Comparison Of Networks Research Articles

Deep Recyclable Trash Sorting Using Integrated Parallel Attention.

Sorting recyclable trash is critical to reducing energy consumption and mitigating environmental pollution. Currently, trash sorting heavily relies on manpower. Computer vision technology enables automated trash sorting. However, existing trash image classification datasets contain a large number of images without backgrounds. Moreover, the models are vulnerable to background interference when categorizing images with complex backgrounds. In this work, we provide a recyclable trash dataset that supports model training and design a model specifically for trash sorting. Firstly, we introduce the TrashIVL dataset, an image dataset for recyclable trash sorting encompassing five classes (TrashIVL-5). All images are collected from public trash datasets, and the original images were captured by RGB imaging sensors, containing trash items with real-life backgrounds. To achieve refined recycling and improve sorting efficiency, the TrashIVL dataset can be further categorized into 12 classes (TrashIVL-12). Secondly, we propose the integrated parallel attention module (IPAM). Considering the susceptibility of sensor-based systems to background interference in real-world trash sorting scenarios, our IPAM is specifically designed to focus on the essential features of trash images from both channel and spatial perspectives. It can be inserted into convolutional neural networks (CNNs) as a plug-and-play module. We have constructed a recyclable trash sorting network building upon the IPAM, which produces an acuracy of 97.42% on TrashIVL-5 and 94.08% on TrashIVL-12. Our work is an effective attempt of computer vision in recyclable trash sorting. It makes a positive contribution to environmental protection and sustainable development.

Mineral classification with X-ray absorption spectroscopy: A deep learning-based approach

The current suite of algorithms used in intelligent mineral sorting equipment is largely generic, lacking the necessary adaptability and the capability for simultaneous non-destructive structural detection and quantitative analysis. To address this, we have developed two specialized algorithms based on X-ray absorption spectroscopy: the Trans-LSTM algorithm based on Transformer and Long Short-Term Memory(LSTM), utilizing knowledge distillation for rough mineral sorting, and the RNN-overhead-xgboost algorithm based on Recurrent Neural Network(RNN) for fine mineral sorting. We collected 3000 X-ray absorption spectra from 15 types of minerals with similar appearances or compositions. We compared the performance of these proposed algorithms with three other general-purpose algorithms for mineral spectral classification. Our study specifically examined the impact of Trans-LSTM on rough mineral sorting and the effect of RNN-overhead-xgboost on fine mineral sorting. In the rough sorting stage, the Trans-LSTM model demonstrated a prediction time of just 0.0171 s per sample, maintaining a classification accuracy of 93.49%, thereby ensuring high precision with high efficiency. During the fine sorting stage, the RNN-overhead-xgboost algorithm significantly improved sorting accuracy to 99.21%, highlighting its effectiveness in achieving precise sorting. These findings underscore the potential of the Trans-LSTM and RNN-overhead-xgboost algorithms to enhance the adaptability and accuracy of intelligent mineral sorting systems, meeting the specific demands of different stages in mineral production.

A smart recycle sort network for garbage sorting

A smart recycle sort network for garbage sorting

Efficient isochronous fixed-weight sampling with applications to NTRU

We present a solution to the open problem of designing a linear-time, unbiased and timing attack-resistant shuffling algorithm for fixed-weight sampling. Although it can be implemented without timing leakages of secret data in any architecture, we illustrate with ARMv7-M and ARMv8-A implementations; for the latter, we take advantage of architectural features such as NEON and conditional instructions, which are representative of features available on architectures targeting similar systems, such as Intel. Our proposed algorithm improves asymptotically upon the current approach based on constant-time sorting networks ( O ( n ) versus O ( n log 2 n ) ), and an implementation of the new algorithm applied to NTRU is also faster in practice, by a factor of up to 6.91 ( 591 % ) on ARMv8-A cores and 12.89 ( 1189 % ) on the Cortex-M4; it also requires fewer uniform random bits. This translates into performance improvements for NTRU encapsulation, compared to state-of-the-art implementations, of up to 50% on ARMv8-A cores and 72% on the Cortex-M4, and small improvements to key generation (up to 2.7% on ARMv8-A cores and 6.1% on the Cortex-M4), with negligible impact on code size and a slight improvement in RAM usage for the Cortex-M4.

