In deep learning, weight initialization or parameter initialization describes the initial step in creating a neural network. A neural network contains trainable parameters that are modified during training: weight initialization is the pre-training step of assigning initial values to these parameters. The choice of weight initialization method affects the speed of convergence, the scale of neural activation within the network, the scale of gradient signals during backpropagation, and the quality of the final model. Proper initialization is necessary for avoiding issues such as vanishing and exploding gradients and activation function saturation. Note that even though this article is titled "weight initialization", both weights and biases are used in a neural network as trainable parameters, so this article describes how both of these are initialized. Similarly, trainable parameters in convolutional neural networks (CNNs) are called kernels and biases, and this article also describes these. == Constant initialization == We discuss the main methods of initialization in the context of a multilayer perceptron (MLP). Specific strategies for initializing other network architectures are discussed in later sections. For an MLP, there are only two kinds of trainable parameters, called weights and biases. Each layer l {\displaystyle l} contains a weight matrix W ( l ) ∈ R n l − 1 × n l {\displaystyle W^{(l)}\in \mathbb {R} ^{n_{l-1}\times n_{l}}} and a bias vector b ( l ) ∈ R n l {\displaystyle b^{(l)}\in \mathbb {R} ^{n_{l}}} , where n l {\displaystyle n_{l}} is the number of neurons in that layer. A weight initialization method is an algorithm for setting the initial values for W ( l ) , b ( l ) {\displaystyle W^{(l)},b^{(l)}} for each layer l {\displaystyle l} . The simplest form is zero initialization: W ( l ) = 0 , b ( l ) = 0 {\displaystyle W^{(l)}=0,b^{(l)}=0} Zero initialization is usually used for initializing biases, but it is not used for initializing weights, as it leads to symmetry in the network, causing all neurons to learn the same features. In this page, we assume b = 0 {\displaystyle b=0} unless otherwise stated. Recurrent neural networks typically use activation functions with bounded range, such as sigmoid and tanh, since unbounded activation may cause exploding values. (Le, Jaitly, Hinton, 2015) suggested initializing weights in the recurrent parts of the network to identity and zero bias, similar to the idea of residual connections and LSTM with no forget gate. In most cases, the biases are initialized to zero, though some situations can use a nonzero initialization. For example, in multiplicative units, such as the forget gate of LSTM, the bias can be initialized to 1 to allow good gradient signal through the gate. For neurons with ReLU activation, one can initialize the bias to a small positive value like 0.1, so that the gradient is likely nonzero at initialization, avoiding the dying ReLU problem. == Random initialization == Random initialization means sampling the weights from a normal distribution or a uniform distribution, usually independently. === LeCun initialization === LeCun initialization, popularized in (LeCun et al., 1998), is designed to preserve the variance of neural activations during the forward pass. It samples each entry in W ( l ) {\displaystyle W^{(l)}} independently from a distribution with mean 0 and variance 1 / n l − 1 {\displaystyle 1/n_{l-1}} . For example, if the distribution is a continuous uniform distribution, then the distribution is U ( ± 3 / n l − 1 ) {\displaystyle {\mathcal {U}}(\pm {\sqrt {3/n_{l-1}}})} . === Glorot initialization === Glorot initialization (or Xavier initialization) was proposed by Xavier Glorot and Yoshua Bengio. It was designed as a compromise between two goals: to preserve activation variance during the forward pass and to preserve gradient variance during the backward pass. For uniform initialization, it samples each entry in W ( l ) {\displaystyle W^{(l)}} independently and identically from U ( ± 6 / ( n l + 1 + n l − 1 ) ) {\displaystyle {\mathcal {U}}(\pm {\sqrt {6/(n_{l+1}+n_{l-1})}})} . In the context, n l − 1 {\displaystyle n_{l-1}} is also called the "fan-in", and n l + 1 {\displaystyle n_{l+1}} the "fan-out". When the fan-in and fan-out are equal, then Glorot initialization is the same as LeCun initialization. === He initialization === As Glorot initialization performs poorly for ReLU activation, He initialization (or Kaiming initialization) was proposed by Kaiming He et al. for networks with ReLU activation. It samples each entry in W ( l ) {\displaystyle W^{(l)}} from N ( 0 , 2 / n l − 1 ) {\displaystyle {\mathcal {N}}(0,2/n_{l-1})} . === Orthogonal initialization === (Saxe et al. 2013) proposed orthogonal initialization: initializing weight matrices as