The DARPA AlphaDogfight was a 2019–2020 DARPA program that pitted computers using F-16 flight simulators against one another. The computers were managed by eight teams of humans, who competed in a single-round elimination for the right to battle a skilled human dogfighter. Heron Systems corporation wrote a deep reinforcement learning software tool that bested the human pilot by a score of 5–0. The tournament program was managed by the Applied Physics Laboratory. The trials took place in October 2019 and January 2020 while the finals were held in August 2020. In 2024 a successor version of the program was tested with in the physical world with the X-62A.
Reflection lines
Engineers use reflection lines to judge a surface's quality. Reflection lines reveal surface flaws, particularly discontinuities in normals indicating that the surface is not C 2 {\displaystyle C^{2}} . Reflection lines may be created and examined on physical surfaces or virtual surfaces with the help of computer graphics. For example, the shiny surface of an automobile body is illuminated with reflection lines by surrounding the car with parallel light sources. Virtually, a surface can be rendered with reflection lines by modulating the surfaces point-wise color according to a simple calculation involving the surface normal, viewing direction and a square wave environment map. == Mathematical definition == Consider a point p {\displaystyle p} on a surface M {\displaystyle M} with (normalized) normal n {\displaystyle n} . If an observer views this point from infinity at view direction v {\displaystyle v} then the reflected view direction r {\displaystyle r} is: r = v − 2 ( n ⋅ v ) n . {\displaystyle r=v-2(n\cdot v)n.} (The vector v {\displaystyle v} is decomposed into its normal part v n = ( n ⋅ v ) v {\displaystyle v_{n}=(n\cdot v)v} and tangential part v t = v − v n {\displaystyle v_{t}=v-v_{n}} . Upon reflection, the tangential part is kept and the normal part is negated.) For reflection lines we consider the surface M {\displaystyle M} surrounded by parallel lines with direction a {\displaystyle a} , representing infinite, non-dispersive light sources. For each point p {\displaystyle p} on M {\displaystyle M} we determine which line is seen from direction v {\displaystyle v} . The position on each line is of no interest. Define the vector r p {\displaystyle r_{p}} to be the reflection direction r {\displaystyle r} projected onto a plane P {\displaystyle P} that is orthogonal to a {\displaystyle a} : r p = r − ( r ⋅ a ) a {\displaystyle r_{p}=r-(r\cdot a)a} and similarly let v p {\displaystyle v_{p}} be the viewing direction projected onto P {\displaystyle P} : v p = v − ( v ⋅ a ) a {\displaystyle v_{p}=v-(v\cdot a)a} Finally, define v o {\displaystyle v_{o}} to be the direction lying in P {\displaystyle P} perpendicular to a {\displaystyle a} and v p {\displaystyle v_{p}} : v o = a × v p {\displaystyle v_{o}=a\times v_{p}} Using these vectors, the reflection line function θ ( p ) : M → ( − π , π ] {\displaystyle \theta (p):M\rightarrow (-\pi ,\pi ]} is a scalar function mapping points p {\displaystyle p} on the surface to angles between v p {\displaystyle v_{p}} and r p {\displaystyle r_{p}} : θ = arctan ( r p ⋅ v o , r p ⋅ v p ) {\displaystyle \theta =\arctan {(r_{p}\cdot v_{o},r_{p}\cdot v_{p})}} where a r c t a n ( y , x ) {\displaystyle arctan(y,x)} is the atan2 function producing a number in the range ( − π , π ] {\displaystyle (-\pi ,\pi ]} . ( v p {\displaystyle v_{p}} and v o {\displaystyle v_{o}} can be viewed as a local coordinate system in P {\displaystyle P} with x {\displaystyle x} -axis in direction v p {\displaystyle v_{p}} and y {\displaystyle y} -axis in direction v o {\displaystyle v_{o}} .) Finally, to render the reflection lines positive values θ > 0 {\displaystyle \theta >0} are mapped to a light color and non-positive values to a dark color. == Highlight lines == Highlight lines are a view-independent alternative to reflection lines. Here the projected normal is directly compared against some arbitrary vector x {\displaystyle x} perpendicular to the light source: θ = arctan ( n a ⋅ a ⊥ , n a ⋅ x ) {\displaystyle \theta =\arctan {(n_{a}\cdot a^{\perp },n_{a}\cdot x)}} where n a {\displaystyle n_{a}} is the surface normal projected on the light source plane P {\displaystyle P} : n a ^ / | n a ^ | , n a ^ = n − ( n ⋅ a ) a {\displaystyle {\hat {n_{a}}}/|{\hat {n_{a}}}|,{\hat {n_{a}}}=n-(n\cdot a)a} The relationship between reflection lines and highlight lines is likened to that between specular and diffuse shading.
