AI Coding Tools

Explore the best AI Coding Tools — independent reviews, comparisons, pricing and step-by-step how-to guides, curated by Aizhi.

• 

  Color picker

  A color picker (also color chooser or color tool) is a graphical user interface widget, usually found within graphics software or online, used to select colors and, in some cases, to create color schemes (the color picker might be more sophisticated than the palette included with the program). Operating systems such as Microsoft Windows or macOS have a system color picker, which can be used by third-party programs (e.g., Adobe Photoshop). == History == The concept of color pickers dates back to the early days of computer graphics and digital design. Early versions were rudimentary, often featuring basic color palettes and limited functionality. One of the first drawing programs to include a color picker was SketchPad (also referred to as LisaSketch), designed by Bill Atkinson in 1983 to showcase LisaGraf's capabilities. It used a black and white pattern system, using dithering to create the illusion of color depth. With the increased popularity of personal computers with color graphics, there soon came software similar to SketchPad that supported more than two colors, like Broderbund's Dazzle Draw for the Apple II or Electronic Arts' Deluxe Paint. However, the color pickers present in those programs relied on indexed colors. Color pickers, resembling ones used in modern software with support for direct, 24-bit color, appeared soon after the release of the Macintosh II, with the release of programs like Adobe Photoshop and Corel Painter. As the increase of color depth allowed the choice of significantly more colors, the shape and form of color pickers started to diverge. For example, Adobe Photoshop used a hue-saturation color wheel with a slider for brightness in version 0.63, later on switching to a rectangular design accompanied by a hue slider. Corel Painter pioneered the triangular saturation and brightness picker with a hue ring around it, aiming to better represent the continuity of the hue spectrum and the relationship between saturation and brightness. == Purpose == A color picker is used to select and adjust color values. In graphic design and image editing, users typically choose colors via an interface with a visual representation of a color—organized with quasi-perceptually-relevant hue, saturation and lightness dimensions (HSL) – instead of keying in alphanumeric text values. Because color appearance depends on comparison of neighboring colors (see color vision), many interfaces attempt to clarify the relationships between colors. == Interface == Color tools can vary in their interface. Some may use sliders, buttons, text boxes for color values, or direct manipulation. Often a two-dimensional square is used to create a range of color values (such as lightness and saturation) that can be clicked on or selected in some other manner. Drag and drop, color droppers, and various other forms of interfaces are commonly used as well. Usually, color values are also displayed numerically, so they can be precisely remembered and keyed-in later, such as three values of 0-255 representing red, green, and blue, respectively. === Eyedropper === The eyedropper is a tool present in most color pickers and graphics software that allows a user to read a color at a specific point in an image, or position on a display. This enables the color to be transferred to other applications particularly quickly. Modern implementations of eyedropper tools are also available as browser extensions, allowing users to pick colors directly from web pages, such as in Google Chrome and Microsoft Edge. == Working == A color picker has two main parts, first a color slider and second a color canvas. The color slider has a linear or radial gradient of the seven rainbow colors i.e. Violet, Indigo, Blue, Green, Yellow, Orange and Red. It allows one to choose any of the seven primary colors. The color value chosen from the color slider instantly reflects in the color canvas. The color canvas is a mixture of two linear color gradients. First a linear gradient of the current chosen color and second a linear gradient of the black color. This mixture of color gradients lets one choose a lighter and darker version of the current chosen color from the color slider.

  Read more →
• 

  Evaluation of binary classifiers

  Evaluation of a binary classifier typically assigns a numerical value, or values, to a classifier that represent its accuracy. An example is error rate, which measures how frequently the classifier makes a mistake. There are many metrics that can be used; different fields have different preferences. For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred. An important distinction is between metrics that are independent of the prevalence or skew (how often each class occurs in the population), and metrics that depend on the prevalence – both types are useful, but they have very different properties. Often, evaluation is used to compare two methods of classification, so that one can be adopted and the other discarded. Such comparisons are more directly achieved by a form of evaluation that results in a single unitary metric rather than a pair of metrics. == Contingency table == Given a data set, a classification (the output of a classifier on that set) gives two numbers: the number of positives and the number of negatives, which add up to the total size of the set. To evaluate a classifier, one compares its output to another reference classification – ideally a perfect classification, but in practice the output of another gold standard test – and cross tabulates the data into a 2×2 contingency table, comparing the two classifications. One then evaluates the classifier relative to the gold standard by computing summary statistics of these 4 numbers. Generally these statistics will be scale invariant (scaling all the numbers by the same factor does not change the output), to make them independent of population size, which is achieved by using ratios of homogeneous functions, most simply homogeneous linear or homogeneous quadratic functions. Say we test some people for the presence of a disease. Some of these people have the disease, and our test correctly says they are positive. They are called true positives (TP). Some have the disease, but the test incorrectly claims they don't. They are called false negatives (FN). Some don't have the disease, and the test says they don't – true negatives (TN). Finally, there might be healthy people who have a positive test result – false positives (FP). These can be arranged into a 2×2 contingency table (confusion matrix), conventionally with the test result on the vertical axis and the actual condition on the horizontal axis. These numbers can then be totaled, yielding both a grand total and marginal totals. Totaling the entire table, the number of true positives, false negatives, true negatives, and false positives add up to 100% of the set. Totaling the columns (adding vertically) the number of true positives and false positives add up to 100% of the test positives, and likewise for negatives. Totaling the rows (adding horizontally), the number of true positives and false negatives add up to 100% of the condition positives (conversely for negatives). The basic marginal ratio statistics are obtained by dividing the 2×2=4 values in the table by the marginal totals (either rows or columns), yielding 2 auxiliary 2×2 tables, for a total of 8 ratios. These ratios come in 4 complementary pairs, each pair summing to 1, and so each of these derived 2×2 tables can be summarized as a pair of 2 numbers, together with their complements. Further statistics can be obtained by taking ratios of these ratios, ratios of ratios, or more complicated functions. The contingency table and the most common derived ratios are summarized below; see sequel for details. Note that the rows correspond to the condition actually being positive or negative (or classified as such by the gold standard), as indicated by the color-coding, and the associated statistics are prevalence-independent, while the columns correspond to the test being positive or negative, and the associated statistics are prevalence-dependent. There are analogous likelihood ratios for prediction values, but these are less commonly used, and not depicted above. == Pairs of metrics == Often accuracy is evaluated with a pair of metrics composed in a standard pattern. === Sensitivity and specificity === The fundamental prevalence-independent statistics are sensitivity and specificity. Sensitivity or True Positive Rate (TPR), also known as recall, is the proportion of people that tested positive and are positive (True Positive, TP) of all the people that actually are positive (Condition Positive, CP = TP + FN). It can be seen as the probability that the test is positive given that the patient is sick. With higher sensitivity, fewer actual cases of disease go undetected (or, in the case of the factory quality control, fewer faulty products go to the market). Specificity (SPC) or True Negative Rate (TNR) is the proportion of people that tested negative and are negative (True Negative, TN) of all the people that actually are negative (Condition Negative, CN = TN + FP). As with sensitivity, it can be looked at as the probability that the test result is negative given that the patient is not sick. With higher specificity, fewer healthy people are labeled as sick (or, in the factory case, fewer good products are discarded). The relationship between sensitivity and specificity, as well as the performance of the classifier, can be visualized and studied using the Receiver Operating Characteristic (ROC) curve. In theory, sensitivity and specificity are independent in the sense that it is possible to achieve 100% in both (such as in the red/blue ball example given above). In more practical, less contrived instances, however, there is usually a trade-off, such that they are inversely proportional to one another to some extent. This is because we rarely measure the actual thing we would like to classify; rather, we generally measure an indicator of the thing we would like to classify, referred to as a surrogate marker. The reason why 100% is achievable in the ball example is because redness and blueness is determined by directly detecting redness and blueness. However, indicators are sometimes compromised, such as when non-indicators mimic indicators or when indicators are time-dependent, only becoming evident after a certain lag time. The following example of a pregnancy test will make use of such an indicator. Modern pregnancy tests do not use the pregnancy itself to determine pregnancy status; rather, human chorionic gonadotropin is used, or hCG, present in the urine of gravid females, as a surrogate marker to indicate that a woman is pregnant. Because hCG can also be produced by a tumor, the specificity of modern pregnancy tests cannot be 100% (because false positives are possible). Also, because hCG is present in the urine in such small concentrations after fertilization and early embryogenesis, the sensitivity of modern pregnancy tests cannot be 100% (because false negatives are possible). === Positive and negative predictive values === In addition to sensitivity and specificity, the performance of a binary classification test can be measured with positive predictive value (PPV), also known as precision, and negative predictive value (NPV). The positive prediction value answers the question "If the test result is positive, how well does that predict an actual presence of disease?". It is calculated as TP/(TP + FP); that is, it is the proportion of true positives out of all positive results. The negative prediction value is the same, but for negatives, naturally. ==== Impact of prevalence on predictive values ==== Prevalence has a significant impact on prediction values. As an example, suppose there is a test for a disease with 99% sensitivity and 99% specificity. If 2000 people are tested and the prevalence (in the sample) is 50%, 1000 of them are sick and 1000 of them are healthy. Thus about 990 true positives and 990 true negatives are likely, with 10 false positives and 10 false negatives. The positive and negative prediction values would be 99%, so there can be high confidence in the result. However, if the prevalence is only 5%, so of the 2000 people only 100 are really sick, then the prediction values change significantly. The likely result is 99 true positives, 1 false negative, 1881 true negatives and 19 false positives. Of the 19+99 people tested positive, only 99 really have the disease – that means, intuitively, that given that a patient's test result is positive, there is only 84% chance that they really have the disease. On the other hand, given that the patient's test result is negative, there is only 1 chance in 1882, or 0.05% probability, that the patient has the disease despite the test result. === Precision and recall === Precision and recall can be interpreted as (estimated) conditional probabilities: Precision is given by P ( C = P | C ^ = P ) {\displaystyle P(C=P|{\hat {C}}=P)} while recall is given by P ( C ^ = P | C = P ) {\displaystyle P({\hat {C}}=P|C=P)} , where C ^ {\

