ImageNet

The ImageNet project is a large visual database designed for use in visual object recognition software research. More than 14 million images have been hand-annotated by the project to indicate what objects are pictured and in at least one million of the images, bounding boxes are also provided. ImageNet contains more than 20,000 categories, with a typical category, such as "balloon" or "strawberry", consisting of several hundred images. The database of annotations of third-party image URLs is freely available directly from ImageNet, though the actual images are not owned by ImageNet. Since 2010, the ImageNet project runs an annual software contest, the ImageNet Large Scale Visual Recognition Challenge (ILSVRC), where software programs compete to correctly classify and detect objects and scenes. The challenge uses a "trimmed" list of one thousand non-overlapping classes. == History == AI researcher Fei-Fei Li began working on the idea for ImageNet in 2006. At a time when most AI research focused on models and algorithms, Li wanted to expand and improve the data available to train AI algorithms. In 2007, Li met with Princeton professor Christiane Fellbaum, one of the creators of WordNet, to discuss the project. As a result of this meeting, Li went on to build ImageNet starting from the roughly 22,000 nouns of WordNet and using many of its features. She was also inspired by a 1987 estimate that the average person recognizes roughly 30,000 different kinds of objects. As an assistant professor at Princeton, Li assembled a team of researchers to work on the ImageNet project. They used Amazon Mechanical Turk to help with the classification of images. Labeling started in July 2008 and ended in April 2010. It took 49K workers from 167 countries filtering and labeling over 160M candidate images. They had enough budget to have each of the 14 million images labelled three times. The original plan called for 10,000 images per category, for 40,000 categories at 400 million images, each verified 3 times. They found that humans can classify at most 2 images/sec. At this rate, it was estimated to take 19 human-years of labor (without rest). They presented their database for the first time as a poster at the 2009 Conference on Computer Vision and Pattern Recognition (CVPR) in Florida, titled "ImageNet: A Preview of a Large-scale Hierarchical Dataset". The poster was reused at Vision Sciences Society 2009. In 2009, Alex Berg suggested adding object localization as a task. Li approached PASCAL Visual Object Classes contest in 2009 for a collaboration. It resulted in the subsequent ImageNet Large Scale Visual Recognition Challenge starting in 2010, which has 1000 classes and object localization, as compared to PASCAL VOC which had just 20 classes and 19,737 images (in 2010). === Significance for deep learning === On 30 September 2012, a convolutional neural network (CNN) called AlexNet achieved a top-5 error of 15.3% in the ImageNet 2012 Challenge, more than 10.8 percentage points lower than that of the runner-up. Using convolutional neural networks was feasible due to the use of graphics processing units (GPUs) during training, an essential ingredient of the deep learning revolution. According to The Economist, "Suddenly people started to pay attention, not just within the AI community but across the technology industry as a whole." In 2015, AlexNet was outperformed by Microsoft's very deep CNN with over 100 layers, which won the ImageNet 2015 contest, having 3.57% error on the test set. Andrej Karpathy estimated in 2014 that with concentrated effort, he could reach 5.1% error rate, and ~10 people from his lab reached ~12-13% with less effort. It was estimated that with maximal effort, a human could reach 2.4%. == Dataset == ImageNet crowdsources its annotation process. Image-level annotations indicate the presence or absence of an object class in an image, such as "there are tigers in this image" or "there are no tigers in this image". Object-level annotations provide a bounding box around the (visible part of the) indicated object. ImageNet uses a variant of the broad WordNet schema to categorize objects, augmented with 120 categories of dog breeds to showcase fine-grained classification. In 2012, ImageNet was the world's largest academic user of Mechanical Turk. The average worker identified 50 images per minute. The original plan of the full ImageNet would have roughly 50M clean, diverse and full resolution images spread over approximately 50K synsets. This was not achieved. The summary statistics given on April 30, 2010: Total number of non-empty synsets: 21841 Total number of images: 14,197,122 Number of images with bounding box annotations: 1,034,908 Number of synsets with SIFT features: 1000 Number of images with SIFT features: 1.2 million === Categories === The categories of ImageNet were filtered from the WordNet concepts. Each concept, since it can contain multiple synonyms (for example, "kitty" and "young cat"), so each concept is called a "synonym set" or "synset". There were more than 100,000 synsets in WordNet 3.0, majority of them are nouns (80,000+). The ImageNet dataset filtered these to 21,841 synsets that