Physics-informed neural networks
In machine learning, physics-informed neural networks (PINNs), also referred to as theory-trained neural networks (TTNs), are a type of universal function approximator that can embed the knowledge of any physical laws that govern a given data-set in the learning process, and can be described by partial differential equations (PDEs). Low data availability for some biological and engineering problems limit the robustness of conventional machine learning models used for these applications. The prior knowledge of general physical laws acts in the training of neural networks (NNs) as a regularization agent that limits the space of admissible solutions, increasing the generalizability of the function approximation. This way, embedding this prior information into a neural network results in enhancing the information content of the available data, facilitating the learning algorithm to capture the right solution and to generalize well even with a low amount of training examples. Because they process continuous spatial and time coordinates and output continuous PDE solutions, they can be categorized as neural fields. == Function approximation == Most of the physical laws that govern the dynamics of a system can be described by partial differential equations. For example, the Navier–Stokes equations are a set of partial differential equations derived from the conservation laws (i.e., conservation of mass, momentum, and energy) that govern fluid mechanics. The solution of the Navier–Stokes equations with appropriate initial and boundary conditions allows the quantification of flow dynamics in a precisely defined geometry. However, these equations cannot be solved exactly and therefore numerical methods must be used (such as finite differences, finite elements and finite volumes). In this setting, these governing equations must be solved while accounting for prior assumptions, linearization, and adequate time and space discretization. Recently, solving the governing partial differential equations of physical phenomena using deep learning has emerged as a new field of scientific machine learning (SciML), leveraging the universal approximation theorem and high expressivity of neural networks. In general, deep neural networks could approximate any high-dimensional function given that sufficient training data are supplied. However, such networks do not consider the physical characteristics underlying the problem, and the level of approximation accuracy provided by them is still heavily dependent on careful specifications of the problem geometry as well as the initial and boundary conditions. Without this preliminary information, the solution is not unique and may lose physical correctness. To remedy this, Physics-Informed Neural Networks (PINNs) leverage governing physical equations in neural network training. Namely, PINNs are designed to be trained to satisfy the given training data as well as the imposed governing equations. In this fashion, a neural network can be guided with training datasets that do not necessarily need to be large or complete. An accurate solution of partial differential equations can potentially be found without knowing the boundary conditions. Therefore, with some knowledge about the physical characteristics of the problem and some form of training data (even sparse and incomplete), PINNs may be used for finding an optimal solution with high fidelity. PINNs can be applied to a wide range of problems in computational science, and are a pioneering technology leading to the development of new classes of numerical solvers for PDEs. PINNs can be thought of as a mesh-free alternative to traditional approaches (e.g., CFD for fluid dynamics), and new data-driven approaches for model inversion and system identification. Notably, a trained PINN network can be used to predict values on simulation grids of different resolutions without needing to be retrained. Additionally, the derivatives used in the partial differential equations can be computed using automatic differentiation (AD), which is assessed to be superior to numerical or symbolic differentiation. == Modeling and computation == A general nonlinear partial differential equation can be written as: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} where u ( t , x ) {\displaystyle u(t,x)} denotes the solution, N [ ⋅ ; λ ] {\displaystyle {\mathcal {N}}[\cdot ;\lambda ]} is a nonlinear operator parameterized by λ {\displaystyle \lambda } , and Ω {\displaystyle \Omega } is a subset of R D {\displaystyle \mathbb {R} ^{D}} . This general form of governing equations summarizes a wide range of problems in mathematical physics, such as conservative laws, diffusion process, advection-diffusion systems, and kinetic equations. Given noisy measurements of a generic dynamic system described by the equation above, PINNs can be designed to solve two classes of problems: data-driven solutions of partial differential equations data-driven discovery of partial differential equations === Data-driven solution of partial differential equations === The data-driven solution of PDE computes the hidden