  Read more →
• 

  Reparameterization trick

  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.

  Read more →
• 

  Data-centric AI

  Data-centric AI is an approach within artificial intelligence that emphasizes on improving the quality, consistency and representativeness of the data used to train machine learning models, rather than focusing primarily on optimizing model architectures or algorithms. This idea has gained traction as researchers and practitioners have come to believe that many performance limitations of machine learning systems stem from issues such as noisy labels, biased datasets, and lack of coverage in the data. Data-centric AI involves disciplined approach to data cleaning, augmentation, labeling, and governance that improves model performance and reliability in applications such as computer vision, natural language processing, and further.

  Read more →
• 

  Automaton

  An automaton ( ; pl.: automata or automatons) is a relatively self-operating machine or control mechanism designed to automatically follow a sequence of operations or respond to predetermined instructions. Some automata, such as bellstrikers in mechanical clocks, are designed to give the illusion to the casual observer that they are operating under their own power or will, like a mechanical robot. The term has long been commonly associated with automated puppets that resemble moving humans or animals, built to impress and/or to entertain people. Animatronics are a modern type of automata with electronics, often used for the portrayal of characters or creatures in films and in theme park attractions. == Etymology == The word automaton is the latinization of the Ancient Greek automaton (αὐτόματον), which means "acting of one's own will". It was first used by Homer to describe an automatic door opening, or automatic movement of wheeled tripods. It is more often used to describe non-electronic moving machines, especially those that have been made to resemble human or animal actions, such as the jacks on old public striking clocks, or the cuckoo and any other animated figures on a cuckoo clock. == History == === Ancient === There are many examples of automata in Greek mythology: Hephaestus created automata for his workshop; Talos was an artificial man of bronze; King Alkinous of the Phaiakians employed gold and silver watchdogs. According to Aristotle, Daedalus used quicksilver to make his wooden statue of Aphrodite move. In other Greek legends he used quicksilver to install voice in his moving statues. The automata in the Hellenistic world were intended as tools, toys, religious spectacles, or prototypes for demonstrating basic scientific principles. Numerous water-powered automata were built by Ktesibios, a Greek inventor and the first head of the Great Library of Alexandria; for example, he "used water to sound a whistle and make a model owl move. He had invented the world's first 'cuckoo clock'". This tradition continued in Alexandria with inventors such as the Greek mathematician Hero of Alexandria (sometimes known as Heron), whose writings on hydraulics, pneumatics, and mechanics described siphons, a fire engine, a water organ, the aeolipile, and a programmable cart. Philo of Byzantium was famous for his inventions. Complex mechanical devices are known to have existed in Hellenistic Greece, though the only surviving example is the Antikythera mechanism, the earliest known analog computer. The clockwork is thought to have come originally from Rhodes, where there was apparently a tradition of mechanical engineering; the island was renowned for its automata; to quote Pindar's seventh Olympic Ode: The animated figures stand Adorning every public street And seem to breathe in stone, or move their marble feet. However, the information gleaned from recent scans of the fragments indicate that it may have come from the colonies of Corinth in Sicily and implies a connection with Archimedes. According to Jewish legend, King Solomon used his wisdom to design a throne with mechanical animals which hailed him as king when he ascended it; upon sitting down an eagle would place a crown upon his head, and a dove would bring him a Torah scroll. It is also said that when King Solomon stepped upon the throne, a mechanism was set in motion. As soon as he stepped upon the first step, a golden ox and a golden lion each stretched out one foot to support him and help him rise to the next step. On each side, the animals helped the King up until he was comfortably seated upon the throne. In ancient China, a curious account of automata is found in the Lie Zi text, believed to have originated around 400 BCE and compiled around the fourth century CE. Within it there is a description of a much earlier encounter between King Mu of Zhou (1023–957 BCE) and a mechanical engineer known as Yan Shi, an 'artificer'. The latter proudly presented the king with a very realistic and detailed life-size, human-shaped figure of his mechanical handiwork: The king stared at the figure in astonishment. It walked with rapid strides, moving its head up and down, so that anyone would have taken it for a live human being. The artificer touched its chin, and it began singing, perfectly in tune. He touched its hand, and it began posturing, keeping perfect time...As the performance was drawing to an end, the robot winked its eye and made advances to the ladies in attendance, whereupon the king became incensed and would have had Yen Shih [Yan Shi] executed on the spot had not the latter, in mortal fear, instantly taken the robot to pieces to let him see what it really was. And, indeed, it turned out to be only a construction of leather, wood, glue and lacquer, variously coloured white, black, red and blue. Examining it closely, the king found all the internal organs complete—liver, gall, heart, lungs, spleen, kidneys, stomach and intestines; and over these again, muscles, bones and limbs with their joints, skin, teeth and hair, all of them artificial...The king tried the effect of taking away the heart, and found that the mouth could no longer speak; he took away the liver and the eyes could no longer see; he took away the kidneys and the legs lost their power of locomotion. The king was delighted. Other notable examples of automata include Archytas' dove, mentioned by Aulus Gellius. Similar Chinese accounts of flying automata are written of the 5th century BC Mohist philosopher Mozi and his contemporary Lu Ban, who made artificial wooden birds (ma yuan) that could successfully fly according to the Han Fei Zi and other texts. === Medieval === The manufacturing tradition of automata continued in the Greek world well into the Middle Ages. On his visit to Constantinople in 949 ambassador Liutprand of Cremona described automata in the emperor Theophilos' palace, including "lions, made either of bronze or wood covered with gold, which struck the ground with their tails and roared with open mouth and quivering tongue," "a tree of gilded bronze, its branches filled with birds, likewise made of bronze gilded over, and these emitted cries appropriate to their species" and "the emperor's throne" itself, which "was made in such a cunning manner that at one moment it was down on the ground, while at another it rose higher and was to be seen up in the air." Similar automata in the throne room (singing birds, roaring and moving lions) were described by Luitprand's contemporary the Byzantine emperor Constantine Porphyrogenitus, in his book De Ceremoniis (Perì tês Basileíou Tákseōs). In the mid-8th century, the first wind powered automata were built: "statues that turned with the wind over the domes of the four gates and the palace complex of the Round City of Baghdad". The "public spectacle of wind-powered statues had its private counterpart in the 'Abbasid palaces where automata of various types were predominantly displayed." Also in the 8th century, the Muslim alchemist, Jābir ibn Hayyān (Geber), included recipes for constructing artificial snakes, scorpions, and humans that would be subject to their creator's control in his coded Book of Stones. In 827, Abbasid caliph al-Ma'mun had a silver and golden tree in his palace in Baghdad, which had the features of an automatic machine. There were metal birds that sang automatically on the swinging branches of this tree built by Muslim inventors and engineers. The Abbasid caliph al-Muqtadir also had a silver and golden tree in his palace in Baghdad in 917, with birds on it flapping their wings and singing. In the 9th century, the Banū Mūsā brothers invented a programmable automatic flute player and which they described in their Book of Ingenious Devices. Al-Jazari described complex programmable humanoid automata amongst other machines he designed and constructed in the Book of Knowledge of Ingenious Mechanical Devices in 1206. His automaton was a boat with four automatic musicians that floated on a lake to entertain guests at royal drinking parties. His mechanism had a programmable drum machine with pegs (cams) that bump into little levers that operate the percussion. The drummer could be made to play different rhythms and drum patterns if the pegs were moved around. Al-Jazari constructed a hand washing automaton first employing the flush mechanism now used in modern toilets. It features a female automaton standing by a basin filled with water. When the user pulls the lever, the water drains and the automaton refills the basin. His "peacock fountain" was another more sophisticated hand washing device featuring humanoid automata as servants who offer soap and towels. Mark E. Rosheim describes it as follows: "Pulling a plug on the peacock's tail releases water out of the beak; as the dirty water from the basin fills the hollow base a float rises and actuates a linkage which makes a servant figure appear from behind a door under the peacock and offer soap.

