The reparameterization trick (aka "reparameterization gradient estimator") is a technique used in statistical machine learning, particularly in variational inference, variational autoencoders, and stochastic optimization. It allows for the efficient computation of gradients through random variables, enabling the optimization of parametric probability models using stochastic gradient descent, and the variance reduction of estimators. It was developed in the 1980s in operations research, under the name of "pathwise gradients", or "stochastic gradients". Its use in variational inference was proposed in 2013. == Mathematics == Let z {\displaystyle z} be a random variable with distribution q ϕ ( z ) {\displaystyle q_{\phi }(z)} , where ϕ {\displaystyle \phi } is a vector containing the parameters of the distribution. === REINFORCE estimator === Consider an objective function of the form: L ( ϕ ) = E z ∼ q ϕ ( z ) [ f ( z ) ] {\displaystyle L(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[f(z)]} Without the reparameterization trick, estimating the gradient ∇ ϕ L ( ϕ ) {\displaystyle \nabla _{\phi }L(\phi )} can be challenging, because the parameter appears in the random variable itself. In more detail, we have to statistically estimate: ∇ ϕ L ( ϕ ) = ∇ ϕ ∫ d z q ϕ ( z ) f ( z ) {\displaystyle \nabla _{\phi }L(\phi )=\nabla _{\phi }\int dz\;q_{\phi }(z)f(z)} The REINFORCE estimator, widely used in reinforcement learning and especially policy gradient, uses the following equality: ∇ ϕ L ( ϕ ) = ∫ d z q ϕ ( z ) ∇ ϕ ( ln q ϕ ( z ) ) f ( z ) = E z ∼ q ϕ ( z ) [ ∇ ϕ ( ln q ϕ ( z ) ) f ( z ) ] {\displaystyle \nabla _{\phi }L(\phi )=\int dz\;q_{\phi }(z)\nabla _{\phi }(\ln q_{\phi }(z))f(z)=\mathbb {E} _{z\sim q_{\phi }(z)}[\nabla _{\phi }(\ln q_{\phi }(z))f(z)]} This allows the gradient to be estimated: ∇ ϕ L ( ϕ ) ≈ 1 N ∑ i = 1 N ∇ ϕ ( ln q ϕ ( z i ) ) f ( z i ) {\displaystyle \nabla _{\phi }L(\phi )\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }(\ln q_{\phi }(z_{i}))f(z_{i})} The REINFORCE estimator has high variance, and many methods were developed to reduce its variance. === Reparameterization estimator === The reparameterization trick expresses z {\displaystyle z} as: z = g ϕ ( ϵ ) , ϵ ∼ p ( ϵ ) {\displaystyle z=g_{\phi }(\epsilon ),\quad \epsilon \sim p(\epsilon )} Here, g ϕ {\displaystyle g_{\phi }} is a deterministic function parameterized by ϕ {\displaystyle \phi } , and ϵ {\displaystyle \epsilon } is a noise variable drawn from a fixed distribution p ( ϵ ) {\displaystyle p(\epsilon )} . This gives: L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ f ( g ϕ ( ϵ ) ) ] {\displaystyle L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[f(g_{\phi }(\epsilon ))]} Now, the gradient can be estimated as: ∇ ϕ L ( ϕ ) = E ϵ ∼ p ( ϵ ) [ ∇ ϕ f ( g ϕ ( ϵ ) ) ] ≈ 1 N ∑ i = 1 N ∇ ϕ f ( g ϕ ( ϵ i ) ) {\displaystyle \nabla _{\phi }L(\phi )=\mathbb {E} _{\epsilon \sim p(\epsilon )}[\nabla _{\phi }f(g_{\phi }(\epsilon ))]\approx {\frac {1}{N}}\sum _{i=1}^{N}\nabla _{\phi }f(g_{\phi }(\epsilon _{i}))} == Examples == For some common distributions, the reparameterization trick takes specific forms: Normal distribution: For z ∼ N ( μ , σ 2 ) {\displaystyle z\sim {\mathcal {N}}(\mu ,\sigma ^{2})} , we can use: z = μ + σ ϵ , ϵ ∼ N ( 0 , 1 ) {\displaystyle z=\mu +\sigma \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,1)} Exponential distribution: For z ∼ Exp ( λ ) {\displaystyle z\sim {\text{Exp}}(\lambda )} , we can use: z = − 1 λ log ( ϵ ) , ϵ ∼ Uniform ( 0 , 1 ) {\displaystyle z=-{\frac {1}{\lambda }}\log(\epsilon ),\quad \epsilon \sim {\text{Uniform}}(0,1)} Discrete distribution can be reparameterized by the Gumbel distribution (Gumbel-softmax trick or "concrete distribution") and diffusion models. In general, any distribution that is differentiable with respect to its parameters can be reparameterized by inverting the multivariable CDF function, then apply the implicit method. See for an exposition and application to the Gamma, Beta, Dirichlet, and von Mises distributions. == Applications == === Variational autoencoder === In Variational Autoencoders (VAEs), the VAE objective function, known as the Evidence Lower Bound (ELBO), is given by: ELBO ( ϕ , θ ) = E z ∼ q ϕ ( z | x ) [ log p θ ( x | z ) ] − D KL ( q ϕ ( z | x ) | | p ( z ) ) {\displaystyle {\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{z\sim q_{\phi }(z|x)}[\log p_{\theta }(x|z)]-D_{\text{KL}}(q_{\phi }(z|x)||p(z))} where q ϕ ( z | x ) {\displaystyle q_{\phi }(z|x)} is the encoder (recognition model), p θ ( x | z ) {\displaystyle p_{\theta }(x|z)} is the decoder (generative model), and p ( z ) {\displaystyle p(z)} is the prior distribution over latent variables. The gradient of ELBO with respect to θ {\displaystyle \theta } is simply E z ∼ q ϕ ( z | x ) [ ∇ θ log p θ ( x | z ) ] ≈ 1 L ∑ l = 1 L ∇ θ log p θ ( x | z l ) {\displaystyle \mathbb {E} _{z\sim q_{\phi }(z|x)}[\nabla _{\theta }\log p_{\theta }(x|z)]\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\theta }\log p_{\theta }(x|z_{l})} but the gradient with respect to ϕ {\displaystyle \phi } requires the trick. Express the sampling operation z ∼ q ϕ ( z | x ) {\displaystyle z\sim q_{\phi }(z|x)} as: z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ , ϵ ∼ N ( 0 , I ) {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon ,\quad \epsilon \sim {\mathcal {N}}(0,I)} where μ ϕ ( x ) {\displaystyle \mu _{\phi }(x)} and σ ϕ ( x ) {\displaystyle \sigma _{\phi }(x)} are the outputs of the encoder network, and ⊙ {\displaystyle \odot } denotes element-wise multiplication. Then we have ∇ ϕ ELBO ( ϕ , θ ) = E ϵ ∼ N ( 0 , I ) [ ∇ ϕ log p θ ( x | z ) + ∇ ϕ log q ϕ ( z | x ) − ∇ ϕ log p ( z ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )=\mathbb {E} _{\epsilon \sim {\mathcal {N}}(0,I)}[\nabla _{\phi }\log p_{\theta }(x|z)+\nabla _{\phi }\log q_{\phi }(z|x)-\nabla _{\phi }\log p(z)]} where z = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ {\displaystyle z=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon } . This allows us to estimate the gradient using Monte Carlo sampling: ∇ ϕ ELBO ( ϕ , θ ) ≈ 1 L ∑ l = 1 L [ ∇ ϕ log p θ ( x | z l ) + ∇ ϕ log q ϕ ( z l | x ) − ∇ ϕ log p ( z l ) ] {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi ,\theta )\approx {\frac {1}{L}}\sum _{l=1}^{L}[\nabla _{\phi }\log p_{\theta }(x|z_{l})+\nabla _{\phi }\log q_{\phi }(z_{l}|x)-\nabla _{\phi }\log p(z_{l})]} where z l = μ ϕ ( x ) + σ ϕ ( x ) ⊙ ϵ l {\displaystyle z_{l}=\mu _{\phi }(x)+\sigma _{\phi }(x)\odot \epsilon _{l}} and ϵ l ∼ N ( 0 , I ) {\displaystyle \epsilon _{l}\sim {\mathcal {N}}(0,I)} for l = 1 , … , L {\displaystyle l=1,\ldots ,L} . This formulation enables backpropagation through the sampling process, allowing for end-to-end training of the VAE model using stochastic gradient descent or its variants. === Variational inference === More generally, the trick allows using stochastic gradient descent for variational inference. Let the variational objective (ELBO) be of the form: ELBO ( ϕ ) = E z ∼ q ϕ ( z ) [ log p ( x , z ) − log q ϕ ( z ) ] {\displaystyle {\text{ELBO}}(\phi )=\mathbb {E} _{z\sim q_{\phi }(z)}[\log p(x,z)-\log q_{\phi }(z)]} Using the reparameterization trick, we can estimate the gradient of this objective with respect to ϕ {\displaystyle \phi } : ∇ ϕ ELBO ( ϕ ) ≈ 1 L ∑ l = 1 L ∇ ϕ [ log p ( x , g ϕ ( ϵ l ) ) − log q ϕ ( g ϕ ( ϵ l ) ) ] , ϵ l ∼ p ( ϵ ) {\displaystyle \nabla _{\phi }{\text{ELBO}}(\phi )\approx {\frac {1}{L}}\sum _{l=1}^{L}\nabla _{\phi }[\log p(x,g_{\phi }(\epsilon _{l}))-\log q_{\phi }(g_{\phi }(\epsilon _{l}))],\quad \epsilon _{l}\sim p(\epsilon )} === Dropout === The reparameterization trick has been applied to reduce the variance in dropout, a regularization technique in neural networks. The original dropout can be reparameterized with Bernoulli distributions: y = ( W ⊙ ϵ ) x , ϵ i j ∼ Bernoulli ( α i j ) {\displaystyle y=(W\odot \epsilon )x,\quad \epsilon _{ij}\sim {\text{Bernoulli}}(\alpha _{ij})} where W {\displaystyle W} is the weight matrix, x {\displaystyle x} is the input, and α i j {\displaystyle \alpha _{ij}} are the (fixed) dropout rates. More generally, other distributions can be used than the Bernoulli distribution, such as the gaussian noise: y i = μ i + σ i ⊙ ϵ i , ϵ i ∼ N ( 0 , I ) {\displaystyle y_{i}=\mu _{i}+\sigma _{i}\odot \epsilon _{i},\quad \epsilon _{i}\sim {\mathcal {N}}(0,I)} where μ i = m i ⊤ x {\displaystyle \mu _{i}=\mathbf {m} _{i}^{\top }x} and σ i 2 = v i ⊤ x 2 {\displaystyle \sigma _{i}^{2}=\mathbf {v} _{i}^{\top }x^{2}} , with m i {\displaystyle \mathbf {m} _{i}} and v i {\displaystyle \mathbf {v} _{i}} being the mean and variance of the i {\displaystyle i} -th output neuron. The reparameterization trick can be applied to all such cases, resulting in the variational dropout method.