uniformly random (according to the Haar measure) semi-orthogonal matrices, multiplied by a factor that depends on the activation function of the layer. It was designed so that if one initializes a deep linear network this way, then its training time until convergence is independent of depth. Sampling a uniformly random semi-orthogonal matrix can be done by initializing X {\displaystyle X} by IID sampling its entries from a standard normal distribution, then calculate ( X X ⊤ ) − 1 / 2 X {\displaystyle \left(XX^{\top }\right)^{-1/2}X} or its transpose, depending on whether X {\displaystyle X} is tall or wide. For CNN kernels with odd widths and heights, orthogonal initialization is done this way: initialize the central point by a semi-orthogonal matrix, and fill the other entries with zero. As an illustration, a kernel K {\displaystyle K} of shape 3 × 3 × c × c ′ {\displaystyle 3\times 3\times c\times c'} is initialized by filling K [ 2 , 2 , : , : ] {\displaystyle K[2,2,:,:]} with the entries of a random semi-orthogonal matrix of shape c × c ′ {\displaystyle c\times c'} , and the other entries with zero. (Balduzzi et al., 2017) used it with stride 1 and zero-padding. This is sometimes called the Orthogonal Delta initialization. Related to this approach, unitary initialization proposes to parameterize the weight matrices to be unitary matrices, with the result that at initialization they are random unitary matrices (and throughout training, they remain unitary). This is found to improve long-sequence modelling in LSTM. Orthogonal initialization has been generalized to layer-sequential unit-variance (LSUV) initialization. It is a data-dependent initialization method, and can be used in convolutional neural networks. It first initializes weights of each convolution or fully connected layer with orthonormal matrices. Then, proceeding from the first to the last layer, it runs a forward pass on a random minibatch, and divides the layer's weights by the standard deviation of its output, so that its output has variance approximately 1. === Fixup initialization === In 2015, the introduction of residual connections allowed very deep neural networks to be trained, much deeper than the ~20 layers of the previous state of the art (such as the VGG-19). Residual connections gave rise to their own weight initialization problems and strategies. These are sometimes called "normalization-free" methods, since using residual connection could stabilize the training of a deep neural network so much that normalizations become unnecessary. Fixup initialization is designed specifically for networks with residual connections and without batch normalization, as follows: Initialize the classification layer and the last layer of each residual branch to 0. Initialize every other layer using a standard method (such as He initialization), and scale only the weight layers inside residual branches by L − 1 2 m − 2 {\displaystyle L^{-{\frac {1}{2m-2}}}} . Add a scalar multiplier (initialized at 1) in every branch and a scalar bias (initialized at 0) before each convolution, linear, and element-wise activation layer. Similarly, T-Fixup initialization is designed for Transformers without layer normalization. === Others === Instead of initializing all weights with random values on the order of O ( 1 / n ) {\displaystyle O(1/{\sqrt {n}})} , sparse initialization initialized only a small subset of the weights with larger random values, and the other weights zero, so that the total variance is still on the order of O ( 1 ) {\displaystyle O(1)} . Random walk initialization was designed for MLP so that during backpropagation, the L2 norm of gradient at each layer performs an unbiased random walk as one moves from the last layer to the first. Looks linear initialization was designed to allow the neural network to behave like a deep linear network at initialization, since W R e L U ( x ) − W R e L U ( − x ) = W x {\displaystyle W\;\mathrm {ReLU} (x)-W\;\mathrm {ReLU} (-x)=Wx} . It initializes a matrix W {\displaystyle W} of shape R n 2 × m {\displaystyle \mathbb {R} ^{{\frac {n}{2}}\times m}} by any method, such as orthogonal initialization, t
Kinematic chain