state u ( t , x ) {\displaystyle u(t,x)} of the system given boundary data and/or measurements z {\displaystyle z} , and fixed model parameters λ {\displaystyle \lambda } . We solve: u t + N [ u ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u]=0,\quad x\in \Omega ,\quad t\in [0,T]} . by defining the residual f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ] {\displaystyle f:=u_{t}+{\mathcal {N}}[u]} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network. This network can be differentiated using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} is the error between the PINN u ( t , x ) {\displaystyle u(t,x)} and the set of boundary conditions and measured data on the set of points Γ {\displaystyle \Gamma } where the boundary conditions and data are defined. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the mean-squared error of the residual function. This second term encourages the PINN to learn the structural information expressed by the PDE during the training process. This approach has been used to yield computationally efficient physics-informed surrogate models with applications in the forecasting of physical processes, model predictive control, multi-physics and multi-scale modeling, and simulation. It has been shown to converge to the solution of the PDE. === Data-driven discovery of partial differential equations === Given noisy and incomplete measurements z {\displaystyle z} of the state of the system, the data-driven discovery of PDEs results in computing the unknown state u ( t , x ) {\displaystyle u(t,x)} and learning model parameters λ {\displaystyle \lambda } that best describe the observed data: u t + N [ u ; λ ] = 0 , x ∈ Ω , t ∈ [ 0 , T ] {\displaystyle u_{t}+{\mathcal {N}}[u;\lambda ]=0,\quad x\in \Omega ,\quad t\in [0,T]} By defining f ( t , x ) {\displaystyle f(t,x)} as: f := u t + N [ u ; λ ] = 0 {\displaystyle f:=u_{t}+{\mathcal {N}}[u;\lambda ]=0} , and approximating u ( t , x ) {\displaystyle u(t,x)} by a deep neural network, f ( t , x ) {\displaystyle f(t,x)} results in a PINN. This network can be derived using automatic differentiation. The parameters of u ( t , x ) {\displaystyle u(t,x)} and f ( t , x ) {\displaystyle f(t,x)} , together with the parameter λ {\displaystyle \lambda } of the differential operator can be then learned by minimizing the following loss function L tot {\displaystyle L_{\text{tot}}} : L tot = L u + L f {\displaystyle L_{\text{tot}}=L_{u}+L_{f}} where: L u = ‖ u − z ‖ Γ {\displaystyle L_{u}=\Vert u-z\Vert _{\Gamma }} , with u {\displaystyle u} and z {\displaystyle z} state solutions and measurements at sparse location Γ {\displaystyle \Gamma } , respectively. L f = ‖ f ‖ Γ {\displaystyle L_{f}=\Vert f\Vert _{\Gamma }} is the residual function. This second term requires the structured information represented by the partial differential equations to be satisfied in the training process. This strategy allows for discovering dynamic models described by nonlinear PDEs assembling computationally efficient and fully differentiable surrogate models that may find application in predictive forecasting, control, and data assimilation. == Extensions and applications == === For piece-wise function approximation === PINNs are unable to approximate PDEs that have strong non-linearity or sharp gradients (such as those that commonly occur in practical fluid flow problems). Piecewise approximation has been an old practic
Neural network Gaussian process
A Neural Network Gaussian Process (NNGP) is a Gaussian process (GP) obtained as the limit of a certain type of sequence of neural networks. Specifically, a wide variety of network architectures converges to a GP in the infinitely wide limit, in the sense of distribution. The concept constitutes an intensional definition, i.e., a NNGP is just a GP, but distinguished by how it is obtained. == Motivation == Bayesian networks are a modeling tool for assigning probabilities to events, and thereby characterizing the uncertainty in a model's predictions. Deep learning and artificial neural networks are approaches used in machine learning to build computational models which learn from training examples. Bayesian neural networks merge these fields. They are a type of neural network whose parameters and predictions are both probabilistic. While standard neural networks often assign high confidence even to incorrect predictions, Bayesian neural networks can more accurately evaluate how likely their predictions are to be correct. Computation in artificial neural networks is usually organized into sequential layers of artificial neurons. The number of neurons in a layer is called the layer width. When we consider a sequence of Bayesian neural networks with increasingly wide layers (see figure), they converge in distribution to a NNGP. This large width limit is of practical interest, since the networks often improve as layers get wider. And the process may give a closed form way to evaluate networks. NNGPs also appears in several other contexts: It describes the distribution over predictions made by wide non-Bayesian artificial neural networks after random initialization of their