Trying to pick the best AI bug finder? An AI bug finder is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI bug finder slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
SeaTable
SeaTable is a no-code platform that allows users to develop and implement business processes. The cloud collaboration service SeaTable is marketed by the GmbH of the same name with headquarters in Mainz and additional offices in Berlin and Beijing, and developed by the same company as Seafile. == History == SeaTable is a collaborative database and low-code application platform developed as part of a joint venture between Seafile Ltd., a software company based in Guangzhou, China, and SeaTable GmbH, a German firm headquartered in Mainz. Founded in 2020, the project represents the international expansion of Seafile, a Chinese developer originally known for its file synchronization and sharing software. While SeaTable's cloud services and European client operations are managed by the German entity, the platform itself is developed in China by Seafile's engineering team. This cross-border structure, described by TechCrunch as an “unconventional path” for a Chinese startup expanding abroad, reflects Seafile's effort to maintain its product development in China while addressing growing scrutiny in Western markets over data governance and corporate control. In 2021, an innovation project led by the Cyber Innovation Hub at the IT School of the German Armed Forces started to evaluate the possibilities of a large-scale deployment at the German Armed Forces. The evaluation project is currently still ongoing. In 2022, SeaTable is optimizing its database backend to allow millions of records within one base in the future. The focus of development is increasingly on automation and visualization. In 2025, SeaTable introduced AI-powered automations with version 6. The update enabled the integration of large language models (LLMs) for text analysis and automated decision-making. SeaTable operates a self-hosted LLM on servers provided by Hetzner (Germany), while self-hosted deployments can connect to any compatible model. == Features == SeaTable combines the traditional capabilities of a spreadsheet such as Excel and supplements them with a wide range of functions for process automation and visualization as well as a fully comprehensive API. SeaTable is not a pure cloud solution, but can alternatively be installed on a private server and operated completely autonomously. In this way, the owner retains full control over their own data. The installation is done via Docker on a Linux server. == Security and privacy == While most no-code platforms exist only as SaaS solutions, SeaTable describes itself as a data-sparse European solution. While initially the SeaTable Cloud was hosted on Amazon AWS, the move to the German data centers of Swiss provider Exoscale then took place in May 2021. This was followed by the replacement of the Freshdesk cloud ticketing system with a self-hosted Zammad instance, and since April 2022 SeaTable has completely dispensed with all tracking cookies on its website.
Cyclodisparity
In vision science, cyclodisparity is the difference in the rotation angle of an object or scene viewed by the left and right eyes. Cyclodisparity can result from the eyes' torsional rotation (cyclorotation) or can be created artificially by presenting to the eyes two images that need to be rotated relative to each other for binocular fusion to take place. == Human and animal vision == The eyes and visual system can compensate for cyclodisparity up to a certain point; if the cyclodisparity is larger than a threshold, the images cannot be fused, resulting stereoblindness, and in double vision in subjects who otherwise have full stereo vision. When a human subject is presented with images that have artificial cyclodisparity, cyclovergence is evoked, that is, a motor response of the eye muscles that rotates the two eyes in opposite directions, thereby reducing cyclodisparity. Visually-induced cyclovergence of up to 8 degrees has been observed in normal subjects. Furthermore, up to about 8 degrees can usually be compensated by purely sensory means, that is, without physical eye rotation. This means that the normal human observer can achieve binocular image fusion in presence of cyclodisparity of up to approximately 16 degrees. Cyclodisparity due to images having been rotated inward can be compensated better when the gaze is directed downwards, and cyclodisparity due to an outward rotation can be compensated better when the gaze is directed upwards. A proposed explanation for this phenomenon is that the motor system is coordinated in such a way that the eyes perform a torsional movement to reduce the size of the search zones and thus the computational load required for solving the correspondence problem. The resulting cyclovergence at near gaze is smaller than the cyclovergence predicted by Listing's law. == Video processing and computer vision == Active camera torsion can be used in machine and computer vision for several purposes. For instance, camera torsion can be used to make improved use of the search range over which matching detectors or stereo matching algorithms operate, or to make a 3D slanted surface appear frontoparallel for further stereo processing. For image compression purposes, images with cyclodisparity are advantageously encoded using global motion compensation using a rotational motion model.
