing GraphNorm with a learnable shift. Empirically, GNNs with GraphNorm converge faster compared to GNNs using other normalization. GraphNorm also improves the generalization of GNNs, achieving better performance on graph classification benchmarks.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