  Read more →
• 

  Qloo

  Qloo (pronounced "clue") is a company that uses artificial intelligence (AI) to understand taste and cultural correlations. It provides companies with an application programming interface (API). It received funding from Leonardo DiCaprio, Elton John, Barry Sternlicht, Pierre Lagrange and others. Qloo establishes consumer preference correlations via machine learning across data spanning cultural domains including music, film, television, dining, nightlife, fashion, books, and travel. The recommender system uses AI to predict correlations for further applications. == History == Qloo was founded in 2012 by chief executive officer Alex Elias and chief operating officer Jay Alger. Qloo initially launched an app designed for consumers, allowing them to understand their own tastes and receive personalized recommendations. The company amassed several million users and built a large catalog of cultural entities and corresponding user sentiment. In 2012, Qloo raised $1.4 million in seed funding from investors including Cedric the Entertainer, and venture capital firm Kindler Capital. Qloo had a public beta release in November 2012 after its initial funding. In 2013, the company raised an additional $1.6 million from Cross Creek Pictures founding partner Tommy Thompson, and Samih Toukan and Hussam Khoury, founders of Maktoob, an Internet services company purchased by Yahoo! for $164 million in 2009. On November 14, 2013, a website and an iPhone app were announced. The company later released an Android app, and tablet versions, in mid-2014. In 2015, Twitter approached Qloo about powering personalized social feeds and targeted eCommerce ads on the platform based on what users were posting. Qloo developed an enterprise-grade API to support Twitter’s needs. Twitter ended up pivoting to enable brands to use the social platform for customer service and support, but Qloo was able to sell access to its cultural intelligence via API to many other enterprise clients, marking the official transition from a B2C company to a B2B company. In 2016, Qloo secured $4.5 million in venture capital investment. The $4.5 million was split between a number of investors, including Barry Sternlicht, Pierre Lagrange, and Leonardo DiCaprio. In July 2017, Qloo raised $6.5 million in funding rounds from AXA Strategic Ventures, and Elton John. Following the investment, the founders stated in an interview with Tech Crunch that they would use the investment to expand Qloo's database. They hoped the move would secure larger contracts with corporate clients. At the time, clients already included Fortune 500 companies such as Twitter, PepsiCo, and BMW. In 2019, the company announced that it had acquired cultural recommendation service TasteDive, with Alex Elias becoming chairman of TasteDive. In September 2019, Qloo was named among the Top 14 Artificial Intelligence APIs by ProgrammableWeb. In 2022, Qloo raised $15M in Series B funding from Eldridge and AXA Venture Partners, enabling the privacy-centric AI leader to expand its team of world-class data scientists, enrich its technology, and build on its sales channels in order to continue to offer premier insights into global consumer taste for Fortune 500 companies across the globe. Qloo was recognized as the "Best Decision Intelligence Company" at the 2023 AI Breakthrough Awards. Also in 2023, the company was awarded a Top Performer Award by SourceForge. As of 2024, Qloo is a three-time Inc. 5000 honoree: No. 360 (2022), No. 344 (2021), No. 187 (2020). Qloo raised $25 million Series C round on February 21, 2024. The round was led by AI Ventures with participation from AXA Venture Partners, Eldridge, and Moderne Ventures, allowing Qloo to address new commercial surface areas for Taste AI, including on-device learning and foundational models leveraging Qloo, as well as introduce self-service platform to make consumer and taste analytics available to small and mid-sized enterprises and individuals. Qloo also announced pursuing opportunistic M&A using its balance sheet along the lines of the TasteDive acquisition completed, which expanded Qloo's first-party data moat and corpus of cultural learning. This latest financing brought the total amount raised since the company's founding in 2012 to over $56 million. == Services and features == Qloo calls itself a cultural AI platform to provide real-time correlation data across domains of culture and entertainment including: film, music, television, dining, nightlife, fashion, books, and travel. Each category contains subcategories. Qloo’s knowledge of a user's taste in one category can be utilized to offer suggestions in other categories. Users then rate the suggestions, providing it with feedback for future suggestions. Qloo has partnerships with companies such as Expedia and iTunes. == Technology == Qloo’s Taste AI technology uses machine learning to decode and predict consumers’ interests, maintaining user anonymity. It is powered by 3.7 billion lifestyle entities (brands, music, film, TV, dining, nightlife, fashion, books, travel, and more) and trillions of anonymized consumer behavioral signals. Through AI, Qloo identifies patterns in these data signals, making predictions about how much interest a person or group has in a concept or thing. Central to Qloo’s technology are algorithms designed to detect and mitigate biases within datasets and models, allowing Qloo to assess the fairness of its AI systems with a focus on attributes such as age, gender, and race, enabling the company to fine-tune its AI models to align with their ethical standards. They also use visualization tools to probe the behavior of their AI models for conducting counterfactual analyses and for comparing the performances of the AI models across diverse demographic segments. Qloo’s Taste AI doesn’t collect or use any Personally Identifiable Information (PII). Instead, it derives recommendations for audience segments based on co-occurrences between lifestyle entities and anonymized behavioral signals. == Applications == Starbucks uses Qloo to create in-store music playlists tailored to specific neighborhoods. Hershey’s uses Qloo to customize the content of assorted candy bags. Michelin uses Qloo to serve recommendations in its Michelin Guide app. Netflix leverages Qloo’s technology to enhance merchandising by identifying actors who resonate with certain demographics. Qloo also works with PepsiCo, Samsung, The New York Mets, BuzzFeed, and Ticketmaster, Universal Music Group, and OOH advertising company JCDecaux.

