While differentiable logic gates have shown promise in feedforward networks, their application to sequential modeling remains unexplored. This paper presents the first implementation of Recurrent Deep Differentiable Logic Gate Networks (RDDLGN), combining Boolean operations with recurrent architectures for sequence-to-sequence learning. Evaluated on WMT'14 English-German translation, RDDLGN achieves 5.00 BLEU and 30.9\% accuracy during training, approaching GRU performance (5.41 BLEU) and graceful degradation (4.39 BLEU) during inference. This work establishes recurrent logic-based neural computation as viable, opening research directions for FPGA acceleration in sequential modeling and other recursive network architectures.

The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with notable disadvantages, such as their "black-box" nature, which hampers interpretability, as well as their tendency to overfit the training data. We introduce a novel method for learning interpretable differentiable logic networks (DLNs) that are architectures that employ multiple layers of binary logic operators. We train these networks by softening and differentiating their discrete components, e.g., through binarization of inputs, binary logic operations, and connections between neurons. This approach enables the use of gradient-based learning methods. Experimental results on twenty classification tasks indicate that differentiable logic networks can achieve accuracies comparable to or exceeding that of traditional NNs. Equally importantly, these networks offer the advantage of interpretability. Moreover, their relatively simple structure results in the number of logic gate-level operations during inference being up to a thousand times smaller than NNs, making them suitable for deployment on edge devices.

The demand for efficient edge vision has spurred the interest in developing stochastic computing approaches for performing image processing tasks. Memristors with inherent stochasticity readily introduce probability into the computations and thus enable stochastic image processing computations. Here, we present a stochastic computing approach for edge detection, a fundamental image processing technique, facilitated with memristor-enabled stochastic logics. Specifically, we integrate the memristors with logic circuits and harness the stochasticity from the memristors to realize compact stochastic logics for stochastic number encoding and processing. The stochastic numbers, exhibiting well-regulated probabilities and correlations, can be processed to perform logic operations with statistical probabilities. This can facilitate lightweight stochastic edge detection for edge visual scenarios characterized with high-level noise errors. As a practical demonstration, we implement a hardware stochastic Roberts cross operator using the stochastic logics, and prove its exceptional edge detection performance, remarkably, with 95% less computational cost while withstanding 50% bit-flip errors. The results underscore the great potential of our stochastic edge detection approach in developing lightweight, error-tolerant edge vision hardware and systems for autonomous driving, virtual/augmented reality, medical imaging diagnosis, industrial automation, and beyond.

Conventional computing paradigm struggles to fulfill the rapidly growing demands from emerging applications, especially those for machine intelligence, because much of the power and energy is consumed by constant data transfers between logic and memory modules. A new paradigm, called "computational random-access memory (CRAM)" has emerged to address this fundamental limitation. CRAM performs logic operations directly using the memory cells themselves, without having the data ever leave the memory. The energy and performance benefits of CRAM for both conventional and emerging applications have been well established by prior numerical studies. However, there lacks an experimental demonstration and study of CRAM to evaluate its computation accuracy, which is a realistic and application-critical metrics for its technological feasibility and competitiveness. In this work, a CRAM array based on magnetic tunnel junctions (MTJs) is experimentally demonstrated. First, basic memory operations as well as 2-, 3-, and 5-input logic operations are studied. Then, a 1-bit full adder with two different designs is demonstrated. Based on the experimental results, a suite of modeling has been developed to characterize the accuracy of CRAM computation. Further analysis of scalar addition, multiplication, and matrix multiplication shows promising results. These results are then applied to a complete application: a neural network based handwritten digit classifier, as an example to show the connection between the application performance and further MTJ development. The classifier achieved almost-perfect classification accuracy, with reasonable projections of future MTJ development. With the confirmation of MTJ-based CRAM's accuracy, there is a strong case that this technology will have a significant impact on power- and energy-demanding applications of machine intelligence.

In many machine learning applications, e.g., tree-based ensembles, floating point numbers are extensively utilized due to their expressiveness. Nowadays performing data analysis on embedded devices from dynamic data masses becomes available, but such systems often lack hardware capabilities to process floating point numbers, introducing large overheads for their processing. Even if such hardware is present in general computing systems, using integer operations instead of floating point operations promises to reduce operation overheads and improve the performance. In this paper, we provide \mdname, a full precision floating point comparison for random forests, by only using integer and logic operations. To ensure the same functionality preserves, we formally prove the correctness of this comparison. Since random forests only require comparison of floating point numbers during inference, we implement \mdname~in low level realizations and therefore eliminate the need for floating point hardware entirely, by keeping the model accuracy unchanged. The usage of \mdname~basically boils down to a one-by-one replacement of conditions: For instance, a comparison statement in C: if(pX[3]<=(float)10.074347) becomes if((*(((int*)(pX))+3))<=((int)(0x41213087))). Experimental evaluation on X86 and ARMv8 desktop and server class systems shows that the execution time can be reduced by up to $\approx 30\%$ with our novel approach.

Recent years have witnessed the success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks the ability of cognitive reasoning. However, the concrete ability of reasoning is critical to many theoretical and practical problems. On the other hand, traditional symbolic reasoning methods do well in making logical inference, but they are mostly hard rule-based reasoning, which limits their generalization ability to different tasks since difference tasks may require different rules. Both reasoning and generalization ability are important for prediction tasks such as recommender systems, where reasoning provides strong connection between user history and target items for accurate prediction, and generalization helps the model to draw a robust user portrait over noisy inputs. In this paper, we propose Logic-Integrated Neural Network (LINN) to integrate the power of deep learning and logic reasoning. LINN is a dynamic neural architecture that builds the computational graph according to input logical expressions. It learns basic logical operations such as AND, OR, NOT as neural modules, and conducts propositional logical reasoning through the network for inference. Experiments on theoretical task show that LINN achieves significant performance on solving logical equations and variables. Furthermore, we test our approach on the practical task of recommendation by formulating the task into a logical inference problem. Experiments show that LINN significantly outperforms state-of-the-art recommendation models in Top-K recommendation, which verifies the potential of LINN in practice.

Backpropagation is an algorithm used for training neural networks. When the word algorithm is used, it represents a set of mathematical- science formula mechanism that will help the system to understand better about the data, variables fed and the desired output. Backpropagation is a kind of method to train the neural network to learn itself and find the desired output set by the user. Neural networks are layers of networks arranged like to represent the human brain with weights (connecting one input to another). This arrangement of layers of inputs is called input neurons, they are followed by their successor called output neurons.

Over past several years, deep learning has achieved huge successes in various applications. However, such a data-driven approach is often criticized for lack of interpretability. Recently, we proposed artificial quadratic neural networks consisting of second-order neurons in potentially many layers. In each second-order neuron, a quadratic function is used in the place of the inner product in a traditional neuron, and then undergoes a nonlinear activation. With a single second-order neuron, any fuzzy logic operation, such as XOR, can be implemented. In this sense, any deep network constructed with quadratic neurons can be interpreted as a deep fuzzy logic system. Since traditional neural networks and second-order counterparts can represent each other and fuzzy logic operations are naturally implemented in second-order neural networks, it is plausible to explain how a deep neural network works with a second-order network as the system model. In this paper, we generalize and categorize fuzzy logic operations implementable with individual second-order neurons, and then perform statistical/information theoretic analyses of exemplary quadratic neural networks.