Harris corner detector
The Harris corner detector is a corner detection operator that is commonly used in computer vision algorithms to extract corners and infer features of an image. It was first introduced by Chris Harris and Mike Stephens in 1988 upon the improvement of Moravec's corner detector. Compared to its predecessor, Harris' corner detector takes the differential of the corner score into account with reference to direction directly, instead of using shifting patches for every 45 degree angles, and has been proved to be more accurate in distinguishing between edges and corners. Since then, it has been improved and adopted in many algorithms to preprocess images for subsequent applications. == Introduction == A corner is a point whose local neighborhood stands in two dominant and different edge directions. In other words, a corner can be interpreted as the junction of two edges, where an edge is a sudden change in image brightness. Corners are the important features in the image, and they are generally termed as interest points which are invariant to translation, rotation and illumination. Although corners are only a small percentage of the image, they contain the most important features in restoring image information, and they can be used to minimize the amount of processed data for motion tracking, image stitching, building 2D mosaics, stereo vision, image representation and other related computer vision areas. In order to capture the corners from the image, researchers have proposed many different corner detectors including the Kanade-Lucas-Tomasi (KLT) operator and the Harris operator which are most simple, efficient and reliable for use in corner detection. These two popular methodologies are both closely associated with and based on the local structure matrix. Compared to the Kanade-Lucas-Tomasi corner detector, the Harris corner detector provides good repeatability under changing illumination and rotation, and therefore, it is more often used in stereo matching and image database retrieval. Although there still exist drawbacks and limitations, the Harris corner detector is still an important and fundamental technique for many computer vision applications. == Development of Harris corner detection algorithm == Source: Without loss of generality, we will assume a grayscale 2-dimensional image is used. Let this image be given by I {\displaystyle I} . Consider taking an image patch ( x , y ) ∈ W {\displaystyle (x,y)\in W} (window) and shifting it by ( Δ x , Δ y ) {\displaystyle (\Delta x,\Delta y)} . The sum of squared differences (SSD) between these two patches, denoted f {\displaystyle f} , is given by: f ( Δ x , Δ y ) = ∑ ( x k , y k ) ∈ W ( I ( x k , y k ) − I ( x k + Δ x , y k + Δ y ) ) 2 {\displaystyle f(\Delta x,\Delta y)={\underset {(x_{k},y_{k})\in W}{\sum }}\left(I(x_{k},y_{k})-I(x_{k}+\Delta x,y_{k}+\Delta y)\right)^{2}} I ( x + Δ x , y + Δ y ) {\displaystyle I(x+\Delta x,y+\Delta y)} can be approximated by a Taylor expansion. Let I x {\displaystyle I_{x}} and I y {\displaystyle I_{y}} be the partial derivatives of I {\displaystyle I} , such that I ( x + Δ x , y + Δ y ) ≈ I ( x , y ) + I x ( x , y ) Δ x + I y ( x , y ) Δ y {\displaystyle I(x+\Delta x,y+\Delta y)\approx I(x,y)+I_{x}(x,y)\Delta x+I_{y}(x,y)\Delta y} This produces the approximation f ( Δ x , Δ y ) ≈ ∑ ( x , y ) ∈ W ( I x ( x , y ) Δ x + I y ( x , y ) Δ y ) 2 , {\displaystyle f(\Delta x,\Delta y)\approx {\underset {(x,y)\in W}{\sum }}\left(I_{x}(x,y)\Delta x+I_{y}(x,y)\Delta y\right)^{2},} which can be written in matrix form: f ( Δ x , Δ y ) ≈ ( Δ x Δ y ) M ( Δ x Δ y ) , {\displaystyle f(\Delta x,\Delta y)\approx {\begin{pmatrix}\Delta x&\Delta y\end{pmatrix}}M{\begin{pmatrix}\Delta x\\\Delta y\end{pmatrix}},} where M is the structure tensor, M = ∑ ( x , y ) ∈ W [ I x 2 I x I y I x I y I y 2 ] = [ ∑ ( x , y ) ∈ W I x 2 ∑ ( x , y ) ∈ W I x I y ∑ ( x , y ) ∈ W I x I y ∑ ( x , y ) ∈ W I y 2 ] {\displaystyle M={\underset {(x,y)\in W}{\sum }}{\begin{bmatrix}I_{x}^{2}&I_{x}I_{y}\\I_{x}I_{y}&I_{y}^{2}\end{bmatrix}}={\begin{bmatrix}{\underset {(x,y)\in W}{\sum }}I_{x}^{2}&{\underset {(x,y)\in W}{\sum }}I_{x}I_{y}\\{\underset {(x,y)\in W}{\sum }}I_{x}I_{y}&{\underset {(x,y)\in W}{\sum }}I_{y}^{2}\end{bmatrix}}} == Process of Harris corner detection algorithm == Commonly, Harris corner detector algorithm can be divided into five steps. Color to grayscale Spatial derivative calculation Structure tensor setup Harris response calculation Non-maximum suppression === Color to grayscale === If we use Harris corner detector in a color image, the first step is to convert it into a grayscale image, which will enhance the processing speed. The value of the gray scale pixel can be computed as a weighted sums of the values R, B and G of the color image, ∑ C ∈ { R , G , B } w C ⋅ C {\displaystyle \sum _{C\,\in \,\{R,G,B\}}w_{C}\cdot C} , where, e.g., w R = 0.299 , w G = 0.587 , w B = 1 − ( w R + w G ) = 0.114. {\displaystyle w_{R}=0.299,\ w_{G}=0.587,\ w_{B}=1-(w_{R}+w_{G})=0.114.} === Spatial derivative calculation === Next, we are going to find the derivative with respect to x and the derivative with respect to y, I x ( x , y ) {\displaystyle I_{x}(x,y)} and I y ( x , y ) {\displaystyle I_{y}(x,y)} . This can be approximated by applying Sobel operators. === Structure tensor setup === With I x ( x , y ) {\displaystyle I_{x}(x,y)} , I y ( x , y ) {\displaystyle I_{y}(x,y)} , we can construct the structure tensor M {\displaystyle M} . === Harris response calculation === For x ≪ y {\displaystyle x\ll y} , one has x ⋅ y x + y = x 1 1 + x / y ≈ x . {\displaystyle {\tfrac {x\cdot y}{x+y}}=x{\tfrac {1}{1+x/y}}\approx x.} In this step, we compute the smallest eigenvalue of the structure tensor using that approximation: λ min ≈ λ 1 λ 2 ( λ 1 + λ 2 ) = det ( M ) tr ( M ) {\displaystyle \lambda _{\min }\approx {\frac {\lambda _{1}\lambda _{2}}{(\lambda _{1}+\lambda _{2})}}={\frac {\det(M)}{\operatorname {tr} (M)}}} with the trace t r ( M ) = m 11 + m 22 {\displaystyle \mathrm {tr} (M)=m_{11}+m_{22}} . Another commonly used Harris response calculation is shown as below, R = λ 1 λ 2 − k ( λ 1 + λ 2 ) 2 = det ( M ) − k tr ( M ) 2 {\displaystyle R=\lambda _{1}\lambda _{2}-k(\lambda _{1}+\lambda _{2})^{2}=\det(M)-k\operatorname {tr} (M)^{2}} where k {\displaystyle k} is an empirically determined constant; k ∈ [ 0.04 , 0.06 ] {\displaystyle k\in [0.04,0.06]} . === Non-maximum suppression === In order to pick up the optimal values to indicate corners, we find the local maxima as corners within the window which is a 3 by 3 filter. == Improvement == Sources: Harris-Laplace Corner Detector Differential Morphological Decomposition Based Corner Detector Multi-scale Bilateral Structure Tensor Based Corner Detector == Applications == Image Alignment, Stitching and Registration 2D Mosaics Creation 3D Scene Modeling and Reconstruction Motion Detection Object Recognition Image Indexing and Content-based Retrieval Video Tracking
Ericom Connect
Ericom Connect is a remote access/application publishing solution produced by Ericom Software that provides secure, centrally managed access to physical or hosted desktops and applications running on Microsoft Windows and Linux systems. == Product overview == Ericom Connect is desktop virtualization and application virtualization software that allows users to run applications remotely, without installing them on the local computer or device. The software is noted for its scalability, ease of deployment, and compatibility with any type of infrastructure, cloud or physical. Ericom Connect uses AccessPad (native client for desktops), AccessToGo (native client for mobile), or AccessNow, one of the first HTML5 RDP solutions to support clientless access to Windows desktops and applications from any device with an HTML5-compatible browser, including Macintosh computers, mobile devices, and Google Chromebooks. Other notable features include performance monitoring, built-in real-time analytics & BI, support for two-factor authentication (using RSA SecurID), multi-tenancy and multi-datacenter support via a single unified web interface, and a “Launch Simulation” feature that allows users to visualize and simulate actual step-by-step user processes directly from within the administration console. In addition to scalability, by distributing configurations, logs, etc., across multiple servers there is no single point of failure, as can be the case if all configuration information is stored on one server. == History == Ericom Connect was introduced in 2015. Ericom Connect is a successor to Ericom PowerTerm Web Connect. PowerTerm Web Connect used an architecture similar to what was then current with Citrix and VMWare, relying on a centralized SQL server, a connection broker, image management for different hypervisors, and a variety of clients. Ericom Connect uses a new grid architecture that provides more scalability, reliability, and flexibility than before.