Dual-path lightweight convolutional neural network for automatic sorting of olive fruit based on cultivar and maturity

Identifying olive cultivars and maturity stages is crucial in the olive industry, as these traits significantly impact the nutritional and sensory properties of olive products and extracted oil. For this purpose, this study presents a novel automatic computer vision system that applies state-of-the-art deep learning technology to sort and classify two Iranian olive cultivars, Zard and Roghani, in five maturity stages, resulting in a total of ten distinct classes. The model was developed by evaluating multiple user-defined and standard structures. It was based on a dual-path lightweight convolutional neural network that uses both regular and dilated convolution operators. Dilated convolutions were used to extract more information and capture different properties by providing larger receptive fields. With a significantly lower number of trainable parameters than standard architectures, the lightweight nature of the model would enhance its potential for delivering fast responses in on-the-go applications. Four optimizers (RMSProp, SGD, Adam, and Nadam) were tested on the developed model to enhance its performance, and Nadam exhibited the greatest accuracy. The proposed model achieved a total classification accuracy of 95.79 % and a loss of 0.2214. The proposed model was completely accurate for some classes, and the classification metrics for all categories were high, ranging from 88 % to 100 % for precision, 83–100 % for recall, and 86–100 % for F1-score. The accuracy of classification within the Roghani cultivar classes stood at 98.28 %, while for the Zard cultivar classes, it achieved 97.76 %. The study found that the proposed model can be efficiently incorporated into an olive sorting system, facilitating the identification of olives with different cultivars and varying levels of maturity, thereby enhancing the production of post-harvest products and superior quality of oil.

LPT-Net: A Line-Pad Transformer Network for efficiency coal gangue segmentation with linear multi-head self-attention mechanism

Accurately separating coal and gangue is a crucial step in coal production. However, existing methods often face efficiency challenges. The high computational complexity hinders real-time gangue sorting. Real-time segmentation is essential for improved sorting results, making efficiency a crucial evaluation metric. Additionally, ensuring real-time segmentation accuracy is crucial. To address these issues, we propose Line-Pad Transformer Network (LPT-Net), a efficient segmentation network for gangue sorting. LPT-Net incorporates L-MSA, a module designed for linear attention calculation. It utilizes linear feature sampling for efficient computation, enabling the rapid extraction of semantic features from coal gangue. Additionally, LPT-Net introduces MSA1 and MSA2, serving as semantic information providers to enable more effective extraction of gangue semantic features. Experimental results on GSTD demonstrate LPT’s effectiveness, achieving 74.71 IoU and 83.85 Acc at 95.7 FPS, outperforming other methods by 1.5–12 times in terms of inference speed. These results highlight LPT’s suitability for efficient gangue sorting tasks.

Stack sort: a new approach with sorting network and a buffer

Knuth introduced the problem of stack sorting. Stack sorting was implemented by t stacks in series. In this paper, we propose a new dimension to stack sorting problem by introducing a stack with sorting network and a petty buffer. Instead of using t stacks in series, it helps to improve the performance by avoiding shuffles the stack. The basic idea behind in this paper is to perform a stack sorting with a single stack, and to achieve greater performance. In this novel approach, 2 bit buffer is compared to stack and insert the element into stack in order to avoid multiple stack. The result shows the time complexity of the proposed algorithm is O (n)