In mechanical engineering, a kinematic chain is an assembly of rigid bodies connected by joints to provide constrained motion that is the mathematical model for a mechanical system. As the word chain suggests, the rigid bodies, or links, are constrained by their connections to other links. An example is the simple open chain formed by links connected in series, like the usual chain, which is the kinematic model for a typical robot manipulator. Mathematical models of the connections, or joints, between two links are termed kinematic pairs. Kinematic pairs model the hinged and sliding joints fundamental to robotics, often called lower pairs and the surface contact joints critical to cams and gearing, called higher pairs. These joints are generally modeled as holonomic constraints. A kinematic diagram is a schematic of the mechanical system that shows the kinematic chain. The modern use of kinematic chains includes analysis of Linkages (mechanical), compliance that arises from flexure joints in precision mechanisms, link compliance in compliant mechanisms and micro-electro-mechanical systems, and cable compliance in cable robotic and tensegrity systems. == Mobility formula == The degrees of freedom, or mobility, of a kinematic chain is the number of parameters that define the configuration of the chain. A system of n rigid bodies moving in space has 6n degrees of freedom measured relative to a fixed frame. This frame is included in the count of bodies, so that mobility does not depend on link that forms the fixed frame. This means the degree-of-freedom of this system is M = 6(N − 1), where N = n + 1 is the number of moving bodies plus the fixed body. Joints that connect bodies impose constraints. Specifically, hinges and sliders each impose five constraints and therefore remove five degrees of freedom. It is convenient to define the number of constraints c that a joint imposes in terms of the joint's freedom f, where c = 6 − f. In the case of a hinge or slider, which are one-degree-of-freedom joints, have f = 1 and therefore c = 6 − 1 = 5. The result in general where d {\displaystyle d} is the degrees of freedom for the mobility of a kinematic chain formed from n moving links and j joints each with freedom fi, i = 1, 2, …, j, is given by M = d n − ∑ i = 1 j ( d − f i ) = d ( N − 1 − j ) + ∑ i = 1 j f i {\displaystyle M=dn-\sum _{i=1}^{j}(d-f_{i})=d(N-1-j)+\sum _{i=1}^{j}f_{i}} Where N is the total number of links and includes the fixed link. Spacial linkages used d = 6 {\displaystyle d=6} and planar linkages use d = 3 {\displaystyle d=3} . This result is known as the Chebychev–Grübler–Kutzbach criterion. == Analysis of kinematic chains == The constraint equations of a kinematic chain couple the range of movement allowed at each joint to the dimensions of the links in the chain, and form algebraic equations that are solved to determine the configuration of the chain associated with specific values of input parameters, called degrees of freedom. The constraint equations for a kinematic chain are obtained using rigid transformations [Z] to characterize the relative movement allowed at each joint and separate rigid transformations [X] to define the dimensions of each link. In the case of a serial open chain, the result is a sequence of rigid transformations alternating joint and link transformations from the base of the chain to its end link, which is equated to the specified position for the end link. A chain of n links connected in series has the kinematic equations, [ T ] = [ Z 1 ] [ X 1 ] [ Z 2 ] [ X 2 ] ⋯ [ X n − 1 ] [ Z n ] , {\displaystyle [T]=[Z_{1}][X_{1}][Z_{2}][X_{2}]\cdots [X_{n-1}][Z_{n}],\!} where [T] is the transformation locating the end-link—notice that the chain includes a "zeroth" link consisting of the ground frame to which it is attached. These equations are called the forward kinematics equations of the serial chain. Kinematic chains of a wide range of complexity are analyzed by equating the kinematics equations of serial chains that form loops within the kinematic chain. These equations are often called loop equations. The complexity (in terms of calculating the forward and inverse kinematics) of the chain is determined by the following factors: Its topology: a serial chain, a parallel manipulator, a tree structure, or a graph. Its geometrical form: how are neighbouring joints spatially connected to each other? Explanation Two or more rigid bodies in space are collectively called a rigid body system. We can hinder the motion of these independent rigid bodies with kinematic constraints. Kinematic constraints are constraints between rigid bodies that result in the decrease of the degrees of freedom of rigid body system. == Synthesis of kinematic chains == The constraint equations of a kinematic chain can be used in reverse to determine the dimensions of the links from a specification of the desired movement of the system. This is termed kinematic synthesis. Perhaps the most developed formulation of kinematic synthesis is for four-bar linkages, which is known as Burmester theory. Ferdinand Freudenstein is often called the father of modern kinematics for his contributions to the kinematic synthesis of linkages beginning in the 1950s. His use of the newly developed computer to solve Freudenstein's equation became the prototype of computer-aided design systems. This work has been generalized to the synthesis of spherical and spatial mechanisms.