parameters, but before training; it appears as a term in neural tangent kernel prediction equations; it is used in deep information propagation to characterize whether hyperparameters and architectures will be trainable. It is related to other large width limits of neural networks. === Scope === The first correspondence result had been established in the 1995 PhD thesis of Radford M. Neal, then supervised by Geoffrey Hinton at University of Toronto. Neal cites David J. C. MacKay as inspiration, who worked in Bayesian learning. Today the correspondence is proven for: Single hidden layer Bayesian neural networks; deep fully connected networks as the number of units per layer is taken to infinity; convolutional neural networks as the number of channels is taken to infinity; transformer networks as the number of attention heads is taken to infinity; recurrent networks as the number of units is taken to infinity. In fact, this NNGP correspondence holds for almost any architecture: Generally, if an architecture can be expressed solely via matrix multiplication and coordinatewise nonlinearities (i.e., a tensor program), then it has an infinite-width GP. This in particular includes all feedforward or recurrent neural networks composed of multilayer perceptron, recurrent neural networks (e.g., LSTMs, GRUs), (nD or graph) convolution, pooling, skip connection, attention, batch normalization, and/or layer normalization. === Illustration === Every setting of a neural network's parameters θ {\displaystyle \theta } corresponds to a specific function computed by the neural network. A prior distribution p ( θ ) {\displaystyle p(\theta )} over neural network parameters therefore corresponds to a prior distribution over functions computed by the network. As neural networks are made infinitely wide, this distribution over functions converges to a Gaussian process for many architectures. The notation used in this section is the same as the notation used below to derive the correspondence between NNGPs and fully connected networks, and more details can be found there. The figure to the right plots the one-dimensional outputs z L ( ⋅ ; θ ) {\displaystyle z^{L}(\cdot ;\theta )} of a neural network for two inputs x {\displaystyle x} and x ∗ {\displaystyle x^{}} against each other. The black dots show the function computed by the neural network on these inputs for random draws of the parameters from p ( θ ) {\displaystyle p(\theta )} . The red lines are iso-probability contours for the joint distribution over network outputs z L ( x ; θ ) {\displaystyle z^{L}(x;\theta )} and z L ( x ∗ ; θ ) {\displaystyle z^{L}(x^{};\theta )} induced by p ( θ ) {\displaystyle p(\theta )} . This is the distribution in function space corresponding to the distribution p ( θ ) {\displaystyle p(\theta )} in parameter space, and the black dots are samples from this distribution. For infinitely wide neural networks, since the distribution over functions computed by the neural network is a Gaussian process, the joint distribution over network outputs is a multivariate Gaussian for any finite set of network inputs. == Discussion == === Infinitely wide fully connected network === This section expands on the correspondence between infinitely wide neural networks and Gaussian processes for the specific case of a fully connected architecture. It provides a proof sketch outlining why the correspondence holds, and introduces the specific functional form of the NNGP for fully connected networks. The proof sketch closely follows the approach by Novak and coauthors. ==== Network architecture specification ==== Consider a fully connected artificial neural network with inputs x {\displaystyle x} , parameters θ {\displaystyle \theta } consisting of weights W l {\displaystyle W^{l}} and biases b l {\displaystyle b^{l}} for each layer l {\displaystyle l} in the network, pre-activations (pre-nonlinearity) z l {\displaystyle z^{l}} , activations (post-nonlinearity) y l {\displaystyle y^{l}} , pointwise nonlinearity ϕ ( ⋅ ) {\displaystyle \phi (\cdot )} , and layer widths n l {\displaystyle n^{l}} . For simplicity, the width n L + 1 {\displaystyle n^{L+1}} of the readout vector z L {\displaystyle z^{L}} is taken to be 1. The parameters of this network have a prior distribution p ( θ ) {\displaystyle p(\theta )} , which consists of an isotropic Gaussian for each weight and bias, with the variance of the weights scaled inversely with layer width. This network is illustrated in the figure to the right, and described by the following set of equations: x ≡ input y l ( x ) = { x l = 0 ϕ ( z l − 1 ( x ) ) l > 0 z i l ( x ) = ∑ j W i j l y j l ( x ) + b i l W i j l ∼ N ( 0 , σ w 2 n l ) b i l ∼ N ( 0 , σ b 2 ) ϕ ( ⋅ ) ≡ nonlinearity y l ( x ) , z l − 1 ( x ) ∈ R n l × 1 n L + 1 = 1 θ = { W 0 , b 0 , … , W L , b L } {\displaystyle {\begin{aligned}x&\equiv {\text{input}}\\y^{l}(x)&=\left\{{\begin{array}{lcl}x&&l=0\\\phi \left(z^{l-1}(x)\right)&&l>0\end{array}}\right.