PhyCV
PhyCV is the first computer vision library which utilizes algorithms directly derived from the equations of physics governing physical phenomena. The algorithms appearing in the first release emulate the propagation of light through a physical medium with natural and engineered diffractive properties followed by coherent detection. Unlike traditional algorithms that are a sequence of hand-crafted empirical rules, physics-inspired algorithms leverage physical laws of nature as blueprints. In addition, these algorithms can, in principle, be implemented in real physical devices for fast and efficient computation in the form of analog computing. Currently PhyCV has three algorithms, Phase-Stretch Transform (PST) and Phase-Stretch Adaptive Gradient-Field Extractor (PAGE), and Vision Enhancement via Virtual diffraction and coherent Detection (VEViD). All algorithms have CPU and GPU versions. PhyCV is now available on GitHub and can be installed from pip. == History == Algorithms in PhyCV are inspired by the physics of the photonic time stretch (a hardware technique for ultrafast and single-shot data acquisition). PST is an edge detection algorithm that was open-sourced in 2016 and has 800+ stars and 200+ forks on GitHub. PAGE is a directional edge detection algorithm that was open-sourced in February, 2022. PhyCV was originally developed and open-sourced by Jalali-Lab @ UCLA in May 2022. In the initial release of PhyCV, the original open-sourced code of PST and PAGE is significantly refactored and improved to be modular, more efficient, GPU-accelerated and object-oriented. VEViD is a low-light and color enhancement algorithm that was added to PhyCV in November 2022. == Background == === Phase-Stretch Transform (PST) === Phase-Stretch Transform (PST) is a computationally efficient edge and texture detection algorithm with exceptional performance in visually impaired images. The algorithm transforms the image by emulating propagation of light through a device with engineered diffractive property followed by coherent detection. It has been applied in improving the resolution of MRI image, extracting blood vessels in retina images, dolphin identification, and waste water treatment, single molecule biological imaging, and classification of UAV using micro Doppler imaging. === Phase-Stretch Adaptive Gradient-Field Extractor (PAGE) === Phase-Stretch Adaptive Gradient-Field Extractor (PAGE) is a physics-inspired algorithm for detecting edges and their orientations in digital images at various scales. The algorithm is based on the diffraction equations of optics. Metaphorically speaking, PAGE emulates the physics of birefringent (orientation-dependent) diffractive propagation through a physical device with a specific diffractive structure. The propagation converts a real-valued image into a complex function. Related information is contained in the real and imaginary components of the output. The output represents the phase of the complex function. === Vision Enhancement via Virtual diffraction and coherent Detection (VEViD) === Vision Enhancement via Virtual diffraction and coherent Detection (VEViD) an efficient and interpretable low-light and color enhancement algorithm that reimagines a digital image as a spatially varying metaphoric light field and then subjects the field to the physical processes akin to diffraction and coherent detection. The term “Virtual” captures the deviation from the physical world. The light field is pixelated and the propagation imparts a phase with an arbitrary dependence on