Artificial brain
An artificial brain (or artificial mind) is software and hardware with cognitive abilities similar to those of the animal or human brain. Research investigating "artificial brains" and brain emulation plays three important roles in science: An ongoing attempt by neuroscientists to understand how the human brain works, known as cognitive neuroscience. A thought experiment in the philosophy of artificial intelligence, demonstrating that it is possible, at least in theory, to create a machine that has all the capabilities of a human being. A long-term project to create machines exhibiting behavior comparable to those of animals with complex central nervous system such as mammals and most particularly humans. The ultimate goal of creating a machine exhibiting human-like behavior or intelligence is sometimes called strong AI. An example of the first objective is the project reported by Aston University in Birmingham, England where researchers are using biological cells to create "neurospheres" (small clusters of neurons) in order to develop new treatments for diseases including Alzheimer's, motor neurone and Parkinson's disease. The second objective is a reply to arguments such as John Searle's Chinese room argument, Hubert Dreyfus's critique of AI or Roger Penrose's argument in The Emperor's New Mind. These critics argued that there are aspects of human consciousness or expertise that can not be simulated by machines. One reply to their arguments is that the biological processes inside the brain can be simulated to any degree of accuracy. This reply was made as early as 1950, by Alan Turing in his classic paper "Computing Machinery and Intelligence". The third objective is generally called artificial general intelligence by researchers. However, Ray Kurzweil prefers the term "strong AI". In his book The Singularity is Near, he focuses on whole brain emulation using conventional computing machines as an approach to implementing artificial brains, and claims (on grounds of computer power continuing an exponential growth trend) that this could be done by 2025. Henry Markram, director of the Blue Brain project (which is attempting brain emulation), made a similar claim (2020) at the Oxford TED conference in 2009. == Approaches to brain simulation == W. Ross Ashby's pioneering work in cybernetics provided an early mathematical framework for understanding adaptive brain-like systems. In his 1952 book Design for a Brain, Ashby proposed that the brain could be modeled as an ultrastable system that maintains equilibrium through continuous adaptation to environmental perturbations. His approach used differential equations and state-space models to describe how neural systems could exhibit purposeful behavior through feedback mechanisms. Ashby's homeostat, a physical machine built in 1948, demonstrated these principles through an electromechanical device with four interconnected units that automatically adjusted their parameters to maintain stability when disturbed. The homeostat represented one of the first attempts to build an artificial system exhibiting brain-like adaptive behavior, influencing subsequent work in adaptive systems, neural networks, and artificial intelligence. Although direct human brain emulation using artificial neural networks on a high-performance computing engine is a commonly discussed approach, there are other approaches. An alternative artificial brain implementation could be based on Holographic Neural Technology (HNeT) non linear phase coherence/decoherence principles. The analogy has been made to quantum processes through the core synaptic algorithm which has strong similarities to the quantum mechanical wave equation. EvBrain is a form of evolutionary software that can evolve "brainlike" neural networks, such as the network immediately behind the retina. In November 2008, IBM received a US$4.9 million grant from the Pentagon for research into creating intelligent computers. The Blue Brain project is being conducted with the assistance of IBM in Lausanne. The project is based on the premise that it is possible to artificially link the neurons "in the computer" by placing thirty million synapses in their proper three-dimensional position. Some proponents of strong AI speculated in 2009 that computers in connection with Blue Brain and Soul Catcher may exceed human intellectual capacity by around 2015, and that it is likely that we will be able to download the human brain at some time around 2050. While Blue Brain is able to represent complex neural connections on the large scale, the project does not achieve the link between brain activity and behaviors executed by the brain. In 2012, project Spaun (Semantic Pointer Architecture Unified Network) attempted to model multiple parts of the human brain through large-scale representations of neural connections that generate complex behaviors in addition to mapping. Spaun's design recreates elements of human brain anatomy. The model, consisting of approximately 2.5 million neurons, includes features of the visual and motor cortices, GABAergic and dopaminergic connections, the ventral tegmental area (VTA), substantia nigra, and others. The design allows for several functions in response to eight tasks, using visual inputs of typed or handwritten characters and outputs carried out by a mechanical arm. Spaun's functions include copying a drawing, recognizing images, and counting. There are good reasons to believe that, regardless of implementation strategy, the predictions of realising artificial brains in the near future are optimistic. In particular brains (including the human brain) and cognition are not currently well understood, and the scale of computation required is unknown. Another near term limitation is that all current approaches for brain simulation require orders of magnitude larger power consumption compared with a human brain. The human brain consumes about 20 W of power, whereas current supercomputers may use as much as 1 MW—i.e., an order of 100,000 more. == Artificial brain thought experiment == Some critics of brain simulation believe that it is simpler to create general intelligent action directly without imitating nature. Some commentators have used the analogy that early attempts to construct flying machines modeled them after birds, but that modern aircraft do not look like birds.