\\z_{i}^{l}(x)&=\sum _{j}W_{ij}^{l}y_{j}^{l}(x)+b_{i}^{l}\\W_{ij}^{l}&\sim {\mathcal {N}}\left(0,{\frac {\sigma _{w}^{2}}{n^{l}}}\right)\\b_{i}^{l}&\sim {\mathcal {N}}\left(0,\sigma _{b}^{2}\right)\\\phi (\cdot )&\equiv {\text{nonlinearity}}\\y^{l}(x),z^{l-1}(x)&\in \mathbb {R} ^{n^{l}\times 1}\\n^{L+1}&=1\\\theta &=\left\{W^{0},b^{0},\dots ,W^{L},b^{L}\right\}\end{aligned}}} ==== ==== z l | y l {\displaystyle z^{l}|y^{l}} is a Gaussian process We first observe that the pre-activations z l {\displaystyle z^{l}} are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . This result holds even at finite width. Each pre-activation z i l {\displaystyle z_{i}^{l}} is a weighted sum of Gaussian random variables, corresponding to the weights W i j l {\displaystyle W_{ij}^{l}} and biases b i l {\displaystyle b_{i}^{l}} , where the coefficients for each of those Gaussian variables are the preceding activations y j l {\displaystyle y_{j}^{l}} . Because they are a weighted sum of zero-mean Gaussians, the z i l {\displaystyle z_{i}^{l}} are themselves zero-mean Gaussians (conditioned on the coefficients y j l {\displaystyle y_{j}^{l}} ). Since the z l {\displaystyle z^{l}} are jointly Gaussian for any set of y l {\displaystyle y^{l}} , they are described by a Gaussian process conditioned on the preceding activations y l {\displaystyle y^{l}} . The covariance or kernel of this Gaussian process depends on the weight and bias variances σ w 2 {\displaystyle \sigma _{w}^{2}} and σ b 2 {\displaystyle \sigma _{b}^{2}} , as well as the second moment matrix K l {\displaystyle K^{l}} of the preceding activations y l {\displaystyle y^{l}} , z i l ∣ y l ∼ G P ( 0 , σ w 2 K l + σ b 2 ) K l ( x , x ′ ) = 1 n l ∑ i y i l ( x ) y i l ( x ′ ) {\displaystyle {\begin{aligned}z_{i}^{l}\mid y^{l}&\sim {\mathcal {GP}}\left(0,\sigma _{w}^{2}K^{l}+\sigma _{b}^{2}\right)\\K^{l}(x,x')&={\frac {1}{n^{l}}}\sum _{i}y_{i}^{l}(x)y_{i}^{l}(x')\end{aligned}}} The effect of the weight scale σ w 2 {\displaystyle \sigma _{w}^{2}} is to rescale the contribution to the covariance matrix from K l {\displaystyle K^{l}} , while the bias is shared for all inputs, and so σ b 2 {\displaystyle \sigma _{b}^{2}} makes the z i l {\displaystyle z_{i}^{l}} for different datapoints more similar and
Pronunciation assessment
Automatic pronunciation assessment uses computer speech recognition to determine how accurately speech has been pronounced, instead of relying on a human instructor or proctor. It is also called speech verification, pronunciation evaluation, and pronunciation scoring. This technology is used to grade speech quality, for language testing, for computer-aided pronunciation teaching (CAPT) in computer-assisted language learning (CALL), for speaking skill remediation, and for accent reduction. Pronunciation assessment is different from dictation or automatic transcription, because instead of determining unknown speech, it verifies learners' pronunciation of known word(s), often from prior transcription of the same utterance; ideally scoring the intelligibility of the learners' speech. Sometimes pronunciation assessment evaluates the prosody of the learners' speech, such as intonation, pitch, tempo, rhythm, and syllable and word stress, although those are usually not essential for being understood in most languages. Pronunciation assessment is also used in reading tutoring, for example in products from Google, Microsoft, and Amira Learning. Automatic pronunciation assessment can also be used to help diagnose and treat speech disorders such as apraxia. == Intelligibility == Intelligibility refers to how well a learner's utterance is understood by a listener, rather than how much it sounds like a native speaker. This is separate from measures of fluency, such as so-called "Goodness of Pronunciation" (GoP) scores, which estimate how closely an utterance aligns with those of native speakers. Intelligibility is widely regarded as the most important communicative goal in pronunciation teaching and assessment. For example, in the Common European Framework of Reference for Languages (CEFR) assessment criteria for "overall phonological control", intelligibility outweighs formally correct pronunciation at all levels. Studies in applied linguistics have shown that accent reduction does not always increase intelligibility because listeners can often comprehend heavily accented speech without difficulty. Pronunciation assessment systems often rely on acoustic methods such as GoP which compare learner speech to reference models to produce phoneme-level scores, which are in turn aggregated to produce word and phrase scores. While these methods are effective for identifying deviations from native speakers' utterances, they do not effectively measure how understandable speech is to human listeners. Intelligibility is influenced by broader linguistic and contextual factors such as stress placement, speech rate, and coarticulation, which are not represented in purely segmental scores. The earliest work on pronunciation assessment avoided measuring genuine listener intelligibility, a shortcoming corrected in 2011 at the Toyohashi University of Technology, and included in the Versant high-stakes English fluency assessment from Pearson and mobile apps from 17zuoye Education & Technology, but still missing in 2023 products