  Read more →
• 

  Supermind AI

  Supermind is a state-funded Chinese artificial intelligence platform that tracks scientists and researchers internationally. The platform is the flagship project of Shenzhen's International Science and Technology Information Center. It mines data from science and technology databases such as Springer, Wiley, Clarivate and Elsevier. It is intended to detect technological breakthroughs and to identify possible sources of talent as part of China's efforts to advance technologically. The platform also uses government data security and security intelligence organizations such as Peng Cheng Laboratory, the China National GeneBank, BGI Group and the Key Laboratory of New Technologies of Security Intelligence. According to Hong Kong-based Asia Times, the platform, "While not an overt espionage tool...may be used to identify key personnel who could be bribed, deceived or manipulated into divulging classified information". The Organisation for Economic Co-operation and Development (OECD) flagged the project as an incident, meaning it may be of interest to policymakers and other stakeholders. US technology group American Edge Project criticized the project as a global risk of China's security services using the platform to place agents in jobs with access to important information, recruit technical personnel, and identify targets for hacking operations.

  Read more →
• 

  Outline of deep learning

  The following outline is provided as an overview of, and topical guide to, deep learning: Deep learning is a subfield of machine learning and artificial intelligence based on artificial neural networks with multiple processing layers. It emphasizes representation learning and is widely used in areas such as computer vision, natural language processing, speech recognition, recommender systems, robotics, and generative artificial intelligence. == Ways to categorize deep learning == A field of study A branch of artificial intelligence A subfield of machine learning A subfield of computer science A form of representation learning A class of methods based on artificial neural networks An approach used in computational statistics == History == === Precursors === Cybernetics Perceptron Connectionism Neocognitron Backpropagation === Milestones === LeNet Long short-term memory Deep belief network AlexNet Sequence to sequence learning Generative adversarial network Residual neural network Transformer BERT Generative pre-trained transformer Diffusion model === Related histories === History of artificial intelligence History of machine learning Timeline of machine learning == Core concepts == == Learning settings == Supervised learning Unsupervised learning Self-supervised learning Semi-supervised learning Reinforcement learning Transfer learning Multitask learning Multimodal learning Online machine learning Continual learning == Common tasks == Image classification Object detection Image segmentation Automatic speech recognition Neural machine translation Question answering Automatic summarization Text-to-image model Protein structure prediction == Architectures == === Feedforward and convolutional architectures === Feedforward neural network Multilayer perceptron Convolutional neural network Radial basis function network Residual neural network U-Net === Recurrent and sequence architectures === Recurrent neural network Long short-term memory Gated recurrent unit Sequence to sequence learning Recursive neural network === Representation-learning architectures === Autoencoder Denoising autoencoder Sparse autoencoder Variational autoencoder Restricted Boltzmann machine Deep belief network === Attention and transformer architectures === Attention (machine learning) Transformer BERT Generative pre-trained transformer Vision transformer === Generative and probabilistic architectures === Autoregressive model Diffusion model Energy-based model Generative adversarial network Mixture of experts === Graph and memory architectures === Graph neural network Graph convolutional network Siamese network Neural Turing machine Memory network Echo state network Capsule neural network == Neural network components and techniques == Artificial neuron Activation function Rectified linear unit Sigmoid function Softmax function Embedding Convolution Pooling layer Attention Batch normalization Layer normalization Residual connections == Training and optimization == Backpropagation Gradient descent Stochastic gradient descent Adam optimization Learning rate Loss function Cross-entropy Mean squared error Regularization Dropout Early stopping Batch normalization Data augmentation Transfer learning Knowledge distillation Ensemble learning Curriculum learning == Datasets and benchmarks == CIFAR-10 ImageNet MNIST database Common Objects in Context (COCO) General Language Understanding Evaluation (GLUE) benchmark LibriSpeech SQuAD == Applications == === Computer vision === Computer vision Facial recognition system Image classification Image segmentation Medical imaging Object detection Optical character recognition === Natural language processing === Automatic summarization Chatbot Information retrieval Large language model Natural language processing Neural machine translation Question answering Sentiment analysis === Speech and audio === Automatic speech recognition Music information retrieval Speaker recognition Speech synthesis === Science and medicine === Bioinformatics Computational biology Drug discovery Medical diagnosis Protein structure prediction === Robotics and control === Autonomous car Computer game bot Control theory Robotics === Recommendation, search, and forecasting === Anomaly detection Forecasting Fraud detection Recommender system Search engine === Generative artificial intelligence === Deepfake Generative artificial intelligence Large language model Speech synthesis Text-to-image model === Computer graphics and video games === Deep Learning Anti-Aliasing (DLAA) Deep Learning Super Sampling (DLSS) == Hardware == AMD Instinct AMD XDNA Application-specific integrated circuit Deep learning processor, Neural processing unit (NPU), or Neural Engine Field-programmable gate array General-purpose computing on graphics processing units (GPGPU) Graphics processing unit NVIDIA Deep Learning Accelerator (NVDLA) Tensor processing unit Vision processing unit Wafer-scale integration === Supporting software platforms === CUDA Metal ROCm == Software == === Open-source frameworks and libraries === === Neural network software === EDLUT Emergent Encog JOONE Neuroph NeuroSolutions OpenNN Peltarion Synapse SNNS === Platforms, tools, and deployment === Amazon SageMaker Google Colab Hugging Face Kaggle Kubeflow MLflow ONNX OpenVINO TensorFlow Hub == Algorithms for deep learning and neural networks == Backpropagation Conjugate gradient method Generalized Hebbian algorithm Gradient descent Levenberg–Marquardt algorithm Perceptron Quasi-Newton method Wake-sleep algorithm == Methods and related topics == === Representation and metric learning === Contrastive learning Embedding Feature learning Manifold learning Metric learning === Generative modeling === Autoregressive model Diffusion model Generative adversarial network Generative model Variational inference === Efficient and scalable deep learning === Knowledge distillation Low-rank approximation Mixture of experts Quantization Sparsity === Reliability, safety, and interpretability === Adversarial machine learning AI alignment Algorithmic bias Catastrophic forgetting Differential privacy Explainable artificial intelligence Federated learning Hallucination (artificial intelligence) == Conferences and workshops == Annual Meeting of the Association for Computational Linguistics Conference on Computer Vision and Pattern Recognition Conference on Neural Information Processing Systems International Conference on Computer Vision International Conference on Learning Representations International Conference on Machine Learning == Organizations == === Research laboratories and institutions === Allen Institute for AI Alberta Machine Intelligence Institute European Laboratory for Learning and Intelligent Systems Google DeepMind Meta AI Mila Microsoft Research Vector Institute === Companies === Anthropic Cerebras Cohere DeepSeek Mistral AI OpenAI Stability AI xAI == Publications == === Books === Deep Learning – Ian Goodfellow and Yoshua Bengio Neural Networks and Deep Learning – Michael Nielsen Perceptrons – Marvin Minsky and Seymour Papert === Journals === IEEE Transactions on Neural Networks and Learning Systems Neural Networks Neural Computation == Influential persons ==