Asynchronous evolution of deep neural network architectures

Many evolutionary algorithms (EAs) take advantage of parallel evaluation of candidates. However, if evaluation times vary significantly, many worker nodes (i.e., compute clients) are idle much of the time, waiting for the next generation to be created. Evolutionary neural architecture search (ENAS), a class of EAs that optimizes the architecture and hyperparameters of deep neural networks, is particularly vulnerable to this issue. This paper proposes a generic asynchronous evaluation strategy (AES) that is then adapted to work with ENAS. AES increases throughput by maintaining a queue of up to K individuals ready to be sent to the workers for evaluation and proceeding to the next generation as soon as M<<K individuals have been evaluated. A suitable value for M is determined experimentally, balancing diversity and efficiency. To showcase the generality and power of AES, it was first evaluated in eight-line sorting network design (a single-population optimization task with limited evaluation-time variability), achieving an over two-fold speedup. Next, it was evaluated in 11-bit multiplexer design (a single-population discovery task with extended variability), where a 14-fold speedup was observed. It was then scaled up to ENAS for image captioning (a multi-population open-ended-optimization task), resulting in an over two-fold speedup. In all problems, a multifold performance improvement was observed, suggesting that AES is a promising method for parallelizing the evolution of complex systems with long and variable evaluation times, such as those in ENAS.

A lightweight multiscale convolutional neural network for garbage sorting

Waste sorting plays a vital role in establishing a sustainable society by effectively reducing resource waste and promoting its recycling. However, traditional garbage sorting heavily relies on manual labor, which is inefficient, costly, and constrained by limited human resources. To address these challenges, this paper employs the convolutional neural network technique in deep learning for intelligent waste sorting. Firstly, a multi-scale processing strategy is introduced to enhance the system's resilience and accuracy by considering feature information at various scales. Secondly, a lightweight approach using tiny convolutions instead of large convolutions is adopted to reduce model parameters. Combining the advantages of both, we constructed a lightweight multiscale convolution (LMConv) and experiments the Lightweight Multiscale Convolutional Neural Network (LMNet) based on LMConv, and its optimal convolutional architecture is determined through ablation experiments. The experiment results demonstrate that LMNet outperforms other well-known convolutional neural network models in the area of garbage sorting.

When does 0–1 Principle Hold for Prefix Sums?

Knuth’s 0–1 principle argues that the correctness of any swap-based sorting network can be verified by testing arbitrary sequences over Boolean values (i.e., 0 and 1). Voigtländer (Proceedings of the 35th ACM SIGPLAN-SIGACT symposium on principles of programming languages, POPL 2008, San Francisco, California, USA, January 7–12, 2008. ACM, New York, NY, pp 29–35, 2008. https://doi.org/10.1145/1328438.1328445) proved a similar result for prefix-sum networks that consist of associative binary operators: the correctness can be verified by testing arbitrary sequences and associative binary operators over three values, namely 0, 1, and 2. He raised the question of whether testing over Boolean values is sufficient if the binary operator is idempotent in addition to associative. This paper answers his question. First, there is an incorrect prefix-sum network for associative idempotent operators, the flaw of which cannot be detected by testing over Boolean values. Second, testing over Boolean values is sufficient if the binary operators are restricted to commutative in addition to associative and idempotent.

Parameterized Complexity Classes Defined by Threshold Circuits and Their Connection with Sorting Networks

The main complexity classes of the Parameterized Intractability Theory are based on weighted Boolean circuit satisfiability problems and organized into a hierarchy so-called W-hierarchy. The W-hierarchy enables fine-grained complexity analyses of parameterized problems that are unlikely to belong to the FPT class. In this paper, we introduce the Th-hierarchy, a natural generalization of the W-hierarchy defined by unweighted threshold circuit satisfiability problems. Investigating the relationship between Th-hierarchy and W-hierarchy, we discuss the complexity of transforming Threshold circuits into Boolean circuits, and observe that sorting networks are powerful tools to handle such transformations. First, we show that these hierarchies collapse at the last level (W[P][Formula: see text][Formula: see text][Formula: see text]Th[P]). After that, we present a time complexity analysis of an AKS sorting network construction, which supports some of our results. Finally, we prove that Th[[Formula: see text]] [Formula: see text] W[SAT] for every [Formula: see text]. As a by-product, our studies suggest that it is relevant to consider a new class based on logarithmic depth circuits in the W-hierarchy.