are countable nouns that can be visually illustrated. Each synset in WordNet 3.0 has a "WordNet ID" (wnid), which is a concatenation of part of speech and an "offset" (a unique identifying number). Every wnid starts with "n" because ImageNet only includes nouns. For example, the wnid of synset "dog, domestic dog, Canis familiaris" is "n02084071". The categories in ImageNet fall into 9 levels, from level 1 (such as "mammal") to level 9 (such as "German shepherd"). === Image format === The images were scraped from online image search (Google, Picsearch, MSN, Yahoo, Flickr, etc) using synonyms in multiple languages. For example: German shepherd, German police dog, German shepherd dog, Alsatian, ovejero alemán, pastore tedesco, 德国牧羊犬. ImageNet consists of images in RGB format with varying resolutions. For example, in ImageNet 2012, "fish" category, the resolution ranges from 4288 x 2848 to 75 x 56. In machine learning, these are typically preprocessed into a standard constant resolution, and whitened, before further processing by neural networks. For example, in PyTorch, ImageNet images are by default normalized by dividing the pixel values so that they fall between 0 and 1, then subtracting by [0.485, 0.456, 0.406], then dividing by [0.229, 0.224, 0.225]. These are the mean and standard deviations for ImageNet, so this whitens the input data. === Labels and annotations === Each image is labelled with exactly one wnid. Dense SIFT features (raw SIFT descriptors, quantized codewords, and coordinates of each descriptor/codeword) for ImageNet-1K were available for download, designed for bag of visual words. The bounding boxes of objects were available for about 3000 popular synsets with on average 150 images in each synset. Furthermore, some images have attributes. They released 25 attributes for ~400 popular synsets: Color: black, blue, brown, gray, green, orange, pink, red, violet, white, yellow Pattern: spotted, striped Shape: long, round, rectangular, square Texture: furry, smooth, rough, shiny, metallic, vegetation, wooden, wet === ImageNet-21K === The full original dataset is referred to as ImageNet-21K. ImageNet-21k contains 14,197,122 images divided into 21,841 classes. Some papers round this up and name it ImageNet-22k. The full ImageNet-21k was released in Fall of 2011, as fall11_whole.tar. There is no official train-validation-test split for ImageNet-21k. Some classes contain only 1-10 samples, while others contain thousands. === ImageNet-1K === There are various subsets of the ImageNet dataset used in various context, sometimes referred to as "versions". One of the most highly used subsets of ImageNet is the "ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2012–2017 image classification and localization dataset". This is also referred to in the research literature as ImageNet-1K or ILSVRC2017, reflecting the original ILSVRC challenge that involved 1,000 classes. ImageNet-1K contains 1,281,167 training images, 50,000 validation images and 100,000 test images. Each category in ImageNet-1K is a leaf category, meaning that there are no child nodes below it, unlike ImageNet-21K. For example, in ImageNet-21K, there are some images categorized as simply "mammal", whereas in ImageNet-1K, there are only images categorized as things like "German shepherd", since there are no child-words below "German shepherd". === Later developments === In the WordNet they built ImageNet on, there were 2832 synsets in the "person" subtree. During 2018--2020 period, they removed the download of the ImageNet-21k as they went through extensive filtering in these person synsets. Out of these 2832 synsets, 1593 were deemed "potentially offensive". Out of the remaining 1239, 1081 were deemed not really "visual". The result was that only 158 syn

Autonomous aircraft

An autonomous aircraft is an aircraft which flies under the control of on-board autonomous robotic systems and needs no intervention from a human pilot or remote control. Most contemporary autonomous aircraft are unmanned aerial vehicles (drones) with pre-programmed algorithms to perform designated tasks, but advancements in artificial intelligence technologies (e.g. machine learning) mean that autonomous control systems are reaching a point where several air taxis and associated regulatory regimes are being developed. == History == === Unmanned aerial vehicles === The earliest recorded use of an unmanned aerial vehicle for warfighting occurred in July 1849, serving as a balloon carrier (the precursor to the aircraft carrier) Significant development of radio-controlled drones started in the early 1900s, and originally focused on providing practice targets for training military personnel. The earliest attempt at a powered UAV was A. M. Low's "Aerial Target" in 1916. Autonomous features such as the autopilot and automated navigation were developed progressively through the twentieth century, although techniques such as terrain contour matching (TERCOM) were applied mainly to cruise missiles. Before the introduction of the Bayraktar Kızılelma some modern drones have a high degree of autonomy, although they were not fully capable and the regulatory environment prohibits their widespread