from Google Search, Microsoft, Educational Testing Service, Speechace, and ELSA. Assessing authentic listener intelligibility is essential for avoiding inaccuracies from accent bias, especially in high-stakes assessments; from words with multiple correct pronunciations; and from phoneme coding errors in machine-readable pronunciation dictionaries. In 2022, researchers found that some newer speech-to-text systems, based on end-to-end reinforcement learning to map audio signals directly into words, produce word and phrase confidence scores (from 10-25ms audio frame logit aggregation) closely correlated with genuine listener intelligibility. Others have been able to assess intelligibility using Levenshtein or dynamic time warping distance measures from Wav2Vec2 representation of good speech. Further work through 2025 has focused specifically on measuring intelligibility. A 2025 study of 42 pronunciation and speech coaching apps (32 mobile and 10 web) found that none offered intelligibility assessment. Instead, most provided only segmental and accent-focused scoring. About two-thirds of the apps provided some form of specific pronunciation feedback, usually with phonetic transcriptions, but accompanied by visual cues (such as animations of the vocal tract or the lips and tongue from the front) in only about 5% of the apps. Less than a third provided feedback on learner perception of exemplar speech. == Evaluation == Although there are as yet no industry-standard benchmarks for evaluating pronunciation assessment accuracy, researchers occasionally release evaluation speech corpuses for others to use for improving assessment quality. Such evaluation databases often emphasize formally unaccented pronunciation to the exclusion of genuine intelligibility evident from blinded listener transcriptions. As of mid-2025, state of the art approaches for automatically transcribing phonemes typically achieve an error rate of about 10% from known good speech. The International Speech Communication Association (ISCA) 2025 Workshop on Speech and Language Technology in Education (SLaTE) administered a Speak & Improve Challenge: Spoken Language Assessment and Feedback, introducing benchmarks for evaluating pronunciation assessment and remediation systems across languages, accents, and learner populations. The challenge emphasized cross-lingual generalization and alignment with human intelligibility judgments, for more robust and interpretable assessment systems. Ethical issues in pronunciation assessment are present in both human and automatic methods. Authentic validity, fairness, and mitigating bias in evaluation are all crucial. Diverse speech data should be included in automatic pronunciation assessment models. Combining human judgments, especially blinded transcriptions from a wide diversity of listeners, with automated feedback can improve accuracy and fairness. Second language learners benefit substantially from their use of widely available speech recognition systems for dictation, virtual assistants, and AI chatbots. In such systems, users naturally try to correct their own errors evident in speech recognition results that they notice. Such use improves their grammar and vocabulary development along with their pronunciation skills. The extent to which explicit pronunciation assessment and remediation approaches improve on such self-directed interactions remains an open question. Similarly, automatic dictation results have been shown to reflect intelligibility about as well as human scorers. == Recent developments == During 2021–22, a smartphone-based CAPT system was used to sense articulation through both audible and inaudible signals, providing feedback at the phoneme level. Some promising areas for improvement which were being developed in 2024 include articulatory feature extraction and transfer learning to suppress unnecessary corrections. Other interesting advances under development include "augmented reality" interfaces for mobile devices using optical character recognition to provide pronunciation training on text found in user environments. In 2024, audio multimodal large language models were first described as assessing pronunciation. That work has been carried forward by other researchers in 2025 who report positive results. Subsequently, researchers demonstrated pronunciation scoring by providing a language model with textual descriptions of speech, including the speech-to-text transcript, phoneme sequences, pauses, and phoneme sequence matching; this approach can achieve performance similar to multimodal LLMs that analyze raw audio while avoiding their higher computational cost. In 2025, the Duolingo English Test authors published a description of their pronunciation assessment method, purportedly built to measure intelligibility rather than accent imitation. While achieving a correlation of 0.82 with expert human ratings, very close to inter-rater agreement and outperforming alternative methods, the method is nonetheless based on experts' scores along the six-point CEFR common reference levels scale, instead of actual blinded listener transcriptions. Further promising