LOSN: Lightweight ore sorting networks for edge device environment

Vision-based intelligent ore sorting technology has been widely applied in current mining production, a trend further facilitated by the emergence of deep learning. However, most available implementations are still based on image classification, i.e., dividing the overall sorting task into two processes: classification and localization, without end-to-end integration. Meanwhile, harsh sorting scenarios make edge computing devices the primary candidate for model deployment, with more stringent limitations for model size, computational complexity, and inference speed. Therefore, this study proposes to integrate the operating processes to locate and classify the ores particles simultaneously. The lightweight structures, attention mechanisms, and multi-scale feature fusion strategies are applied in the architecture design to meet the deployment requirements of edge device environments and achieve a preferred accuracy–efficiency tradeoff, which leads to a new lightweight ore sorting networks called LOSN. In the case study, LOSN has the highest accuracy in multi-type and multi-class ore sorting tasks (78.87% and 80.64% in the gas coal and anthracite dataset, respectively) with fewer parameters (5.970M), lower GFLOPs (6.829G) and higher FPS (89.92), which is superior to commonly used high-performance object detection architectures (e.g., Yolo series, EfficientDet, Faster-RCNN, and CenterNet). Grad-CAM visualizations also demonstrate the feature extraction capability of LOSN.

Algorithmic coincidence classification of mesh patterns

Permutations have connections to other mathematical objects such as Schubert varieties, sorting networks, and genome rearrangements. Often the connection is described in terms of patterns that are absent from the permutations. There can be ambiguity in this description, in the sense that the same subset of permutations can be defined with two different patterns. This is called coincidence and we focus on the coincidence of mesh patterns, one of the most descriptive version of patterns in permutations. We review and extend previous results on coincidence of mesh patterns. We introduce the notion of a force on a permutation pattern and apply it to the coincidence classification of mesh patterns, completing the classification up to size three. We also show that this concept can be used to enumerate classical permutation classes.

A Low-Complexity Sorting Network for a Fast List Polar Decoder

Fast list decoding algorithms for polar codes have been proposed to achieve low latency and high error correction performance. In the Rate-1 and SPC nodes of fast list decoding, a high-complexity sorter is required if multiple bits are to be decoded simultaneously in a single clock cycle. This paper proposes a partitioned sorting network (PSN) that reduces the complexity of metric sorter in Rate-1 and single parity check (SPC) decoders for fast list decoding. The proposed PSN consists of two sorting networks. For the first sorting network, we analyze the order of the path metrics (PMs) and reduce the number of input candidate paths. Furthermore, for the second sorting network, we analyze the cumulative results of path selection and identify relatively frequently selected paths. The proposed PSN has up to 90% fewer compare-and-swap units (CASUs) and up to 137% higher operating frequencies than existing sorting networks for Rate-1 and SPC decoders with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L=8$ </tex-math></inline-formula> .

Large deviations for the interchange process on the interval and incompressible flows

We use the framework of permuton processes to show that large deviations of the interchange process are controlled by the Dirichlet energy. This establishes a rigorous connection between processes of permutations and one-dimensional incompressible Euler equations. While our large deviation upper bound is valid in general, the lower bound applies to processes corresponding to incompressible flows, studied in this context by Brenier. These results imply the Archimedean limit for relaxed sorting networks and allow us to asymptotically count such networks.