frequency which can be different from the quadratic behavior of physical diffraction. VEViD can be further accelerated through mathematical approximations that reduce the computation time without appreciable sacrifice in image quality. A closed-form approximation for VEViD which we call VEViD-lite can achieve up to 200 FPS for 4K video enhancement. == PhyCV on the Edge == Featuring low-dimensionality and high-efficiency, PhyCV is ideal for edge computing applications. In this section, we demonstrate running PhyCV on NVIDIA Jetson Nano in real-time. === NVIDIA Jetson Nano Developer Kit === NVIDIA Jetson Nano Developer Kit is a small- sized and power-efficient platform for edge computing applications. It is equipped with an NVIDIA Maxwell architecture GPU with 128 CUDA cores, a quad-core ARM Cortex-A57 CPU, 4GB 64-bit LPDDR4 RAM, and supports video encoding and decoding up to 4K resolution. Jetson Nano also offers a variety of interfaces for connectivity and expansion, making it ideal for a wide range of AI and IoT applications. In our setup, we connect a USB camera to the Jetson Nano to acquire videos and demonstrate using PhyCV to process the videos in real-time. === Real-time PhyCV on Jetson Nano === We use the Jetson Nano (4GB) with NVIDIA JetPack SDK version 4.6.1, which comes with pre- installed Python 3.6, CUDA 10.2, and OpenCV 4.1.1. We further install PyTorch 1.10 to enable the GPU accelerated PhyCV. We demonstrate the results and metrics of running PhyCV on Jetson Nano in real-time for edge detection and low-light enhancement tasks. For 480p videos, both operations achieve beyond 38 FPS, which is sufficient for most cameras that capture videos at 30 FPS. For 720p videos, PhyCV low-light enhancement can operate at 24 FPS and PhyCV edge detection can operate at 17 FPS. == Highlights == === Modular Code Architecture === The code in PhyCV has a modular design which faithfully follows the physical process from which the algorithm was originated. Both PST and PAGE modules in the PhyCV library emulate the propagation of the input signal (original digital image) through a device with engineered diffractive property followed by coherent (phase) detection. The dispersive propagation applies a phase kernel to the frequency domain of the original image. This process has three steps in general, loading the image, initializing the kernel and applying the kernel. In the implementation of PhyCV, each algorithm is represented as a class in Python and each class has methods that simulate the steps described above. The modular code architecture follows the physics behind the algorithm. Please refer to the source code on GitHub for more details. === GPU Acceleration === PhyCV supports GPU acceleration. The GPU versions of PST and PAGE are built on PyTorch accelerated by the CUDA toolkit. The acceleration is beneficial for applying the algorithms in real-time image video processing and other deep learning tasks. The running time per frame of PhyCV algorithms on CPU (Intel i9-9900K) and GPU (NVIDIA TITAN RTX) for videos at different resolutions are shown below. Note that the PhyCV low-light enhancement operates in the HSV color space, so the running time also includes RGB to HSV conversion. However, for all running times using GPUs, we ignore the time of moving data from CPUs to GPUs and count the algorithm operation time only. == Installation and Examples == Please refer to the GitHub README file for a detailed technical documentation. == Current Limitations == === I/O (Input/Output) Bottleneck for Real-time Video Processing === When dealing with real-time video streams from cameras, the frames are captured and buffered in CPU and have to be moved to GPU to run the GPU-accelerated PhyCV algorithms. This process is time-consuming and it is a common bottleneck for real-time video-processing algorithms. === Lack of Parameter Adaptivity for Different Images === Currently, the parameters of PhyCV algorithms have to be manually tuned for different images. Although a set of pre-selected parameters work relatively well for a wide range of images, the lack of parameter adaptivity for different images remains a limitation for now.