  Read more →
• 

  Artificial intelligence in education

  Artificial intelligence in education (often abbreviated as AIEd) is a subfield of educational technology that studies how to use artificial intelligence to create learning environments. Considerations in the field include data-driven decision-making, AI ethics, data privacy and AI literacy. Concerns include the potential for cheating, over-reliance, equity of access, reduced critical thinking, and the perpetuation of misinformation and bias. == History == Efforts to integrate AI into educational contexts have often followed technological advancement in the history of artificial intelligence. In the 1960s, educators and researchers began developing computer-based instruction systems, such as PLATO, developed by the University of Illinois. In the 1970s and 1980s, intelligent tutoring systems (ITS) were being adapted for classroom instruction. The International Artificial Intelligence in Education Society was founded in 1993. Coinciding with the AI boom of the 2020s, the use of large language models in the global north has been promoted and funded by venture capital and big tech. Companies creating AI services have targeted students and educational institutions as customers. Similarly, pre-AI boom educational companies have expanded their use of AI technologies. These commercial incentives for AIEd use may be related to a potential AI bubble. In the U.S., bipartisan support of AI development in K-12 education has been expressed, but specific implementations and best practices remain contentious. == Theory == AIEd applies theory from education studies, machine learning, and related fields. A 2019 review of the previous decade of studies found that most research prioritized technological design over pedagogical integration. Ouyang and Jiao (2021) propose three paradigms for AI in education, which follow roughly from least to most learner-centered and from requiring least to most technical complexity from the AI systems: AI-directed, learner-as-recipient: AIEd systems present a pre-set curriculum based on statistical patterns that do not adjust to learner's feedback. AI-supported, learner-as-collaborator: Systems that incorporate responsiveness to learner's feedback through, for example, natural language processing, wherein AI can support knowledge construction. AI-empowered, learner-as-leader: This model seeks to position AI as a supplement to human intelligence wherein learners take agency and AI provides consistent and actionable feedback. Some scholars place AI in education within a socio-technical framework. This positions AI alongside other emerging educational technologies, such as computing, the internet, and social media. The framework of Tsao, Heinrichs and Camit (2025) draws on new materialism and posthumanism, specifically Donna Haraway's concept of sympoiesis (making-with). This perspective views learning as an entanglement of human and non-human actors (students, teachers, and AI algorithms), where knowledge is co-composed in contact zones between human context and algorithmic prediction. AI agents have been trained on biased datasets, and thus continue to perpetuate societal biases. Since LLMs were created to produce human-like text, algorithmic bias can be introduced and reproduced. AI's data processing and monitoring reinforce neoliberal approaches to education rather than addressing inequalities. == Applications == Uses of generative AI chatbots in education have included assessment and feedback, machine translations, proof-reading exam question generation and copy editing, or as virtual assistants. Emotional AI in education is the study and development of systems that can detect learners' emotions or provide emotional support in learning. == Usage == === Schools and educators === Following the release of ChatGPT in November 2022, some schools and large school districts blocked access to the site and issued warnings that the use of such tools would be seen as cheating. Governmental and non-governmental organizations such as UNESCO, Article 4 of the European Union's AI Act, and the U.S. Department of Education have published reports advocating for specific AIEd approaches. National higher-education bodies have also published guidance on generative AI, including Ireland's Higher Education Authority, which issued a policy framework for higher education teaching and learning in December 2025. In 2024, UNESCO released updated global guidance for generative AI in education, emphasizing ethical use, teacher training, and data protection to ensure responsible integration of AI tools in learning environments. According to Taso (2025), policy implementation in higher education is interpreted and enacted differently by various organizations. These decentralized policies can lead to inconsistent enforcement and confusion among students regarding what constitutes acceptable use, with the burden of ethical navigation falling on individual teachers and students. AI integration in classrooms has created new forms of invisible labour for educators, who must navigate ambiguous policies, redesign assessments to be AI-resilient, and adjudicate potential academic integrity violations. The use of AI detection tools has also been criticised for creating an adversarial relationship between students and institutions, where students may be falsely accused of misconduct based on probabilistic software. AIEd advocates say that efforts should be made towards increasing global accessibility and training educators to serve underprivileged areas. === Students === Reliance on generative AI has been linked with reduced academic self-esteem and performance, and heightened learned helplessness. Algorithm errors and hallucinations are common flaws in AI agents, making them less trustworthy and reliable. According to a 2025 survey from Inside Higher Ed, 85% of higher education students use generative AI technology in some way, with 25% using AI to complete assignments for them. The most common reason cited for using AI to cheat was pressure to get high grades. 97% of students wanted some form of action from schools on the threat to academic integrity caused by AI, with the most popular options being clearer policies and more education about ethical uses of AI. In September 2025, The Atlantic published an op-ed from a high school senior arguing that the normalization of AI cheating was eroding critical thinking, academic integrity, creativity, and the shared student experience.

  Read more →
• 

  Resisting AI

  Resisting AI: An Anti-fascist Approach to Artificial Intelligence is a book on artificial intelligence (AI) by Dan McQuillan, published in 2022 by Bristol University Press. == Content == Resisting AI takes the form of an extended essay, which contrasts optimistic visions about AI's potential by arguing that AI may best be seen as a continuation and reinforcement of bureaucratic forms of discrimination and violence, ultimately fostering authoritarian outcomes. For McQuillan, AI's promise of objective calculability is antithetical to an egalitarian and just society. McQuillan uses the expression "AI violence" to describe how – based on opaque algorithms – various actors can discriminate against categories of people in accessing jobs, loans, medical care, and other benefits. The book suggests that AI has a political resonance with soft eugenic approaches to the valuation of life by modern welfare states, and that AI exhibits eugenic features in its underlying logic, as well as in its technical operations. The parallel is with historical eugenicists achieving saving to the state by sterilizing defectives so the state would not have to care for their offspring. The analysis of McQuillan goes beyond the known critique of AI systems fostering precarious labour markets, addressing "necropolitics", the politics of who is entitled to live, and who to die. Although McQuillan offers a brief history of machine learning at the beginning of the book – with its need for "hidden and undercompensated labour", he is concerned more with the social impacts of AI rather than with its technical aspects. McQuillan sees AI as the continuation of existing bureaucratic systems that already marginalize vulnerable groups – aggravated by the fact that AI systems trained on existing data are likely to reinforce existing discriminations, e.g. in attempting to optimize welfare distribution based on existing data patterns, ultimately creating a system of "self-reinforcing social profiling". In elaborating on the continuation between existing bureaucratic violence and AI, McQuillan connects to Hannah Arendt's concept of the thoughtless bureaucrat in Eichmann in Jerusalem: A Report on the Banality of Evil, which now becomes the algorithm that, lacking intent, cannot be accountable, and is thus endowed with an "algorithmic thoughtlessness". McQuillan defends the "fascist" in the title of the work by arguing that while not all AI is fascist, this emerging technology of control may end up being deployed by fascist or authoritarian regimes. For McQuillan, AI can support the diffusion of states of exception, as a technology impossible to properly regulate and a mechanism for multiplying exceptions more widely. An example of a scenario where AI systems of surveillance could bring discrimination to a new high is the initiative to create LGBT-free zones in Poland. Skeptical of ethical regulations to control the technology, McQuillan suggests people's councils and workers' councils, and other forms of citizens' agency to resist AI. A chapter titled "Post-Machine Learning" makes an appeal for resistance via currents of thought from feminist science (standpoint theory), post-normal science (extended peer communities), and new materialism; McQuillan encourages the reader to question the meaning of "objectivity" and calls for the necessity of alternative ways of knowing. Among the virtuous examples of resistance – possibly to be adopted by the AI workers themselves – McQuillan notes the Lucas Plan of the workers of Lucas Aerospace Corporation, in which a workforce declared redundant took control, reorienting the enterprise toward useful products. McQuillan advocates for what he calls decomputing, an opposition to the sweeping application and expansion of artificial intelligence. Similar to degrowth, the approach criticizes AI as an outgrowth of the systemic issues within capitalist systems. McQuillan argues that a different future is possible, in which distance between people is reduced rather than increased through AI intermediaries. The work of McQuillan warns against "watered-down forms of engagement" with AI, such as citizen juries, which superficially look like democratic deliberation but may actually obscure important decisions about AI that are outside the purview of the engagement situation (McQuillan 2022, 128). In an interview about the book, McQuillan describes himself as an "AI abolitionist". == Reception == The book has been praised for how it "masterfully disassembles AI as an epistemological, social, and political paradigm". On the critical side, a review in the academic journal Justice, Power and Resistance took exception to the "nightmarish visions of Big Brother" offered by McQuillan, and argued that while many elements of AI may pose concern, a critique should not be based on a caricature of what AI is, concluding that McQuillan's work is "less of a theory and more of a Manifesto". Another review notes "a disconnect between the technical aspects of AI and the socio-political analysis McQuillan provides." Although the book was published before the ChatGPT and large language model debate heated up, the book has not lost relevance to the AI discussion. It is noted for suggesting a link between beliefs in artificial intelligence and beliefs in a racialised and gendered visions of intelligence overall, whereby a certain type of rational, measurable intelligence is privileged, leading to "historical notions of hierarchies of being". The blog Reboot praised McQuillan for offering a theory of harm of AI (why AI could end up hurting people and society) that does not just encourage tackling in isolation specific predicted problems with AI-centric systems: bias, non-inclusiveness, exploitativeness, environmental destructiveness, opacity, and non-contestability. For educational policies could also look at AI following the reading of McQuillan: In his book Resisting AI, Dan McQuillan argues that "When we're thinking about the actuality of AI, we can't separate the calculations in the code from the social context of its application" .... McQuillan's particular concern is how many contemporary applications of AI are amplifying existing inequalities and injustices as well as deepening social divisions and instabilities. His book makes a powerful case for anticipating these effects and actively resisting them for the good of societies. Videos and podcasts with an interest in AI and emerging technology have discussed the book.