work in 2025 includes assessment feedback aligning learner speech to synthetic utterances using interpretable features, identifying continuous spans of words for remediation feedback; synthesizing corrected speech matching learners' self-perceived voices, which they prefer and imitate more accurately as corrections; and streaming such interactions. On January 21, 2026, Educational Testing Service's TOEFL iBT high-stakes English language test, required by US university admissions and employers from English as a foreign language applicants more often than all other internet-based tests combined, changed its speaking assessments. While official rubrics claim that the new scoring will be based primarily on intelligibility, the new test's technical description indicates that it ju
Computational photography
Computational photography refers to digital image capture and processing techniques that use digital computation instead of optical processes. Computational photography can improve the capabilities of a camera, or introduce features that were not possible at all with film-based photography, or reduce the cost or size of camera elements. Examples of computational photography include in-camera computation of digital panoramas, high-dynamic-range images, and light field cameras. Light field cameras use novel optical elements to capture three-dimensional scene information, which can then be used to produce 3D images, enhanced depth-of-field, and selective de-focusing (or "post focus"). Enhanced depth-of-field reduces the need for mechanical focusing systems. All of these features use computational imaging techniques. The definition of computational photography has evolved to cover a number of subject areas in computer graphics, computer vision, and applied optics. These areas are given below, organized according to a taxonomy proposed by Shree K. Nayar. Within each area is a list of techniques, and for each technique, one or two representative papers or books are cited. Deliberately omitted from the taxonomy are image processing (see also digital image processing) techniques applied to traditionally captured images to produce better images. Examples of such techniques are image scaling, dynamic range compression (i.e. tone mapping), color management, image completion (a.k.a. inpainting or hole filling), image compression, digital watermarking, and artistic image effects. Also omitted are techniques that produce range data, volume data, 3D models, 4D light fields, 4D, 6D, or 8D BRDFs, or other high-dimensional image-based representations. Epsilon photography is a sub-field of computational photography. == Effect on photography == Photos taken using computational photography can allow amateurs to produce photographs rivalling the quality of professional photographers, but as of 2019 do not outperform the use of professional-level equipment. == Computational illumination == This is controlling photographic illumination in a structured fashion, then processing the captured images, to create new images. The applications include image-based relighting, image enhancement, image deblurring, geometry/material recovery and so forth. High-dynamic-range imaging uses differently exposed pictures of the same scene to extend dynamic range. Other examples include processing and merging differently illuminated images of the same subject matter ("lightspace"). == Computational optics == This is a capture of optically coded images, followed by computational decoding to produce new images. Coded aperture imaging was mainly applied in astronomy and X-ray imaging to boost the image quality. Instead of a single pin-hole, a pinhole pattern is applied in imaging, and deconvolution is performed to recover the image. In coded exposure imaging, the on/off state of the shutter is coded to modify the kernel of motion blur. In this way, motion deblurring becomes a well-conditioned problem. Similarly, in a lens based coded aperture, the aperture can be modified by inserting a broadband mask. Thus, out of focus deblurring becomes a well-conditioned problem. The coded aperture can also improve the quality in light field acquisition using Hadamard transform optics. Coded aperture patterns can also be designed using color filters, in order to apply different codes at different wavelengths. This allows for increase the amount of light that reaches the camera sensor, compared to binary masks. == Computational imaging == Computational imaging is a set of imaging techniques that combine data acquisition and data processing to create the image of an object through indirect means to yield enhanced resolution, additional information such as optical phase or 3D reconstruction. The information is often recorded without using a conventional optical microscope configuration or with limited datasets. Computational imaging allows going beyond physical limitations of optical systems, such as numerical aperture, or even obliterates the need for optical elements. For parts of the optical spectrum where imaging elements such as objectives are difficult to manufacture or image sensors cannot be miniaturized, computational imaging