use in civil aviation. However some limited trials had been undertaken. On December 17, 2025, two Bayraktar Kızılelma performed the world's first autonomous close-formation flight by two unmanned fighter jets, using artificial intelligence. This was the first time in the history of aviation when two unmanned aerial vehicles flew in close formation on their own. === Passengers === As flight, navigation and communications systems have become more sophisticated, safely carrying passengers has emerged as a practical possibility. Autopilot systems are relieving the human pilot of progressively more duties, but the pilot currently remains necessary. A number of air taxis are under development and larger autonomous transports are also being planned. The personal air vehicle is another class where from one to four passengers are not expected to be able to pilot the aircraft and autonomy is seen as necessary for widespread adoption. == Control system architecture == The computing capability of aircraft flight and navigation systems followed the advances of computing technology, beginning with analog controls and evolving into microcontrollers, then system-on-a-chip (SOC) and single-board computers (SBC). === Sensors === Position and movement sensors give information about the aircraft state. Exteroceptive sensors deal with external information like distance measurements, while proprioceptive ones correlate internal and external states. Degrees of freedom (DOF) refers to both the amount and quality of sensors on board: 6 DOF implies 3-axis gyroscopes and accelerometers (a typical inertial measurement unit – IMU), 9 DOF refers to an IMU plus a compass, 10 DOF adds a barometer and 11 DOF usually adds a GPS receiver. === Actuators === UAV actuators include digital electronic speed controllers (which control the RPM of the motors) linked to motors/engines and propellers, servomotors (for planes and helicopters mostly), weapons, payload actuators, LEDs and speakers. === Software === UAV software called the flight stack or autopilot. The purpose of the flight stack is to obtain data from sensors, control motors to ensure UAV stability, and facilitate ground control and mission planning communication. UAVs are real-time systems that require rapid response to changing sensor data. As a result, UAVs rely on single-board computers for their computational needs. Examples of such single-board computers include Raspberry Pis, Beagleboards, etc. shielded with NavIO, PXFMini, etc. or designed from scratch such as NuttX, preemptive-RT Linux, Xenomai, Orocos-Robot Operating System or DDS-ROS 2.0. Civil-use open-source stacks include: Due to the open-source nature of UAV software, they can be customized to fit specific applications. For example, researchers from the Technical University of Košice have replaced the default control algorithm of the PX4 autopilot. This flexibility and collaborative effort has led to a large number of different open-source stacks, some of which are forked from others, such as CleanFlight, which is forked from BaseFlight and from which three other stacks are forked from. === Loop principles === UAVs employ open-loop, closed-loop or hybrid control architectures. Open loop – This type provides a positive control signal (faster, slower, left, right, up, down) without incorporating feedback from sensor data. Closed loop – This type incorporates sensor feedback to adjust behavior (reduce speed to reflect tailwind, move to altitude 300 feet). The PID controller is common. Sometimes, feedforward is employed, transferring the need to close the loop further. == Communications == Most UAVs use a radio for remote control and exchange of video and other data. Early UAVs had only narrowband uplink. Downlinks came later. These bi-directional narrowband radio links carried command and control (C&C) and telemetry data about the status of aircraft systems to the remote operator. For very long range flights, military UAVs also use satellite receivers as part of satellite navigation systems. In cases when video transmission was required, the UAVs will implement a separate analog video radio link. In most modern autonomous applications, video transmission is required. A broadband link is used to carry all types of data on a single radio link. These broadband links can leverage quality of service techniques to optimize the C&C traffic for low latency. Usually, these broadband links carry TCP/IP traffic that can be routed over the Internet. Communications can be established with: Ground control – a military ground control station (GCS). The MAVLink protocol is increasingly becoming popular to carry command and control data between the ground control and the vehicle. Remote network system, such as satellite duplex data links for some military powers. Downstream digital video over mobile networks has also entered consumer markets, while direct UAV control uplink over the cellular mesh and LTE have been demonstrated and are in trials. Another aircraft, serving as a relay or mobile control station – military manned-unmanned teaming (MUM-T). As mobile networks have increased in performance and reliability over the years, drones have begun