Skipper (computer software)
Skipper is a visualization tool and code/schema generator for PHP ORM frameworks like Doctrine2, Doctrine, Propel, and CakePHP, which are used to create database abstraction layer. Skipper is developed by Czech company Inventic, s.r.o. based in Brno, and was known as ORM Designer prior to rebranding in 2014. == Overview == Generates visual model from the schema definition files Repetitive import/export of schema definitions in supported formats (XML, YML, PHP annotations) Schema definition files are automatically generated from the visual model Visual representation uses ER diagram extended by concepts of inheritance and many-to-many Supports customization using .xml configuration files and JavaScript Does not support direct connections to the database Crude and simplistic visual representation and menus == Architecture == Skipper was built on the Qt framework. Import/export of the schema definitions uses XSL transformations powered by LibXslt library. Imported source files are first converted to XML format: no conversion for XML, simple conversion for YML, creating the Abstract Syntax Tree and its subsequent conversion to XML for PHP annotations. The import/export scripts are configured in JavaScript and can be freely customized. == Supported ORM frameworks == Frameworks supported for visual model and schema files generation: Doctrine2 Doctrine CakePHP == History == Skipper was created as an internal tool for the web applications developed by Inventic. It was first published as a commercial tool under the name ORM Designer in 2009. Application was reworked and optimized in January 2013, and released as ORM Designer 2. In May 2013 ORM Designer became part of the South Moravian Innovation Center Incubator program (support program for innovative technological startups). In June 2014, ORM Designer version 3 was released and rebranded under the name of Skipper
Endomondo
Endomondo is a health and wellness website. It allows users to track their health statistics and provides insights on fitness trends. Originally launched in 2007, Endomondo was acquired by Under Armour in 2015. Under Armour shut down Endomondo in 2020, but, by 2024, Endomondo re-launched as its own entity. == History == Endomondo started in Denmark in 2007 by Mette Lykke, Christian Birk and Jakob Nordenhof Jønck. In 2011, the company opened an office in Silicon Valley, USA, but kept its research and development department in Denmark. In 2013, Endomondo LLC was listed in Red Herring as a European finalists for promising start-ups. The same year, Christian Birk and Jakob Nordenhof Jønck left the daily operation of the company, but kept co-ownership. In February 2015, Endomondo LLC was acquired by athletic apparel maker Under Armour for $85 million. Endomondo, at that time, had over 20 million users. In October 2020, Under Armour announced that Endomondo would be shutting down and selling off MyFitnessPal to the private equity firm Francisco Partners for $345 million. Service stopped on 31 December 2020, giving customers until 15 February 2021 to download an archive of their historic data. In 2024, Endomondo.com was brought back online as a professional fitness guidance website. == Features == Endomondo provides numerous workouts, guidance on exercises, performance-enhancing nutrition, and tips. Previously, Endomondo was able to track numerous fitness attributes such as running routes, distance, duration, and calories. The software helped analyze performance and recommend improvements. There was a free and a paid version available of Endomondo. The free version had advertisements. The paid Premium version was free of advertisements and included additional features such as the possibility to create one's own training plan. The offering of additional features was different between the Android, IOS and Windows platforms, and had significantly better features for tracking performance over time than UnderArmours suggested replacement. Endomondo offered challenges of various types to the user and allowed users to create their own challenges.