Cut, copy, and paste
Cut, copy, and paste are essential commands of modern human–computer interaction and user interface design. They offer an interprocess communication technique for transferring data through a computer's user interface. The cut command removes the selected data from its original position, and the copy command creates a duplicate; in both cases the selected data is kept in temporary storage called the clipboard. Clipboard data is later inserted wherever a paste command is issued. The data remains available to any application supporting the feature, thus allowing easy data transfer between applications. The command names are a (skeuomorphic) interface metaphor based on the physical procedure used in manuscript print editing to create a page layout, like with paper. The commands were pioneered into computing by Xerox PARC in 1974, popularized by Apple Computer in the 1983 Lisa workstation and the 1984 Macintosh computer, and in a few home computer applications such as the 1984 word processor Cut & Paste. This interaction technique has close associations with related techniques in graphical user interfaces (GUIs) that use pointing devices such as a computer mouse (by drag and drop, for example). Typically, clipboard support is provided by an operating system as part of its GUI and widget toolkit. The capability to replicate information with ease, changing it between contexts and applications, involves privacy concerns because of the risks of disclosure when handling sensitive information. Terms like cloning, copy forward, carry forward, or re-use refer to the dissemination of such information through documents, and may be subject to regulation by administrative bodies. == History == === Origins === The term "cut and paste" comes from the traditional practice in manuscript editing, whereby people cut paragraphs from a page with scissors and paste them onto another page. This practice remained standard into the 1980s. Stationery stores sold "editing scissors" with blades long enough to cut an 8½"-wide page. The advent of photocopiers made the practice easier and more flexible. The act of copying or transferring text from one part of a computer-based document ("buffer") to a different location within the same or different computer-based document was a part of the earliest on-line computer editors. As soon as computer data entry moved from punch-cards to online files (in the mid/late 1960s) there were "commands" for accomplishing this operation. This mechanism was often used to transfer frequently-used commands or text snippets from additional buffers into the document, as was the case with the QED text editor. === Early methods === The earliest editors (designed for teleprinter terminals) provided keyboard commands to delineate a contiguous region of text, then delete or move it. Since moving a region of text requires first removing it from its initial location and then inserting it into its new location, various schemes had to be invented to allow for this multi-step process to be specified by the user. Often this was done with a "move" command, but some text editors required that the text be first put into some temporary location for later retrieval/placement. In 1983, the Apple Lisa became the first text editing system to call that temporary location "the clipboard". Earlier control schemes such as NLS used a verb—object command structure, where the command name was provided first and the object to be copied or moved was second. The inversion from verb—object to object—verb on which copy and paste are based, where the user selects the object to be operated before initiating the operation, was an innovation crucial for the success of the desktop metaphor as it allowed copy and move operations based on direct manipulation. === Popularization === Inspired by early line and character editors, such as Pentti Kanerva's TV-Edit, that broke a move or copy operation into two steps—between which the user could invoke a preparatory action such as navigation—Lawrence G. "Larry" Tesler proposed the names "cut" and "copy" for the first step and "paste" for the second step. Beginning in 1974, he and colleagues at Xerox PARC implemented several text editors that used cut/copy-and-paste commands to move and copy text. Apple Computer popularized this paradigm with its Lisa (1983) and Macintosh (1984) operating systems and applications. The functions were mapped to key combinations using the ⌘ Command key as a special modifier, which is held down while also pressing X for cut, C for copy, or V for paste. These few keyboard shortcuts allow the user to perform all the basic editing operations, and the keys are clustered at the left end of the bottom row of the standard QWERTY keyboard. These are the standard shortcuts: Control-Z (or ⌘ Command+Z) to undo Control-X (or ⌘ Command+X) to cut Control-C (or ⌘ Command+C) to copy Control-V (or ⌘ Command+V) to paste The IBM Common User Access (CUA) standard also uses combinations