  Read more →
• 

  Inductive bias

  The inductive bias (also known as learning bias) of a learning algorithm is the set of assumptions that the learner uses to predict outputs of given inputs that it has not encountered. Inductive bias is anything which makes the algorithm learn one pattern instead of another pattern (e.g., step-functions in decision trees instead of continuous functions in linear regression models). Learning involves searching a space of solutions for a solution that provides a good explanation of the data. However, in many cases, there may be multiple equally appropriate solutions. An inductive bias allows a learning algorithm to prioritize one solution (or interpretation) over another, independently of the observed data. In machine learning, the aim is to construct algorithms that are able to learn to predict a certain target output. To achieve this, the learning algorithm is presented some training examples that demonstrate the intended relation of input and output values. Then the learner is supposed to approximate the correct output, even for examples that have not been shown during training. Without any additional assumptions, this problem cannot be solved since unseen situations might have an arbitrary output value. The kind of necessary assumptions about the nature of the target function are subsumed in the phrase inductive bias. A classical example of an inductive bias is Occam's razor, assuming that the simplest consistent hypothesis about the target function is actually the best. Here, consistent means that the hypothesis of the learner yields correct outputs for all of the examples that have been given to the algorithm. Approaches to a more formal definition of inductive bias are based on mathematical logic. Here, the inductive bias is a logical formula that, together with the training data, logically entails the hypothesis generated by the learner. However, this strict formalism fails in many practical cases in which the inductive bias can only be given as a rough description (e.g., in the case of artificial neural networks), or not at all. == Types == The following is a list of common inductive biases in machine learning algorithms. Maximum conditional independence: if the hypothesis can be cast in a Bayesian framework, try to maximize conditional independence. This is the bias used in the Naive Bayes classifier. Minimum cross-validation error: when trying to choose among hypotheses, select the hypothesis with the lowest cross-validation error. Although cross-validation may seem to be free of bias, the "no free lunch" theorems show that cross-validation must be biased, for example assuming that there is no information encoded in the ordering of the data. Maximum margin: when drawing a boundary between two classes, attempt to maximize the width of the boundary. This is the bias used in support vector machines. The assumption is that distinct classes tend to be separated by wide boundaries. Minimum description length: when forming a hypothesis, attempt to minimize the length of the description of the hypothesis. Minimum features: unless there is good evidence that a feature is useful, it should be deleted. This is the assumption behind feature selection algorithms. Nearest neighbors: assume that most of the cases in a small neighborhood in feature space belong to the same class. Given a case for which the class is unknown, guess that it belongs to the same class as the majority in its immediate neighborhood. This is the bias used in the k-nearest neighbors algorithm. The assumption is that cases that are near each other tend to belong to the same class. == Shift of bias == Although most learning algorithms have a static bias, some algorithms are designed to shift their bias as they acquire more data. This does not avoid bias, since the bias shifting process itself must have a bias.