PlantUML
PlantUML is an open-source tool allowing users to create diagrams from a plain text language. Besides various UML diagrams, PlantUML has support for various other software development related formats (such as Archimate, Block diagram, BPMN, C4, Computer network diagram, ERD, Gantt chart, Mind map, and WBD), as well as visualisation of JSON and YAML files. The language of PlantUML is an example of a domain-specific language. Besides its own DSL, PlantUML also understands AsciiMath, Creole, DOT, and LaTeX. It uses Graphviz software to lay out its diagrams and Tikz for LaTeX support. Images can be output as PNG, SVG, LaTeX and even ASCII art. PlantUML has also been used to allow blind people to design and read UML diagrams. == Applications that use PlantUML == There are various extensions or add-ons that incorporate PlantUML. Atom has a community maintained PlantUML syntax highlighter and viewer. Confluence wiki has a PlantUML plug-in for Confluence Server, which renders diagrams on-the-fly during a page reload. There is an additional PlantUML plug-in for Confluence Cloud. Doxygen integrates diagrams for which sources are provided after the startuml command. Eclipse has a PlantUML plug-in. Google Docs has an add-on called PlantUML Gizmo that works with the PlantUML.com server. IntelliJ IDEA can create and display diagrams embedded into Markdown (built-in) or in standalone files (using a plugin). LaTeX using the Tikz package has limited support for PlantUML. LibreOffice has Libo_PlantUML extension to use PlantUML diagrams. MediaWiki has a PlantUML plug-in which renders diagrams in pages as SVG or PNG. Microsoft Word can use PlantUML diagrams via a Word Template Add-in. There is an additional Visual Studio Tools for Office add-in called PlantUML Gizmo that works in a similar fashion. NetBeans has a PlantUML plug-in. Notepad++ has a PlantUML plug-in. Obsidian has a PlantUML plug-in. Org-mode has a PlantUML org-babel support. Rider has a PlantUML plug-in. Sublime Text has a PlantUML package called PlantUmlDiagrams for Sublime Text 2 and 3. Visual Studio Code has various PlantUML extensions on its marketplace, most popular being PlantUML by jebbs. Vnote open source notetaking markdown application has built in PlantUML support. Xcode has a community maintained Source Editor Extension to generate and view PlantUML class diagrams from Swift source code. == Text format to communicate UML at source code level == PlantUML uses well-formed and human-readable code to render the diagrams. There are other text formats for UML modelling, but PlantUML supports many diagram types, and does not need an explicit layout, though it is possible to tweak the diagrams if necessary. +--------------------------------------+ | TEDx Talks Recommendation | | System | +--------------------------------------+ | +----------------------------------+ | | | Visitor | | | +----------------------------------+ | | | + View Recommended Talks | | | | + Search Talks | | | +----------------------------------+ | +--------------------------------------+ | | V +--------------------------------------+ | Authenticated User | +--------------------------------------+ | +----------------------------------+ | | | User | | | +----------------------------------+ | | | + View Recommended Talks | | | | + Search Talks | | | | + Save Favorite Talks | | | +----------------------------------+ | +--------------------------------------+ | | V +--------------------------------------+ | Admin | +--------------------------------------+ | +----------------------------------+ | | | Admin | | | +----------------------------------+ | | | + CRUD Talks | | | | + Manage Users | | | +----------------------------------+ | +--------------------------------------+
Security information management
Security information management (SIM) is an information security industry term for the collection of data such as log files into a central repository for trend analysis. == Overview == SIM products generally are software agents running on the computer systems that are monitored. The recorded log information is then sent to a centralized server that acts as a "security console". The console typically displays reports, charts, and graphs of that information, often in real time. Some software agents can incorporate local filters to reduce and manipulate the data that they send to the server, although typically from a forensic point of view you would collect all audit and accounting logs to ensure you can recreate a security incident. The security console is monitored by an administrator who reviews the consolidated information and takes action in response to any alerts issued. The data that is sent to the server to be correlated and analyzed are normalized by the software agents into a common form, usually XML. Those data are then aggregated in order to reduce their overall size. == Terminology == The terminology can easily be mistaken as a reference to the whole aspect of protecting one's infrastructure from any computer security breach. Due to historic reasons of terminology evolution; SIM refers to just the part of information security which consists of discovery of 'bad behavior' or policy violations by using data collection