Residual neural network
A residual neural network (also referred to as a residual network or ResNet) is a deep learning architecture in which the layers learn residual functions with reference to the layer inputs. It was developed in 2015 for image recognition, and won the ImageNet Large Scale Visual Recognition Challenge (ILSVRC) of that year. As a point of terminology, "residual connection" refers to the specific architectural motif of x ↦ f ( x ) + x {\displaystyle x\mapsto f(x)+x} , where f {\displaystyle f} is an arbitrary neural network module. The motif had been used previously (see §History for details). However, the publication of ResNet made it widely popular for feedforward networks, appearing in neural networks that are seemingly unrelated to ResNet. The residual connection stabilizes the training and convergence of deep neural networks with hundreds of layers, and is a common motif in deep neural networks, such as transformer models (e.g., BERT, and GPT models such as ChatGPT), the AlphaGo Zero system, the AlphaStar system, and the AlphaFold system. == Mathematics == === Residual connection === In a multilayer neural network model, consider a (non-residual) subnetwork with a certain number of stacked layers (e.g., 2 or 3). Let H ( x ; α ) {\displaystyle H(x;\alpha )} denote the subnetwork. Suppose H ∗ {\displaystyle H^{}} is the desired optimal output of this subnetwork. Residual learning simply adds x {\displaystyle x} directly to the output, such that the optimal learned output now becomes be H ∗ − x {\displaystyle H^{}-x} , which is interpreted as a "residual" with respect to x {\displaystyle x} . The operation of "adding x {\displaystyle x} " is implemented via a "skip connection" that performs an identity mapping to connect the input of the subnetwork with its output. This connection is referred to as a "residual connection" in later work. Let F ( x ; α ) = H ( x ; a ) + x {\displaystyle F(x;\alpha )=H(x;a)+x} . The function F {\displaystyle F} is often represented by matrix multiplication interlaced with activation functions and normalization operations (e.g., batch normalization or layer normalization). As a whole, one of these subnetworks is referred to as a "residual block". A deep residual network is constructed by simply stacking these blocks. Long short-term memory (LSTM) has a memory mechanism that serves as a residual connection. In an LSTM without a forget gate, an input x t {\displaystyle x_{t}} is processed by a function F {\displaystyle F} and added to a memory cell c t {\displaystyle c_{t}} , resulting in c t + 1 = c t + F ( x t ) {\displaystyle c_{t+1}=c_{t}+F(x_{t})} . An LSTM with a forget gate essentially functions as a highway network. To stabilize the variance of the layers' inputs, it is recommended to replace the residual connections x + f ( x ) {\displaystyle x+f(x)} with x / L + f ( x ) {\displaystyle x/L+f(x)} , where L {\displaystyle L} is the total number of residual layers. === Projection connection === If the function F {\displaystyle F} is of type F : R n → R m {\displaystyle F:\mathbb {R} ^{n}\to \mathbb {R} ^{m}} where n ≠ m {\displaystyle n\neq m} , then F ( x ) + x {\displaystyle F(x)+x} is undefined. To handle this special case, a projection connection is used: y = F ( x ) + P ( x ) {\displaystyle y=F(x)+P(x)} where P {\displaystyle P} is typically a linear projection, defined by P ( x ) = M x {\displaystyle P(x)=Mx} where M {\displaystyle M} is a m × n {\displaystyle m\times n} matrix. The matrix is trained via backpropagation, as is any other parameter of the model. === Signal propagation === The introduction of identity mappings facilitates signal propagation in both forward and backward paths. ==== Forward propagation ==== If the output of the ℓ {\displaystyle \ell } -th residual block is the input to the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th residual block (assuming no activation function between blocks), then the ( ℓ + 1 ) {\displaystyle (\ell +1)} -th input is: x ℓ + 1 = F ( x ℓ ) + x ℓ {\displaystyle x_{\ell +1}=F(x_{\ell })+x_{\ell }} Applying this formulation recursively, e.g.: x ℓ + 2 = F ( x ℓ + 1 ) + x ℓ + 1 = F ( x ℓ + 1 ) + F ( x ℓ ) + x ℓ {\displaystyle {\begin{aligned}x_{\ell +2}&=F(x_{\ell +1})+x_{\ell +1}\\&=F(x_{\ell +1})+F(x_{\ell })+x_{\ell }\end{aligned}}} yields the general relationship: x L = x ℓ + ∑ i = ℓ L − 1 F ( x i ) {\displaystyle x_{L}=x_{\ell }+\sum _{i=\ell }^{L-1}F(x_{i})} where L {\textstyle L} is the index of a residual block and ℓ {\textstyle \ell } is the index of some earlier block. This formulation suggests that there is always a signal that is directly sent from a shallower block ℓ {\textstyle \ell } to a deeper block L {\textstyle L} . ==== Backward propagation ==== The residual learning formulation provides the added benefit of mitigating the vanishing gradient problem to some extent. However, it is crucial to acknowledge that the vanishing gradient issue is not the root cause of the degradation problem, which is tackled through the use of normalization. To observe the effect of residual blocks on backpropagation, consider the partial derivative of a loss function E {\displaystyle {\mathcal {E}}} with respect to some residual block input x ℓ {\displaystyle x_{\ell }} . Using the equation above from forward propagation for a later residual block L > ℓ {\displaystyle L>\ell } : ∂ E ∂ x ℓ = ∂ E ∂ x L ∂ x L ∂ x ℓ = ∂ E ∂ x L ( 1 + ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) ) = ∂ E ∂ x L + ∂ E ∂ x L ∂ ∂ x ℓ ∑ i = ℓ L − 1 F ( x i ) {\displaystyle {\begin{aligned}{\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial x_{L}}{\partial x_{\ell }}}\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}\left(1+{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\right)\\&={\frac {\partial {\mathcal {E}}}{\partial x_{L}}}+{\frac {\partial {\mathcal {E}}}{\partial x_{L}}}{\frac {\partial }{\partial x_{\ell }}}\sum _{i=\ell }^{L-1}F(x_{i})\end{aligned}}} This formulation suggests that the gradient computation of a shallower layer, ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} , always has a later term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} that is directly added. Even if the gradients of the F ( x i ) {\displaystyle F(x_{i})} terms are small, the total gradient ∂ E ∂ x ℓ {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{\ell }}}} resists vanishing due to the added term ∂ E ∂ x L {\textstyle {\frac {\partial {\mathcal {E}}}{\partial x_{L}}}} . == Variants of residual blocks == === Basic block === A basic block is the simplest building block studied in the original ResNet. This block consists of two sequential 3x3 convolutional layers and a residual connection. The input and output dimensions of both layers are equal. === Bottleneck block === A bottleneck block consists of three sequential convolutional layers and a residual connection. The first layer in this block is a 1×1 convolution for dimension reduction (e.g., to 1/2 of the input dimension); the second layer performs a 3×3 convolution; the last layer is another 1×1 convolution for dimension restoration. The models of ResNet-50, ResNet-101, and ResNet-152 are all based on bottleneck blocks. === Pre-activation block === The pre-activation residual block applies activation functions before applying the residual function F {\displaystyle F} . Formally, the computation of a pre-activation residual block can be written as: x ℓ + 1 = F ( ϕ ( x ℓ ) ) + x ℓ {\displaystyle x_{\ell +1}=F(\phi (x_{\ell }))+x_{\ell }} where ϕ {\displaystyle \phi } can be any activation (e.g. ReLU) or normalization (e.g. LayerNorm) operation. This design reduces the number of non-identity mappings between residual blocks, and allows an identity mapping directly from the input to the output. This design was used to train models with 200 to over 1000 layers, and was found to consistently outperform variants where the residual path is not an identity function. The pre-activation ResNet with 200 layers took 3 weeks to train for ImageNet on 8 GPUs in 2016. Since GPT-2, transformer blocks have been mostly implemented as pre-activation blocks. This is often referred to as "pre-normalization" in the literature of transformer models. == Applications == Originally, ResNet was designed for computer vision. All transformer architectures include residual connections. Indeed, very deep transformers cannot be trained without them. The original ResNet paper made no claim on being inspired by biological systems. However, later research has related ResNet to biologically-plausible algorithms. A study published in Science in 2023 disclosed the complete connectome of an insect brain (specifically that of a fruit fly larva). This study discovered "multilayer shortcuts" that resemble the skip connections in artificial neural networks, including ResNets. == History == === Previous work === Residual connections were noticed in neu