  Read more →
• 

  Manifold regularization

  In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. == Manifold regularizer == === Motivation === Manifold regularization is a type of regularization, a family of techniques that reduces overfitting and ensures that a problem is well-posed by penalizing complex solutions. In particular, manifold regularization extends the technique of Tikhonov regularization as applied to Reproducing kernel Hilbert spaces (RKHSs). Under standard Tikhonov regularization on RKHSs, a learning algorithm attempts to learn a function f {\displaystyle f} from among a hypothesis space of functions H {\displaystyle {\mathcal {H}}} . The hypothesis space is an RKHS, meaning that it is associated with a kernel K {\displaystyle K} , and so every candidate function f {\displaystyle f} has a norm ‖ f ‖ K {\displaystyle \left\|f\right\|_{K}} , which represents the complexity of the candidate function in the hypothesis space. When the algorithm considers a candidate function, it takes its norm into account in order to penalize complex functions. Formally, given a set of labeled training data ( x 1 , y 1 ) , … , ( x ℓ , y ℓ ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{\ell },y_{\ell })} with x i ∈ X , y i ∈ Y {\displaystyle x_{i}\in X,y_{i}\in Y} and a loss function V {\displaystyle V} , a learning algorithm using Tikhonov regularization will attempt to solve the expression arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ ‖ f ‖ K 2 {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma \left\|f\right\|_{K}^{2}} where γ {\displaystyle \gamma } is a hyperparameter that controls how much the algorithm will prefer simpler functions over functions that fit the data better. Manifold regularization adds a second regularization term, the intrinsic regularizer, to the ambient regularizer used in standard Tikhonov regularization. Under the manifold assumption in machine learning, the data in question do not come from the entire input space X {\displaystyle X} , but instead from a nonlinear manifold M ⊂ X {\displaystyle M\subset X} . The geometry of this manifold, the intrinsic space, is used to determine the regularization norm. === Laplacian norm === There are many possible choices for the intrinsic regularizer ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} . Many natural choices involve the gradient on the manifold ∇ M {\displaystyle \nabla _{M}} , which can provide a measure of how smooth a target function is. A smooth function should change slowly where the input data are dense; that is, the gradient ∇ M f ( x ) {\displaystyle \nabla _{M}f(x)} should be small where the marginal probability density P X ( x ) {\displaystyle {\mathcal {P}}_{X}(x)} , the probability density of a randomly drawn data point appearing at x {\displaystyle x} , is large. This gives one appropriate choice for the intrinsic regularizer: ‖ f ‖ I 2 = ∫ x ∈ M ‖ ∇ M f ( x ) ‖ 2 d P X ( x ) {\displaystyle \left\|f\right\|_{I}^{2}=\int _{x\in M}\left\|\nabla _{M}f(x)\right\|^{2}\,d{\mathcal {P}}_{X}(x)} In practice, this norm cannot be computed directly because the marginal distribution P X {\displaystyle {\mathcal {P}}_{X}} is unknown, but it can be estimated from the provided data. === Graph-based approach of the Laplacian norm === When the distances between input points are interpreted as a graph, then the Laplacian matrix of the graph can help to estimate the marginal distribution. Suppose that the input data include ℓ {\displaystyle \ell } labeled examples (pairs of an input x {\displaystyle x} and a label y {\displaystyle y} ) and u {\displaystyle u} unlabeled examples (inputs without associated labels). Define W {\displaystyle W} to be a matrix of edge weights for a graph, where W i j {\displaystyle W_{ij}} is a similarity built from distance measure between the data points x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} (so that more close implies higher W i j {\displaystyle W_{ij}} ). Define D {\displaystyle D} to be a diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D − W {\displaystyle D-W} . Then, as the number of data points ℓ + u {\displaystyle \ell +u} increases, L {\displaystyle L} converges to the Laplace–Beltrami operator Δ M {\displaystyle \Delta _{M}} , which is the divergence of the gradient ∇ M {\displaystyle \nabla _{M}} . Then, if f {\displaystyle \mathbf {f} } is a vector of the values of f {\displaystyle f} at the data, f = [ f ( x 1 ) , … , f ( x l + u ) ] T {\displaystyle \mathbf {f} =[f(x_{1}),\ldots ,f(x_{l+u})]^{\mathrm {T} }} , the intrinsic norm can be estimated: ‖ f ‖ I 2 = 1 ( ℓ + u ) 2 f T L f {\displaystyle \left\|f\right\|_{I}^{2}={\frac {1}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As the number of data points ℓ + u {\displaystyle \ell +u} increases, this empirical definition of ‖ f ‖ I 2 {\displaystyle \left\|f\right\|_{I}^{2}} converges to the definition when P X {\displaystyle {\mathcal {P}}_{X}} is known. === Solving the regularization problem with graph-based approach === Using the weights γ A {\displaystyle \gamma _{A}} and γ I {\displaystyle \gamma _{I}} for the ambient and intrinsic regularizers, the final expression to be solved becomes: arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ A ‖ f ‖ K 2 + γ I ( ℓ + u ) 2 f T L f {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma _{A}\left\|f\right\|_{K}^{2}+{\frac {\gamma _{I}}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As with other kernel methods, H {\displaystyle {\mathcal {H}}} may be an infinite-dimensional space, so if the regularization expression cannot be solved explicitly, it is impossible to search the entire space for a solution. Instead, a representer theorem shows that under certain conditions on the choice of the norm ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} , the optimal solution f ∗ {\displaystyle f^{}} must be a linear combination of the kernel centered at each of the input points: for some weights α i {\displaystyle \alpha _{i}} , f ∗ ( x ) = ∑ i = 1 ℓ + u α i K ( x i , x ) {\displaystyle f^{}(x)=\sum _{i=1}^{\ell +u}\alpha _{i}K(x_{i},x)} Using this result, it is possible to search for the optimal solution f ∗ {\displaystyle f^{}} by searching the finite-dimensional space defined by the possible choices of α i {\displaystyle \alpha _{i}} . === Functional approach of the Laplacian norm === The idea beyond the graph-Laplacian is to use neighbors to estimate the Laplacian. This method is akin to local averaging methods, that are known to scale poorly in high-dimensional problems. Indeed, the graph Laplacian is known to suffer from the curse of dimensionality. Luckily, it is possible to leverage expected smoothness of the function to estimate thanks to more advanced functional analysis. This method consists of estimating the Laplacian operator using derivatives of the kernel reading ∂ 1 , j K ( x i , x ) {\displaystyle \partial _{1,j}K(x_{i},x)} where ∂ 1 , j {\displaystyle \partial _{1,j}} denotes the partial derivatives according to the j-th coordinate of the first variable. This second approach to the Laplacian norm is to put in relation with meshfree methods, that contrast with the finite difference method in PDE. == Applications == Manifold regularization can extend a variety of algorithms that can be expressed using Tikhonov regularization, by choosing an appropriate loss function V {\displaystyle V} and hypothesis space H {\displaystyle {\mathcal {H}}} . Two commonly used examples are the families of support vector machines and regularized least squares algorithm

  Read more →
• 

  Electronic sell-through

  Electronic sell-through (EST) is a method of media distribution whereby consumers pay a one-time fee to download a media file for storage on a hard drive. Although EST is often described as a transaction that grants content "ownership" to the consumer, the content may become unusable after a certain period and may not be viewable using competing platforms. EST is used by a wide array of digital media products, including movies, television, music, games, and mobile applications. The term is sometimes used interchangeably with download to own (DTO). == Film and television == The film and television industry's $18.8 billion home entertainment market consists of rental and sell-through segments, the latter of which includes the electronic sell-through of digital content. In 2010, EST generated $683 million of total home entertainment revenues, putting it behind the more lucrative revenue streams of cable video-on-demand (VOD) and internet video-on-demand (iVOD), which brought in a combined $1.8 billion in the same period. In 2010, Apple's iTunes Store accounted for three quarters of the U.S. EST business. The rest of the EST market was captured by Microsoft (via its Zune Video platform), Sony, Amazon VOD (now Amazon Video), and Walmart (via its VUDU service). A number of industry trends indicate the future expansion of EST's share of digital distribution revenues. David Bishop, worldwide president of Sony Pictures Home Entertainment, describes the following outlook: "With the launch of UltraViolet (the cloud-based digital copy locker system) establishing a common digital distribution platform later this year, prices potentially coming down on digital sales, more marketing devoted to digital sellthrough, and studios adding more value to the sellthrough product by making HD available and building in smarter extra features, we see the balance tilting even more toward owning and collecting digital movies."

  Read more →
• 

  Wumpus world

  Wumpus world is a simple world use in artificial intelligence for which to represent knowledge and to reason. Wumpus world was introduced by Michael Genesereth, and is discussed in the Russell-Norvig Artificial Intelligence book Artificial Intelligence: A Modern Approach. Wumpus World is loosely inspired by the 1972 video game Hunt the Wumpus. == Problem description == In Artificial Intelligence: A Modern Approach, the wumpus world features a 4x4 grid, containing a monster called a wumpus, multiple bottomless pits and hidden gold. The agent starts at (1,1) and has to find the gold and return to the starting position. The agent loses 1 point for every move and gains 1000 points for bringing the gold to the starting position. The agent can sense pits by a breeze, stench indicates a wumpus, and sparkle indicates gold. The wumpus can be killed by an arrow but costs 10 points.