techniques. The term commonly used to represent an entire security infrastructure that protects an environment is commonly called information security management (InfoSec). Security information management is also referred to as log management and is different from SEM (security event management), but makes up a portion of a SIEM (security information and event management) solution. == Regulatory compliance == Security information management systems support compliance with regulatory frameworks that require centralized collection and analysis of security data. The Health Insurance Portability and Accountability Act (HIPAA) Security Rule requires covered entities to implement audit controls that record and examine activity in information systems containing electronic protected health information (45 CFR 164.312(b))."45 CFR § 164.312 - Technical safeguards". Legal Information Institute. Retrieved April 1, 2026. SIM platforms aggregate these audit records to support the required regular review of information system activity records (45 CFR 164.308(a)(1)(ii)(D)). The December 2024 HIPAA Security Rule NPRM proposed requiring regulated entities to deploy automated systems capable of monitoring and recording access to ePHI, including the ability to detect unauthorized access attempts in near real-time."HIPAA Security Rule To Strengthen the Cybersecurity of Electronic Protected Health Information". Federal Register. January 6, 2025. Retrieved April 1, 2026. The Payment Card Industry Data Security Standard (PCI DSS) similarly requires centralized log management and daily review of security events (Requirements 10.4 and 10.6)."PCI DSS v4.0" (PDF). PCI Security Standards Council. March 2022. Retrieved April 1, 2026. NIST Special Publication 800-53 addresses security information management through the AU (Audit and Accountability) control family, which specifies requirements for audit event generation, content, storage, and analysis."NIST SP 800-53 Rev. 5: Security and Privacy Controls". National Institute of Standards and Technology. September 2020. Retrieved April 1, 2026.
Box blur
A box blur (also known as a box linear filter) is a spatial domain linear filter in which each pixel in the resulting image has a value equal to the average value of its neighboring pixels in the input image. It is a form of low-pass ("blurring") filter. A 3 by 3 box blur ("radius 1") can be written as matrix 1 9 [ 1 1 1 1 1 1 1 1 1 ] . {\displaystyle {\frac {1}{9}}{\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}.} Due to its property of using equal weights, it can be implemented using a much simpler accumulation algorithm, which is significantly faster than using a sliding-window algorithm. Box blurs are frequently used to approximate a Gaussian blur. By the central limit theorem, repeated application of a box blur will approximate a Gaussian blur. In the frequency domain, a box blur has zeros and negative components. That is, a sine wave with a period equal to the size of the box will be blurred away entirely, and wavelengths shorter than the size of the box may be phase-reversed, as seen when two bokeh circles touch to form a bright spot where there would be a dark spot between two bright spots in the original image. == Extensions == Gwosdek, et al. has extended Box blur to take a fractional radius: the edges of the 1-D filter are expanded with a fraction. It makes slightly better gaussian approximation possible due to the elimination of integer-rounding error. Mario Klingemann has a "stack blur" that tries to better emulate gaussian's look in one pass by stacking weights: 1 9 [ 1 2 3 2 1 ] {\displaystyle {\frac {1}{9}}{\begin{bmatrix}1&2&3&2&1\end{bmatrix}}} The triangular impulse response it forms decomposes to two rounds of box blur. Stacked Integral Image by Bhatia et al. takes the weighted average of a few box blurs to fit the gaussian response curve. == Implementation == The following pseudocode implements a 3x3 box blur. The example does not handle the edges of the image, which would not fit inside the kernel, so that these areas remain unblurred. In practice, the issue is better handled by: Introducing an alpha channel to represent the absence of colors; Extending the boundary by filling in values, ranked by quality: Fill in a mirrored image at the border Fill in a constant color extending from the last pixel Pad in a fixed color A number of optimizations can be applied when implementing the box blur of a radius r and N pixels: The box blur is a separable filter, so that only two 1D passes of averaging 2 r + 1 pixels will be needed, one horizontal and one vertical, for each pixel. This lowers the complexity from O(Nr2) to O(Nr). In digital signal processing terminology, each pass is a moving-average filter. Accumulation. Instead of discarding the sum for each pixel, the algorithm re-uses the previous sum, and updates it by subtracting away the old pixel and adding the new pixel in the blurring range. A summed-area table can be used similarly. This lowers the complexity from O(Nr) to O(N). When being used in multiple passes to approximate a Gaussian blur, the cascaded integrator–comb filter construction allows for doing the equivalent operation in a single pass.