Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userGENNI: Visualising the Geometry of Equivalences for Neural Network Identifiability
329
0
0.0
(
0
)
Added by
Daniel Lengyel
Publication date
2020
fields
Informatics Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We propose an efficient algorithm to visualise symmetries in neural networks. Typically, models are defined with respect to a parameter space, where non-equal parameters can produce the same input-output map. Our proposed method, GENNI, allows us to efficiently identify parameters that are functionally equivalent and then visualise the subspace of the resulting equivalence class. By doing so, we are now able to better explore questions surrounding identifiability, with applications to optimisation and generalizability, for commonly used or newly developed neural network architectures.
rate research
Read More
In this paper, we propose a neuro-symbolic framework called weighted Signal Temporal Logic Neural Network (wSTL-NN) that combines the characteristics of neural networks and temporal logics. Weighted Signal Temporal Logic (wSTL) formulas are recursively composed of subformulas that are combined using logical and temporal operators. The quantitative semantics of wSTL is defined such that the quantitative satisfaction of subformulas with higher weights has more influence on the quantitative satisfaction of the overall wSTL formula. In the wSTL-NN, each neuron corresponds to a wSTL subformula, and its output corresponds to the quantitative satisfaction of the formula. We use wSTL-NN to represent wSTL formulas as features to classify time series data. STL features are more explainable than those used in classical methods. The wSTL-NN is end-to-end differentiable, which allows learning of wSTL formulas to be done using back-propagation. To reduce the number of weights, we introduce two techniques to sparsify the wSTL-NN.We apply our framework to an occupancy detection time-series dataset to learn a classifier that predicts the occupancy status of an office room.
Symbolic regression is a powerful technique that can discover analytical equations that describe data, which can lead to explainable models and generalizability outside of the training data set. In contrast, neural networks have achieved amazing levels of accuracy on image recognition and natural language processing tasks, but are often seen as black-box models that are difficult to interpret and typically extrapolate poorly. Here we use a neural network-based architecture for symbolic regression called the Equation Learner (EQL) network and integrate it with other deep learning architectures such that the whole system can be trained end-to-end through backpropagation. To demonstrate the power of such systems, we study their performance on several substantially different tasks. First, we show that the neural network can perform symbolic regression and learn the form of several functions. Next, we present an MNIST arithmetic task where a separate part of the neural network extracts the digits. Finally, we demonstrate prediction of dynamical systems where an unknown parameter is extracted through an encoder. We find that the EQL-based architecture can extrapolate quite well outside of the training data set compared to a standard neural network-based architecture, paving the way for deep learning to be applied in scientific exploration and discovery.
Throughout this paper, we focus on the improvement of the direct feedback alignment (DFA) algorithm and extend the usage of the DFA to convolutional and recurrent neural networks (CNNs and RNNs). Even though the DFA algorithm is biologically plausible and has a potential of high-speed training, it has not been considered as the substitute for back-propagation (BP) due to the low accuracy in the CNN and RNN training. In this work, we propose a new DFA algorithm for BP-level accurate CNN and RNN training. Firstly, we divide the network into several modules and apply the DFA algorithm within the module. Second, the DFA with the sparse backward weight is applied. It comes with a form of dilated convolution in the CNN case, and in a form of sparse matrix multiplication in the RNN case. Additionally, the error propagation method of CNN becomes simpler through the group convolution. Finally, hybrid DFA increases the accuracy of the CNN and RNN training to the BP-level while taking advantage of the parallelism and hardware efficiency of the DFA algorithm.
Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly active area of research. Recent work has shown that deep neural networks can be optimized in randomly-projected subspaces of much smaller dimensionality than their native parameter space. While such training is promising for more efficient and scalable optimization schemes, its practical application is limited by inferior optimization performance. Here, we improve on recent random subspace approaches as follows: Firstly, we show that keeping the random projection fixed throughout training is detrimental to optimization. We propose re-drawing the random subspace at each step, which yields significantly better performance. We realize further improvements by applying independent projections to different parts of the network, making the approximation more efficient as network dimensionality grows. To implement these experiments, we leverage hardware-accelerated pseudo-random number generation to construct the random projections on-demand at every optimization step, allowing us to distribute the computation of independent random directions across multiple workers with shared random seeds. This yields significant reductions in memory and is up to 10 times faster for the workloads in question.
The recurrent network architecture is a widely used model in sequence modeling, but its serial dependency hinders the computation parallelization, which makes the operation inefficient. The same problem was encountered in serial adder at the early stage of digital electronics. In this paper, we discuss the similarities between recurrent neural network (RNN) and serial adder. Inspired by carry-lookahead adder, we introduce carry-lookahead module to RNN, which makes it possible for RNN to run in parallel. Then, we design the method of parallel RNN computation, and finally Carry-lookahead RNN (CL-RNN) is proposed. CL-RNN takes advantages in parallelism and flexible receptive field. Through a comprehensive set of tests, we verify that CL-RNN can perform better than existing typical RNNs in sequence modeling tasks which are specially designed for RNNs.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