A non-destructive dropped fruit impact signal imaging-based deep learning approach for smart sorting of kiwifruit

This paper focuses on developing an intelligent kiwifruit sorting system that uses an imaging method based on the dropped fruit impact signal, which combines with convolutional neural network (CNN) for the high-quality sorting of soft and hard kiwifruits. The kiwifruit sorting system detects the hardness of kiwifruit by analyzing the change in the force signal during the fall of kiwifruit on the sorting tray. The proposed signal imaging method constructs peak image (PI) by intelligently extracting the peak features of the data directly from the original time-domain force and force acceleration data in chronological order, and learns the features of PI for hardness classification by two-dimensional (2D) CNN. In addition, the performance of PI based on different peak, force signal or force acceleration signal in 2D CNN classifier is tested, and the 2D CNN classifier based on PI is compared with the 2D CNN classifier based on classical time-series imaging methods such as recurrence plot (RP) and Markov transition field (MTF), and further compared with the one-dimensional (1D) CNN model based on original time-domain features. A total of 18 CNN models are constructed for experiments in this paper, and the accuracy of the 2D CNN classifiers based on PI, MTF and RP are 98.89%, 94.75% and 98.34% at the time series length of 75 and the number of PI peaks of 5, respectively. The experimental results show that the PI-based 2D CNN classifier proposed in this paper achieves the best performances compared with other similar models, and demonstrates the feasibility of the MTF and RP-based 2D CNN classifier in kiwifruit hardness sorting.

Vectorized and performance‐portable quicksort

AbstractRecent works showed that implementations of quicksort using vector CPU instructions can outperform the non‐vectorized algorithms in widespread use. However, these implementations are typically single‐threaded, implemented for a particular instruction set, and restricted to a small set of key types. We lift these three restrictions: our proposed vqsort algorithm integrates into the state‐of‐the‐art parallel sorter , with a geometric mean speedup of 1.59. The same implementation works on seven instruction sets (including SVE and RISC‐V V) across four platforms. It also supports floating‐point and 16–128 bit integer keys. To the best of our knowledge, this is the fastest sort for large arrays of non‐tuple keys on CPUs, up to 20 times as fast as the sorting algorithms implemented in standard libraries. This article focuses on the practical engineering aspects enabling the speed and portability, which we have not yet seen demonstrated for a quicksort implementation. Furthermore, we introduce compact and transpose‐free sorting networks for in‐register sorting of small arrays, and a vector‐friendly pivot sampling strategy that is robust against adversarial input.

Polarized deep diffractive neural network for sorting, generation, multiplexing, and de-multiplexing of orbital angular momentum modes.

The multiplexing and de-multiplexing of orbital angular momentum (OAM) beams are critical issues in optical communication. Optical diffractive neural networks have been introduced to perform sorting, generation, multiplexing, and de-multiplexing of OAM beams. However, conventional diffractive neural networks cannot handle OAM modes with a varying spatial distribution of polarization directions. Herein, we propose a polarized optical deep diffractive neural network that is designed based on the concept of dielectric rectangular micro-structure meta-material. Our proposed polarized optical diffractive neural network is optimized to sort, generate, multiplex, and de-multiplex polarized OAM beams. The simulation results show that our network framework can successfully sort 14 kinds of orthogonally polarized vortex beams and de-multiplex the hybrid OAM beams into Gauss beams at two, three, and four spatial positions, respectively. Six polarized OAM beams with identical total intensity and eight cylinder vector beams with different topology charges have also been sorted effectively. Additionally, results reveal that the network can generate hybrid OAM beams with high quality and multiplex two polarized linear beams into eight kinds of cylinder vector beams.