  Read more →
• 

  Energy-based model

  An energy-based model (EBM), also called Canonical Ensemble Learning (CEL) or Learning via Canonical Ensemble (LCE), is an application of canonical ensemble formulation from statistical physics for learning from data. The approach prominently appears in generative artificial intelligence. EBMs provide a unified framework for many probabilistic and non-probabilistic approaches to such learning, particularly for training graphical and other structured models. An EBM learns the characteristics of a target dataset and generates a similar but larger dataset. EBMs detect the latent variables of a dataset and generate new datasets with a similar distribution. Energy-based generative neural networks is a class of generative models, which aim to learn explicit probability distributions of data in the form of energy-based models, the energy functions of which are parameterized by modern deep neural networks. Boltzmann machines are a special form of energy-based models with a specific parametrization of the energy. == Description == For a given input x {\displaystyle x} , the model describes an energy E θ ( x ) {\displaystyle E_{\theta }(x)} such that the Boltzmann distribution P θ ( x ) = e − β E θ ( x ) Z ( θ ) {\displaystyle P_{\theta }(x)={e^{-\beta E_{\theta }(x)} \over Z(\theta )}} is a probability (density), and typically β = 1 {\displaystyle \beta =1} . Since the normalization constant: Z ( θ ) := ∫ x ∈ X e − β E θ ( x ) d x {\displaystyle Z(\theta ):=\int _{x\in X}e^{-\beta E_{\theta }(x)}dx} (also known as the partition function) depends on all the Boltzmann factors of all possible inputs x {\displaystyle x} , it cannot be easily computed or reliably estimated during training simply using standard maximum likelihood estimation. However, for maximizing the likelihood during training, the gradient of the log-likelihood of a single training example x {\displaystyle x} is given by using the chain rule: ∂ θ log ⁡ ( P θ ( x ) ) = E x ′ ∼ P θ [ ∂ θ E θ ( x ′ ) ] − ∂ θ E θ ( x ) ( ∗ ) {\displaystyle \partial _{\theta }\log \left(P_{\theta }(x)\right)=\mathbb {E} _{x'\sim P_{\theta }}[\partial _{\theta }E_{\theta }(x')]-\partial _{\theta }E_{\theta }(x)\,()} The expectation in the above formula for the gradient can be approximately estimated by drawing samples x ′ {\displaystyle x'} from the distribution P θ {\displaystyle P_{\theta }} using Markov chain Monte Carlo (MCMC). Early energy-based models, such as the 2003 Boltzmann machine by Hinton, estimated this expectation via blocked Gibbs sampling. Newer approaches make use of more efficient Stochastic Gradient Langevin Dynamics (LD), drawing samples using: x 0 ′ ∼ P 0 , x i + 1 ′ = x i ′ − α 2 ∂ E θ ( x i ′ ) ∂ x i ′ + ϵ {\displaystyle x_{0}'\sim P_{0},x_{i+1}'=x_{i}'-{\frac {\alpha }{2}}{\frac {\partial E_{\theta }(x_{i}')}{\partial x_{i}'}}+\epsilon } , where ϵ ∼ N ( 0 , α ) {\displaystyle \epsilon \sim {\mathcal {N}}(0,\alpha )} . A replay buffer of past values x i ′ {\displaystyle x_{i}'} is used with LD to initialize the optimization module. The parameters θ {\displaystyle \theta } of the neural network are therefore trained in a generative manner via MCMC-based maximum likelihood estimation: the learning process follows an "analysis by synthesis" scheme, where within each learning iteration, the algorithm samples the synthesized examples from the current model by a gradient-based MCMC method (e.g., Langevin dynamics or Hybrid Monte Carlo), and then updates the parameters θ {\displaystyle \theta } based on the difference between the training examples and the synthesized ones – see equation ( ∗ ) {\displaystyle ()} . This process can be interpreted as an alternating mode seeking and mode shifting process, and also has an adversarial interpretation. Essentially, the model learns a function E θ {\displaystyle E_{\theta }} that associates low energies to correct values, and higher energies to incorrect values. After training, given a converged energy model E θ {\displaystyle E_{\theta }} , the Metropolis–Hastings algorithm can be used to draw new samples. The acceptance probability is given by: P a c c ( x i → x ∗ ) = min ( 1 , P θ ( x ∗ ) P θ ( x i ) ) . {\displaystyle P_{acc}(x_{i}\to x^{})=\min \left(1,{\frac {P_{\theta }(x^{})}{P_{\theta }(x_{i})}}\right).} == History == The term "energy-based models" was first coined in a 2003 JMLR paper where the authors defined a generalisation of independent components analysis to the overcomplete setting using EBMs. Other early work on EBMs proposed models that represented energy as a composition of latent and observable variables. == Characteristics == EBMs demonstrate useful properties: Simplicity and stability. The EBM is the only object that needs to be designed and trained. Separate networks need not be trained to ensure balance. Adaptive computation time. An EBM can generate sharp, diverse samples or (more quickly) coarse, less diverse samples. Given infinite time, this procedure produces true samples. Flexibility. In Variational Autoencoders (VAE) and flow-based models, the generator learns a map from a continuous space to a (possibly) discontinuous space containing different data modes. EBMs can learn to assign low energies to disjoint regions (multiple modes). Adaptive generation. EBM generators are implicitly defined by the probability distribution, and automatically adapt as the distribution changes (without training), allowing EBMs to address domains where generator training is impractical, as well as minimizing mode collapse and avoiding spurious modes from out-of-distribution samples. Compositionality. Individual models are unnormalized probability distributions, allowing models to be combined through product of experts or other hierarchical techniques. == Experimental results == On image datasets such as CIFAR-10 and ImageNet 32x32, an EBM model generated high-quality images relatively quickly. It supported combining features learned from one type of image for generating other types of images. It was able to generalize using out-of-distribution datasets, outperforming flow-based and autoregressive models. EBM was relatively resistant to adversarial perturbations, behaving better than models explicitly trained against them with training for classification. == Applications == Target applications include natural language processing, robotics and computer vision. The first energy-based generative neural network is the generative ConvNet proposed in 2016 for image patterns, where the neural network is a convolutional neural network. The model has been generalized to various domains to learn distributions of videos, and 3D voxels. They are made more effective in their variants. They have proven useful for data generation (e.g., image synthesis, video synthesis, 3D shape synthesis, etc.), data recovery (e.g., recovering videos with missing pixels or image frames, 3D super-resolution, etc), data reconstruction (e.g., image reconstruction and linear interpolation ). == Alternatives == EBMs compete with techniques such as variational autoencoders (VAEs), generative adversarial networks (GANs) or normalizing flows. == Extensions == === Joint energy-based models === Joint energy-based models (JEM), proposed in 2020 by Grathwohl et al., allow any classifier with softmax output to be interpreted as energy-based model. The key observation is that such a classifier is trained to predict the conditional probability p θ ( y | x ) = e f → θ ( x ) [ y ] ∑ j = 1 K e f → θ ( x ) [ j ] for y = 1 , … , K and f → θ = ( f 1 , … , f K ) ∈ R K , {\displaystyle p_{\theta }(y|x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{\sum _{j=1}^{K}e^{{\vec {f}}_{\theta }(x)[j]}}}\ \ {\text{ for }}y=1,\dotsc ,K{\text{ and }}{\vec {f}}_{\theta }=(f_{1},\dotsc ,f_{K})\in \mathbb {R} ^{K},} where f → θ ( x ) [ y ] {\displaystyle {\vec {f}}_{\theta }(x)[y]} is the y-th index of the logits f → {\displaystyle {\vec {f}}} corresponding to class y. Without any change to the logits it was proposed to reinterpret the logits to describe a joint probability density: p θ ( y , x ) = e f → θ ( x ) [ y ] Z ( θ ) , {\displaystyle p_{\theta }(y,x)={\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}},} with unknown partition function Z ( θ ) {\displaystyle Z(\theta )} and energy E θ ( x , y ) = − f θ ( x ) [ y ] {\displaystyle E_{\theta }(x,y)=-f_{\theta }(x)[y]} . By marginalization, we obtain the unnormalized density p θ ( x ) = ∑ y p θ ( y , x ) = ∑ y e f → θ ( x ) [ y ] Z ( θ ) =: e − E θ ( x ) , {\displaystyle p_{\theta }(x)=\sum _{y}p_{\theta }(y,x)=\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}=:e^{-E_{\theta }(x)},} therefore, E θ ( x ) = − log ⁡ ( ∑ y e f → θ ( x ) [ y ] Z ( θ ) ) , {\displaystyle E_{\theta }(x)=-\log \left(\sum _{y}{\frac {e^{{\vec {f}}_{\theta }(x)[y]}}{Z(\theta )}}\right),} so that any classifier can be used to define an energy function E θ ( x ) {\displaystyle E_{\theta }(x)} .

  Read more →