to use mobile networks for communication. Mobile networks can be used for drone tracking, remote piloting, over the air updates, and cloud computing. Modern networking standards have explicitly considered autonomous aircraft and therefore include optimizations. The 5G standard has mandated reduced user plane latency to 1ms while using ultra-reliable and low-latency communications. == Autonomy == Basic autonomy comes from proprioceptive sensors. Advanced autonomy calls for situational awareness, knowledge about the environment surrounding the aircraft from exteroceptive sensors: sensor fusion integrates information from multiple sensors. Civil aviation regulators and standards bodies have published high-level roadmaps and discussion papers focused on assurance, safety and governance of AI-enabled systems in aviation, particularly as autonomy increases in operations and decision support. === Basic principles === One way to achieve autonomous control employs multiple control-loop layers, as in hierarchical control systems. As of 2016 the low-layer loops (i.e. for flight control) tick as fast as 32,000 times per second, while higher-level loops may cycle once per second. The principle is to decompose the aircraft's behavior into manageable "chunks", or states, with known transitions. Hierarchical control system types range from simple scripts to finite state machines, behavior trees and hierarchical task planners. The most common control mechanism used in these layers is the PID controller which can be used to achieve hover for a quadcopter by using data from the IMU to calculate precise inputs for the electronic speed controllers and motors. Examples of mid-layer algorithms: Path planning: determining an optimal path for vehicle to follow while meeting mission objectives and constraints, such as obstacles or fuel requirements Trajectory generation (motion planning): determining control maneuvers to take in order to follow a given path or to go from one location to another Trajectory regulation: constraining a vehicle within some tolerance to a trajectory Evolved UAV hierarchical task planners use methods like state tree searches or genetic algorithms. === Autonomy features === UAV manufacturers often build in specific autonomous operations, such as: Self-level: attitude stabilization on the pitch and roll axes. Altitude hold: The aircraft maint

Learnable function class

In statistical learning theory, a learnable function class is a set of functions for which an algorithm can be devised to asymptotically minimize the expected risk, uniformly over all probability distributions. The concept of learnable classes are closely related to regularization in machine learning, and provides large sample justifications for certain learning algorithms. == Definition == === Background === Let Ω = X × Y = { ( x , y ) } {\displaystyle \Omega ={\mathcal {X}}\times {\mathcal {Y}}=\{(x,y)\}} be the sample space, where y {\displaystyle y} are the labels and x {\displaystyle x} are the covariates (predictors). F = { f : X ↦ Y } {\displaystyle {\mathcal {F}}=\{f:{\mathcal {X}}\mapsto {\mathcal {Y}}\}} is a collection of mappings (functions) under consideration to link x {\displaystyle x} to y {\displaystyle y} . L : Y × Y ↦ R {\displaystyle L:{\mathcal {Y}}\times {\mathcal {Y}}\mapsto \mathbb {R} } is a pre-given loss function (usually non-negative). Given a probability distribution P ( x , y ) {\displaystyle P(x,y)} on Ω {\displaystyle \Omega } , define the expected risk I P ( f ) {\displaystyle I_{P}(f)} to be: I P ( f ) = ∫ L ( f ( x ) , y ) d P ( x , y ) {\displaystyle I_{P}(f)=\int L(f(x),y)dP(x,y)} The general goal in statistical learning is to find the function in F {\displaystyle {\mathcal {F}}} that minimizes the expected risk. That is, to find solutions to the following problem: f ^ = arg ⁡ min f ∈ F I P ( f ) {\displaystyle {\hat {f}}=\arg \min _{f\in {\mathcal {F}}}I_{P}(f)} But in practice the distribution P {\displaystyle P} is unknown, and any learning task can only be based on finite samples. Thus we seek instead to find an algorithm that asymptotically minimizes the empirical risk, i.e., to find a sequence of functions { f ^ n } n = 1 ∞ {\displaystyle \{{\hat {f}}_{n}\}_{n=1}^{\infty }} that satisfies lim n → ∞ P ( I P ( f ^ n ) − inf f ∈ F I P ( f ) > ϵ ) = 0 {\displaystyle \lim _{n\rightarrow \infty }\mathbb {P} (I_{P}({\hat {f}}_{n})-\inf _{f\in {\mathcal {F}}}I_{P}(f)>\epsilon )=0} One usual algorithm to find such a sequence is through empirical risk minimization. === Learnable function class === We can make the condition given in the above equation stronger by requiring that the convergence is uniform for all probability distributions. That is: The intuition behind the more strict requirement is as such: the rate at which sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} converges to the minimizer of the expected risk can be very different for different P ( x , y ) {\displaystyle P(x,y)} . Because in real world the true distribution P {\displaystyle P} is always unknown, we would want to select a sequence that performs well under all cases. However, by the no free lunch theorem, such a sequence that satisfies (1) does not exist if F {\displaystyle {\mathcal {F}}} is too complex. This means we need to be careful and not allow too "many" functions in F {\displaystyle {\mathcal {F}}} if we want (1) to be a meaningful requirement. Specifically, function classes that ensure the existence of a sequence { f ^ n } {\displaystyle \{{\hat {f}}_{n}\}} that satisfies (1) are known as learnable classes. It is worth noting that at least for supervised classification and regression problems, if a function class is learnable, then the empirical risk minimization automatically satisfies (1). Thus in these settings not only do we know that the problem posed by (1) is solvable, we also immediately have an algorithm that gives the solution. == Interpretations == If the true relationship between y {\displaystyle y} and x {\displaystyle x} is y ∼ f ∗ ( x ) {\displaystyle y\sim f^{}(x)} , then by selecting the appropriate loss function, f ∗ {\displaystyle f^{}} can always be expressed as the minimizer of the expected loss across all possible functions. That is, f ∗ = arg ⁡ min f ∈ F ∗ I P ( f ) {\displaystyle f^{}=\arg \min _{f\in {\mathcal {F}}^{}}I_{P}(f)} Here we let F ∗ {\displaystyle {\mathcal {F}}^{}} be the collection of all possible functions mapping X {\displaystyle {\mathcal {X}}} onto Y {\displaystyle {\mathcal {Y}}} . f ∗ {\displaystyle f^{}} can be interpreted as the actual data generating mechanism. However, the no free lunch theorem tells us that in practice, with finite samples we cannot hope to search for the expected risk minimizer over F ∗ {\displaystyle {\mathcal {F}}^{}} . Thus we often consider a subset of F ∗ {\displaystyle {\mathcal {F}}^{}} , F {\displaystyle {\mathcal {F}}} , to carry out searches on. By doing so, we risk that f ∗ {\displaystyle f^{}} might not be an element of F {\displaystyle {\mathcal {F}}} . This tradeoff can be mathematically expressed as In the above decomposition, part ( b ) {\displaystyle (b)} does not depend on the data and is non-stochastic. It describes how far away our assumptions ( F {\displaystyle {\mathcal {F}}} ) are from the truth ( F ∗ {\displaystyle {\mathcal {F}}^{}} ). ( b ) {\displaystyle (b)} will be strictly greater than 0 if we make assumptions that are too strong ( F {\displaystyle {\mathcal {F}}} too small). On the other hand, failing to put enough restrictions on F {\displaystyle {\mathcal {F}}} will cause it to be not learnable, and part ( a ) {\displaystyle (a)} will not stochastically converge to 0. This is the well-known overfitting problem in statistics and machine learning literature. == Example: Tikhonov regularization == A good example where learnable classes are used is the so-called Tikhonov regularization in reproducing kernel Hilbert space (RKHS). Specifically, let F ∗ {\displaystyle {\mathcal {F^{}}}} be an RKHS, and | | ⋅ | | 2 {\displaystyle ||\cdot ||_{2}} be the norm on F ∗ {\displaystyle {\mathcal {F^{}}}} given by its inner product. It is shown in that F = { f : | | f | | 2 ≤ γ } {\displaystyle {\mathcal {F}}=\{f:||f||_{2}\leq \gamma \}} is a learnable class for any finite, positive γ {\displaystyle \gamma } . The empirical minimization algorithm to the dual form of this problem is arg ⁡ min f ∈ F ∗ { ∑ i = 1 n L ( f ( x i ) , y i ) + λ | | f | | 2 } {\displaystyle \arg \min _{f\in {\mathcal {F}}^{}}\left\{\sum _{i=1}^{n}L(f(x_{i}),y_{i})+\lambda ||f||_{2}\right\}} This was first introduced by Tikhonov to solve ill-posed problems. Many statistical learning algorithms can be expressed in such a form (for example, the well-known ridge regression). The tradeoff between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in (2) is geometrically more intuitive with Tikhonov regularization in RKHS. We can consider a sequence of { F γ } {\displaystyle \{{\mathcal {F}}_{\gamma }\}} , which are essentially balls in F ∗ {\displaystyle {\mathcal {F^{}}}} with centers at 0. As γ {\displaystyle \gamma } gets larger, F γ {\displaystyle {\mathcal {F}}_{\gamma }} gets closer to the entire space, and ( b ) {\displaystyle (b)} is likely to become smaller. However we will also suffer smaller convergence rates in ( a ) {\displaystyle (a)} . The way to choose an optimal γ {\displaystyle \gamma } in finite sample settings is usually through cross-validation. == Relationship to empirical process theory == Part ( a ) {\displaystyle (a)} in (2) is closely linked to empirical process theory in statistics, where the empirical risk { ∑ i = 1 n L ( y i , f ( x i ) ) , f ∈ F } {\displaystyle \{\sum _{i=1}^{n}L(y_{i},f(x_{i})),f\in {\mathcal {F}}\}} are known as empirical processes. In this field, the function class F {\displaystyle {\mathcal {F}}} that satisfies the stochastic convergence are known as uniform Glivenko–Cantelli classes. It has been shown that under certain regularity conditions, learnable classes and uniformly Glivenko-Cantelli classes are equivalent. Interplay between ( a ) {\displaystyle (a)} and ( b ) {\displaystyle (b)} in statistics literature is often known as the bias-variance tradeoff. However, note that in the authors gave an example of stochastic convex optimization for General Setting of Learning where learnability is not equivalent with uniform convergence.