of the Insert, Del, Shift and Control keys. Early versions of Windows used the IBM standard. Microsoft later also adopted the Apple key combinations with the introduction of Windows, using the control key as modifier key. Similar patterns of key combinations, later borrowed by others, are widely available in most GUI applications. The original cut, copy, and paste workflow, as implemented at PARC, utilizes a unique workflow: With two windows on the same screen, the user could use the mouse to pick a point at which to make an insertion in one window (or a segment of text to replace). Then, by holding shift and selecting the copy source elsewhere on the same screen, the copy would be made as soon as the shift was released. Similarly, holding shift and control would copy and cut (delete) the source. This workflow requires many fewer keystrokes/mouse clicks than the current multi-step workflows, and did not require an explicit copy buffer. It was dropped, one presumes, because the original Apple and IBM GUIs were not high enough density to permit multiple windows, as were the PARC machines, and so multiple simultaneous windows were rarely used. == Cut and paste == Computer-based editing can involve very frequent use of cut-and-paste operations. Most software-suppliers provide several methods for performing such tasks, and this can involve (for example) key combinations, pulldown menus, pop-up menus, or toolbar buttons. The user selects or "highlights" the text or file for moving by some method, typically by dragging over the text or file name with the pointing-device or holding down the Shift key while using the arrow keys to move the text cursor. The user performs a "cut" operation via key combination Ctrl+x (⌘+x for Macintosh users), menu, or other means. Visibly, "cut" text immediately disappears from its location. "Cut" files typically change color to indicate that they will be moved. Conceptually, the text has now moved to a location often called the clipboard. The clipboard typically remains invisible. On most systems only one clipboard location exists, hence another cut or copy operation overwrites the previously stored information. Many UNIX text-editors provide multiple clipboard entries, as do some Macintosh programs such as Clipboard Master, and Windows clipboard-manager programs such as the one in Microsoft Office. The user selects a location for insertion by some method, typically by clicking at the desired insertion point. A paste operation takes place which visibly inserts the clipboard text at the insertion point. (The paste operation does not typically destroy the clipboard text: it remains available in the clipboard and the user can insert additional copies at other points). Whereas cut-and-paste often takes place with a mouse-equivalent in Windows-like GUI environments, it may also occur entirely from the keyboard, especially in UNIX text editors, such as Pico or vi. Cutting and pasting without a mouse can involve a selection (for which Ctrl+x is pressed in most graphical systems) or the entire current line, but it may also involve text after the cursor until the end of the line and other more sophisticated operations. The clipboard usually stays invisible, because the operations of cutting and pasting, while actually independent, usually take place in quick succession, and the user (usually) needs no assistance in understanding the operation or maintaining mental context. Some application programs provide a means of viewing, or sometimes even editing, the data on the clipboard. == Copy and paste == The term "copy-and-paste" refers to the popular, simple method of reproducing text or other data from a source to a destination. It differs from cut and paste in that the original source text or data does not get deleted or removed. The popularity of this method stems from its simplicity and the ease with which users can move data between various applications visually – without resorting to permanent storage. Use in healthcare do
Format-transforming encryption
In cryptography, format-transforming encryption (FTE) refers to encryption where the format of the input plaintext and output ciphertext are configurable. Descriptions of formats can vary, but are typically compact set descriptors, such as a regular expression. Format-transforming encryption is closely related to, and a generalization of, format-preserving encryption. == Applications of FTE == === Restricted fields or formats === Similar to format-preserving encryption, FTE can be used to control the format of ciphertexts. The canonical example is a credit card number, such as 1234567812345670 (16 bytes long, digits only). However, FTE does not enforce that the input format must be the same as the output format. === Censorship circumvention === FTE is used by the Tor Project to circumvent deep packet inspection by pretending to be some other protocols. The implementation is fteproxy; it was written by the authors who came up with the FTE concept.
