Specifically,one frequently observes failures when quantities that lie outside the numerical range used during training are encountered at test time, even when the target functionissimple (e.g., itdepends only onaggregating counts orlinear extrapolation). This failure patternindicates that the learned behavior is better characterized by memorization than by systematic abstraction.

This failure pattern indicates that the learned behavior is better characterized by memorization than by systematic abstraction.

We introduce the Neural Power Unit (NPU).

Conventional Neural Networks can approximate simple arithmetic operations, but fail to generalize beyond the range of numbers that were seen during training. Neural Arithmetic Units aim to overcome this difficulty, but current arithmetic units are either limited to operate on positive numbers or can only represent a subset of arithmetic operations. We introduce the Neural Power Unit (NPU) that operates on the full domain of real numbers and is capable of learning arbitrary power functions in a single layer. The NPU thus fixes the shortcomings of existing arithmetic units and extends their expressivity. We achieve this by using complex arithmetic without requiring a conversion of the network to complex numbers. A simplification of the unit to the RealNPU yields a highly transparent model. We show that the NPUs outperform their competitors in terms of accuracy and sparsity on artificial arithmetic datasets, and that the RealNPU can discover the governing equations of a dynamical system only from data.

The big problem for neural network models which are trained to count instances is that whenever test range goes high training range generalization error increases i.e. they are not good generalizers outside training range. Consider the case of automating cell counting process where more dense images with higher cell counts are commonly encountered as compared to images used in training data. By making better predictions for higher ranges of cell count we are aiming to create better generalization systems for cell counting. With architecture proposal of neural arithmetic logic units (NALU) for arithmetic operations, task of counting has become feasible for higher numeric ranges which were not included in training data with better accuracy. As a part of our study we used these units and different other activation functions for learning cell counting task with two different architectures namely Fully Convolutional Regression Network and U-Net. These numerically biased units are added in the form of residual concatenated layers to original architectures and a comparative experimental study is done with these newly proposed changes . This comparative study is described in terms of optimizing regression loss problem from these models trained with extensive data augmentation techniques. We were able to achieve better results in our experiments of cell counting tasks with introduction of these numerically biased units to already existing architectures in the form of residual layer concatenation connections. Our results confirm that above stated numerically biased units does help models to learn numeric quantities for better generalization results.

Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we propose an architecture that represents numerical quantities as linear activations which are manipulated using primitive arithmetic operators, controlled by learned gates. We call this module a neural arithmetic logic unit (NALU), by analogy to the arithmetic logic unit in traditional processors. Experiments show that NALU-enhanced neural networks can learn to track time, perform arithmetic over images of numbers, translate numerical language into real-valued scalars, execute computer code, and count objects in images. In contrast to conventional architectures, we obtain substantially better generalization both inside and outside of the range of numerical values encountered during training, often extrapolating orders of magnitude beyond trained numerical ranges.

Neural networks can learn to represent and manipulate numerical information, but they seldom generalize well outside of the range of numerical values encountered during training. To encourage more systematic numerical extrapolation, we propose an architecture that represents numerical quantities as linear activations which are manipulated using primitive arithmetic operators, controlled by learned gates. We call this module a neural arithmetic logic unit (NALU), by analogy to the arithmetic logic unit in traditional processors. Experiments show that NALU-enhanced neural networks can learn to track time, perform arithmetic over images of numbers, translate numerical language into real-valued scalars, execute computer code, and count objects in images. In contrast to conventional architectures, we obtain substantially better generalization both inside and outside of the range of numerical values encountered during training, often extrapolating orders of magnitude beyond trained numerical ranges.