Twin-width II: small classes

The recently introduced twin-width of a graph \(G\) is the minimum integer \(d\) such that \(G\) has a \(d\)-contraction sequence, that is, a sequence of \(\left| V(G) \right|-1\) iterated vertex identifications for which the overall maximum number of red edges incident to a single vertex is at most \(d\), where a red edge appears between two sets of identified vertices if they are not homogeneous in \(G\) (not fully adjacent nor fully non-adjacent). We show that if a graph admits a \(d\)-contraction sequence, then it also has a linear-arity tree of \(f(d)\)-contractions, for some function \(f\). Informally if we accept to worsen the twin-width bound, we can choose the next contraction from a set of \(\Theta(\left| V(G) \right|)\) pairwise disjoint pairs of vertices. This has two main consequences. First it permits to show that every bounded twin-width class is small, i.e., has at most \(n!c^n\) graphs labeled by \([n]\), for some constant \(c\). This unifies and extends the same result for bounded treewidth graphs [Beineke and Pippert, JCT '69], proper subclasses of permutations graphs [Marcus and Tardos, JCTA '04], and proper minor-free classes [Norine et al., JCTB '06]. It implies in turn that bounded-degree graphs, interval graphs, and unit disk graphs have unbounded twin-width. The second consequence is an \(O(\log n)\)-adjacency labeling scheme for bounded twin-width graphs, confirming several cases of the implicit graph conjecture. We then explore the small conjecture that, conversely, every small hereditary class has bounded twin-width. The conjecture passes many tests. Inspired by sorting networks of logarithmic depth, we show that \(\log_{\Theta(\log \log d)}n\)-subdivisions of \(K_n\) (a small class when \(d\) is constant) have twin-width at most \(d\). We obtain a rather sharp converse with a surprisingly direct proof: the \(\log_{d+1}n\)-subdivision of \(K_n\) has twin-width at least \(d\). Secondly graphs with bounded stack or queue number (also small classes) have bounded twin-width. These sparse classes are surprisingly rich since they contain certain (small) classes of expanders. Thirdly we show that cubic expanders obtained by iterated random 2-lifts from \(K_4\) [Bilu and Linial, Combinatorica '06] also have bounded twin-width. These graphs are related to so-called separable permutations and also form a small class. We suggest a promising connection between the small conjecture and group theory. Finally we define a robust notion of sparse twin-width. We show that for a hereditary class \(\mathcal C\) of bounded twin-width the five following conditions are equivalent: every graph in \(\mathcal C\) (1) has no \(K_{t,t}\) subgraph for some fixed \(t\), (2) has an adjacency matrix without a \(d\)-by-\(d\) division with a 1 entry in each of the \(d^2\) cells for some fixed \(d\), (3) has at most linearly many edges, (4) the subgraph closure of \(\mathcal C\) has bounded twin-width, and (5) \(\mathcal C\) has bounded expansion. We discuss how sparse classes with similar behavior with respect to clique subdivisions compare to bounded sparse twin-width.Mathematics Subject Classifications: 68R10, 05C30, 05C48Keywords: Twin-width, small classes, expanders, clique subdivisions, sparsity

Sorting Short Keys in Circuits of Size ${o(n \log n)}$

We consider the classical problem of sorting an input array containing $n$ elements, where each element is described with a $k$-bit comparison-key and a $w$-bit payload. A long-standing open problem is whether there exist $(k + w) \cdot o(n \log n)$-sized boolean circuits for sorting. We show that one can overcome the $n\log n$ barrier when the keys to be sorted are short. Specifically, we prove that there is a circuit with $(k + w) \cdot O(n k) \cdot \poly(\log^*n - \log^* (w + k))$ boolean gates capable of sorting any input array containing $n$ elements, each described with a $k$-bit key and a $w$-bit payload. Therefore, if the keys to be sorted are short, say, $k < o(\log n)$, our result is asymptotically better than the classical AKS sorting network (ignoring $\poly\log^*$ terms); and we also overcome the $n \log n$ barrier in such cases. Such a result might be surprising initially because it is long known that comparator-based techniques must incur $\Omega(n \log n)$ comparator gates even when the keys to be sorted are only $1$-bit long (e.g., see Knuth's Art of Programming textbook). To the best of our knowledge, we are the first to achieve non-trivial results for sorting circuits using non-comparison-based techniques. We also show that if the Li-Li network coding conjecture is true, our upper bound is optimal, barring $\poly\log^*$ terms, for every $k$ as long as $k = O(\log n)$.