BREACH
BREACH (a backronym: Browser Reconnaissance and Exfiltration via Adaptive Compression of Hypertext) is a security vulnerability against HTTPS when using HTTP compression. BREACH is built based on the CRIME security exploit. BREACH was announced at the August 2013 Black Hat USA conference by security researchers Angelo Prado, Neal Harris and Yoel Gluck. == Details == While the CRIME attack was presented as a general attack that could work effectively against a large number of protocols, only exploits against SPDY request compression and TLS compression were demonstrated and largely mitigated in browsers and servers. The CRIME exploits against HTTP compression has not been mitigated at all, even though the authors of CRIME have warned that this vulnerability might be even more widespread than SPDY and TLS compression combined. BREACH is an instance of the CRIME attack against HTTP compression—the use of gzip or DEFLATE data compression algorithms via the content-encoding option within HTTP by many web browsers and servers. Given this compression oracle, the rest of the BREACH attack follows the same general lines as the CRIME exploit, by performing an initial blind brute-force search to guess a few bytes, followed by divide-and-conquer search to expand a correct guess to an arbitrarily large amount of content. == Mitigation == BREACH exploits the compression in the underlying HTTP protocol. Therefore, turning off TLS compression makes no difference to BREACH, which can still perform a chosen-plaintext attack against the HTTP payload. As a result, clients and servers are either forced to disable HTTP compression completely (thus reducing performance), or to adopt workarounds to try to foil BREACH in individual attack scenarios, such as using cross-site request forgery (CSRF) protection. Another suggested approach is to disable HTTP compression whenever the referrer header indicates a cross-site request, or when the header is not present. This approach allows effective mitigation of the attack without losing functionality, only incurring a performance penalty on affected requests. Another approach is to add padding at the TLS, HTTP header, or payload level. Around 2013–2014, there was an IETF draft proposal for a TLS extension for length-hiding padding that, in theory, could be used as a mitigation against this attack. It allows the actual length of the TLS payload to be disguised by the insertion of padding to round it up to a fixed set of lengths, or to randomize the external length, thereby decreasing the likelihood of detecting small changes in compression ratio that is the basis for the BREACH attack. However, this draft has since expired without further action. A very effective mitigation is HTB (Heal-the-BREACH) that adds random-sized padding to compressed data, providing some variance in the size of the output contents. This randomness delays BREACH from guessing the correct characters in the secret token by a factor of 500 (10-byte max) to 500,000 (100-byte max). HTB protects all websites and pages in the server with minimal CPU usage and minimal bandwidth increase.
Contrast-to-noise ratio
Contrast-to-noise ratio (CNR) is a measure used to determine image quality. CNR is similar to the metric signal-to-noise ratio (SNR), but subtracts a term before taking the ratio. This is important when there is a significant bias in an image, such as from haze. As can be seen in the picture at right, the intensity is rather high even though the features of the image are washed out by the haze. Thus this image may have a high SNR metric, but will have a low CNR metric. One way to define contrast-to-noise ratio is: C = | S A − S B | σ o {\displaystyle C={\frac {|S_{A}-S_{B}|}{\sigma _{o}}}} where SA and SB are signal intensities for signal producing structures A and B in the region of interest and σo is the standard deviation of the pure image noise.
Pinoy baiting
Pinoy baiting is a phrase that has been used to refer to acts by non-Filipino individuals, usually celebrities or YouTubers, of posting content online purportedly with the intention of getting the attention of Filipinos, by being surprised about the Philippines or its people. Pinoy baiters are defined as giving superficial and allegedly insincere praises and similar reactions that give recognition to the Philippines or its people. Subsequent responses by Filipinos to what have been referred to as acts of Pinoy baiting have been criticized as a form of cultural cringe. This criticism would subsequently give the advice that Filipinos should not constantly require validation from non-Filipinos about themselves or their country. == Pinoy baiting mediums == === Reaction videos === On social media such as YouTube, channels with specific focus on showing their reaction towards and opinions about certain videos or topics are called reaction channels. Reaction videos are very popular and require minimal effort to create, and thus made it easy for alleged Pinoy baiting to thrive within this video-making genre. === Travel vlogs === Vlogging, short for video blogging, grew in popularity in the 2020s. Most of the popular alleged Pinoy-baiting channels tend to be vlog channels, normally following the same script under such titles as "The Philippines changed us/me", "First impression of the Philippines", "Is this really Manila?" and "Filipinos are such Kind/Good People!", and made while travelling to touristy areas such as Boracay or Bonifacio Global City and taste-testing the fast food chain Jollibee, among others. == Criticism of the phrase == Philippines-based Korean vlogger Jessica Lee had been accused by some YouTube viewers of engaging in Pinoy baiting. In a response vlog, Lee acknowledged that there may be individuals engaging in this "business strategy" of gaining views and subscribers from one of the largest communities online. However, she questioned the objectivity of some use of the phrase, citing any vlogging subject as fair game for a negative impression of being a "baiting" tool for the vlogger treating of that subject. She also invoked vloggers' freedom to choose whatever subject they want to talk about in a deep or shallow manner, while enjoining citizens to exercise their free-market right to unfollow vloggers they hate and follow those vloggers that "make them happy". She also gave her critics an explanation why she ended up vlogging about Philippine and Filipino subjects.