provides useful alternatives, in fields such as X-ray and THz radiations. === Common techniques === Among common computational imaging techniques are lensless imaging, computational speckle imaging , ptychography and Fourier ptychography. Computational imaging technique often draws on compressive sensing or phase retrieval techniques, where the angular spectrum of the object is reconstructed. Other techniques are related to the field of computational imaging, such as digital holography, computer vision and inverse problems such as tomography. == Computational processing == This is the processing of non-optically-coded images to produce new images. == Computational sensors == These are detectors that combine sensing and processing, typically in hardware, like the oversampled binary image sensor. == Early work in computer vision == Although computational photography is a currently popular buzzword in computer graphics, many of its techniques first appeared in the computer vision literature, either under other names or within papers aimed at 3D shape analysis. == Art history == Computational photography, as an art form, has been practiced by capturing differently exposed pictures of the same subject matter and combining them. This was the inspiration for the development of the wearable computer in the 1970s and early 1980s. Computational photography was inspired by the work of Charles Wyckoff, and thus computational photography datasets (e.g. differently exposed pictures of the same subject matter that are taken in order to make a single composite image) are sometimes referred to as Wyckoff Sets, in his honor. Early work in this area (joint estimation of image projection and exposure value) was undertaken by Mann and Candoccia. Charles Wyckoff devoted much of his life to creating special kinds of 3-layer photographic films that captured different exposures of the same subject matter. A picture of a nuclear explosion, taken on Wyckoff's film, appeared on the cover of Life Magazine and showed the dynamic range from the dark outer areas to the inner core.
Automatic acquisition of lexicon
Automatic acquisition of lexicon is a computerized process used for the development of a complex morphological lexicon of a language. The lexicon is essential for the NLP (Natural language processing), as well as a prerequisite to any wide-coverage parser. The two main requirements represent raw corpus and the morphological description of the language. The aim is to provide lemmas that will serve to the explanation of all the words that occur within the corpus. For the achievement of a quality lexicon it is necessary to manually validate the generated lemmas and iterate the whole process several times. The process is focused on the open word classes (e.g. nouns, adjectives, verbs). Closed classes (e.g. prepositions, pronouns, numerals) are excluded. This method is applicable to the languages with a rich morphology, such as Slovak, Russian or Croatian. Applied to Slovak, being an inflectional language, the automatic acquisition focuses on the inflectional morphology as well as on the derivational morphology. This fact enables the users to find out the information about derivational relations (e.g. adjectivizations, prefixes) in the lexicon. For example, Slovak word korpusový is an adjectivization of korpus (eng. corpus). == Three-step loop == Conformably to Benoît Sagot, there are three stages involved in the acquisition of lemmas: Generation and inflection Ranking Manual validation The more iteration will be performed, the more accurate lexicon will be obtained. For each iteration are essential the information given by a manual validator. === Generation and inflection === Firstly, all words which represent the closed word classes (pronouns, prepositions, numerals) are manually excluded from the given corpus. Number of their occurrences in the corpus is provided. Then the automatic generation comes, when the hypothetical lemmas according to the morphological description of a language are created. Generated lemmas are consequently being inflected, so that all of their inflected forms are built. Obtained forms are associated with the corresponding lemma and a morphological tag. === Ranking === There was created a probabilistic model, represented by a fix-point algorithm, to rank the hypothetical lemmas generated in the first step. Best ranked lemmas are expected to be ideally all correct, whereas the least ranked tend to be incorrect. === Manual validation === Correctness of the best- ranked lemmas created in the previous step are checked by the manual validator, who should be a native speaker. Lemmas are at this stage divided into three categories: valid lemmas, appended to lexicon erroneous lemmas generated by valid forms (later associated to another lemmas) erroneous lemmas generated by invalid forms (these need to be excluded) == Future development == Automatic acquisition, in comparison to a purely manual development of the lexicons, seems to be promising, considering the future development, because of the short validation time needed and the relatively small amount of human labor involved.