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Physical computing toolkits for children expose young minds to the concepts of computing and electronics within a target activity. To this end, these kits usually make use of a custom Visual Programming Language (or VPL) environment that extends past the functionality of simply programming, often also incorporating representations of electronics aspects in the interface. These representations of the electronics function as a scaffold to help the child focus on programming, instead of having to handle both the programming and details of the electronics at the same time. This paper presents a review of existing physical computing toolkits, looking at the What, How, and Where of electronics representations in their VPL interfaces. We then discuss potential research directions for the design of VPL interfaces for physical computing toolkits for children.more » « less

We present LBWNet, an efficient optimization based method for quantization and training of the low bitwidth convolutional neural networks (CNNs). Specifically, we quantize the weights to zero or powers of 2 by minimizing the Euclidean distance between fullprecision weights and quantized weights during backpropagation (weight learning). We characterize the combinatorial nature of the low bitwidth quantization problem. For 2bit (ternary) CNNs, the quantization of N weights can be done by an exact formula in O(N log N) complexity. When the bitwidth is 3 and above, we further propose a semianalytical thresholding scheme with a single free parameter for quantization that is computationally inexpensive. The free parameter is further determined by network retraining and object detection tests. The LBWNet has several desirable advantages over fullprecision CNNs, including considerable memory savings, energy efficiency, and faster deployment. Our experiments on PASCAL VOC dataset show that compared with its 32bit floatingpoint counterpart, the performance of the 6bit LBWNet is nearly lossless in the object detection tasks, and can even do better in real world visual scenes, while empirically enjoying more than 4× faster deployment.more » « less

Training activation quantized neural networks involves minimizing a piecewise constant function whose gradient vanishes almost everywhere, which is undesirable for the standard backpropagation or chain rule. An empirical way around this issue is to use a straightthrough estimator (STE) (Bengio et al., 2013) in the backward pass only, so that the “gradient” through the modified chain rule becomes nontrivial. Since this unusual “gradient” is certainly not the gradient of loss function, the following question arises: why searching in its negative direction minimizes the training loss? In this paper, we provide the theoretical justification of the concept of STE by answering this question. We consider the problem of learning a twolinearlayer network with binarized ReLU activation and Gaussian input data. We shall refer to the unusual “gradient” given by the STEmodifed chain rule as coarse gradient. The choice of STE is not unique. We prove that if the STE is properly chosen, the expected coarse gradient correlates positively with the population gradient (not available for the training), and its negation is a descent direction for minimizing the population loss. We further show the associated coarse gradient descent algorithm converges to a critical point of the population loss minimization problem. Moreover, we show that a poor choice of STE leads to instability of the training algorithm near certain local minima, which is verified with CIFAR10 experiments.more » « less

Quantized deep neural networks (QDNNs) are attractive due to their much lower memory storage and faster inference speed than their regular fullprecision counterparts. To maintain the same performance level especially at low bitwidths, QDNNs must be retrained. Their training involves piecewise constant activation functions and discrete weights; hence, mathematical challenges arise. We introduce the notion of coarse gradient and propose the blended coarse gradient descent (BCGD) algorithm, for training fully quantized neural networks. Coarse gradient is generally not a gradient of any function but an artificial ascent direction. The weight update of BCGD goes by coarse gradient correction of a weighted average of the fullprecision weights and their quantization (the socalled blending), which yields sufficient descent in the objective value and thus accelerates the training. Our experiments demonstrate that this simple blending technique is very effective for quantization at extremely low bitwidth such as binarization. In full quantization of ResNet18 for ImageNet classification task, BCGD gives 64.36% top1 accuracy with binary weights across all layers and 4bit adaptive activation. If the weights in the first and last layers are kept in full precision, this number increases to 65.46%. As theoretical justification, we show convergence analysis of coarse gradient descent for a twolinearlayer neural network model with Gaussian input data and prove that the expected coarse gradient correlates positively with the underlying true gradient.more » « less

We propose BinaryRelax, a simple twophase algorithm, for training deep neural networks with quantized weights. The set constraint that characterizes the quantization of weights is not imposed until the late stage of training, and a sequence of pseudo quantized weights is maintained. Specifically, we relax the hard constraint into a continuous regularizer via Moreau envelope, which turns out to be the squared Euclidean distance to the set of quantized weights. The pseudo quantized weights are obtained by linearly interpolating between the float weights and their quantizations. A continuation strategy is adopted to push the weights towards the quantized state by gradually increasing the regularization parameter. In the second phase, exact quantization scheme with a small learning rate is invoked to guarantee fully quantized weights. We test BinaryRelax on the benchmark CIFAR and ImageNet color image datasets to demonstrate the superiority of the relaxed quantization approach and the improved accuracy over the stateoftheart training methods. Finally, we prove the convergence of BinaryRelax under an approximate orthogonality condition.more » « less

Free, publiclyaccessible full text available August 1, 2024

Free, publiclyaccessible full text available July 1, 2024

Abstract A study of the charge conjugation and parity ( $$\textit{CP}$$ CP ) properties of the interaction between the Higgs boson and $$\tau $$ τ leptons is presented. The study is based on a measurement of $$\textit{CP}$$ CP sensitive angular observables defined by the visible decay products of $$\tau $$ τ leptons produced in Higgs boson decays. The analysis uses 139 fb $$^{1}$$  1 of proton–proton collision data recorded at a centreofmass energy of $$\sqrt{s}= 13$$ s = 13 TeV with the ATLAS detector at the Large Hadron Collider. Contributions from $$\textit{CP}$$ CP violating interactions between the Higgs boson and $$\tau $$ τ leptons are described by a single mixing angle parameter $$\phi _{\tau }$$ ϕ τ in the generalised Yukawa interaction. Without constraining the $$H\rightarrow \tau \tau $$ H → τ τ signal strength to its expected value under the Standard Model hypothesis, the mixing angle $$\phi _{\tau }$$ ϕ τ is measured to be $$9^{\circ } \pm 16^{\circ }$$ 9 ∘ ± 16 ∘ , with an expected value of $$0^{\circ } \pm 28^{\circ }$$ 0 ∘ ± 28 ∘ at the 68% confidence level. The pure $$\textit{CP}$$ CP odd hypothesis is disfavoured at a level of 3.4 standard deviations. The results are compatible with the predictions for the Higgs boson in the Standard Model.more » « lessFree, publiclyaccessible full text available July 1, 2024