Rademacher complexity

In computational learning theory (machine learning and theory of computation), Rademacher complexity, named after Hans Rademacher, measures richness of a class of sets with respect to a probability distribution. The concept can also be extended to real valued functions. == Definitions == === Rademacher complexity of a set === Given a set A ⊆ R m {\displaystyle A\subseteq \mathbb {R} ^{m}} , the Rademacher complexity of A is defined as follows: Rad ⁡ ( A ) := 1 m E σ [ sup a ∈ A ∑ i = 1 m σ i a i ] {\displaystyle \operatorname {Rad} (A):={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{a\in A}\sum _{i=1}^{m}\sigma _{i}a_{i}\right]} where σ 1 , σ 2 , … , σ m {\displaystyle \sigma _{1},\sigma _{2},\dots ,\sigma _{m}} are independent random variables drawn from the Rademacher distribution i.e. Pr ( σ i = + 1 ) = Pr ( σ i = − 1 ) = 1 / 2 {\displaystyle \Pr(\sigma _{i}=+1)=\Pr(\sigma _{i}=-1)=1/2} for i ∈ { 1 , 2 , … , m } {\displaystyle i\in \{1,2,\dots ,m\}} , and a = ( a 1 , … , a m ) ∈ A {\displaystyle a=(a_{1},\ldots ,a_{m})\in A} . Some authors take the absolute value of the sum before taking the supremum, but if A {\displaystyle A} is symmetric this makes no difference. === Rademacher complexity of a function class === Let S = { z 1 , z 2 , … , z m } ⊆ Z {\displaystyle S=\{z_{1},z_{2},\dots ,z_{m}\}\subseteq Z} be a sample of points and consider a function class F {\displaystyle {\mathcal {F}}} of real-valued functions over Z {\displaystyle Z} . Then, the empirical Rademacher complexity of F {\displaystyle {\mathcal {F}}} given S {\displaystyle S} is defined as: Rad S ⁡ ( F ) = 1 m E σ [ sup f ∈ F | ∑ i = 1 m σ i f ( z i ) | ] {\displaystyle \operatorname {Rad} _{S}({\mathcal {F}})={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{f\in {\mathcal {F}}}\left|\sum _{i=1}^{m}\sigma _{i}f(z_{i})\right|\right]} This can also be written using the previous definition: Rad S ⁡ ( F ) = Rad ⁡ ( F ∘ S ) {\displaystyle \operatorname {Rad} _{S}({\mathcal {F}})=\operatorname {Rad} ({\mathcal {F}}\circ S)} where F ∘ S {\displaystyle {\mathcal {F}}\circ S} denotes function composition, i.e.: F ∘ S := { ( f ( z 1 ) , … , f ( z m ) ) ∣ f ∈ F } {\displaystyle {\mathcal {F}}\circ S:=\{(f(z_{1}),\ldots ,f(z_{m}))\mid f\in {\mathcal {F}}\}} The worst case empirical Rademacher complexity is Rad ¯ m ( F ) = sup S = { z 1 , … , z m } Rad S ⁡ ( F ) {\displaystyle {\overline {\operatorname {Rad} }}_{m}({\mathcal {F}})=\sup _{S=\{z_{1},\dots ,z_{m}\}}\operatorname {Rad} _{S}({\mathcal {F}})} Let P {\displaystyle P} be a probability distribution over Z {\displaystyle Z} . The Rademacher complexity of the function class F {\displaystyle {\mathcal {F}}} with respect to P {\displaystyle P} for sample size m {\displaystyle m} is: Rad P , m ⁡ ( F ) := E S ∼ P m [ Rad S ⁡ ( F ) ] {\displaystyle \operatorname {Rad} _{P,m}({\mathcal {F}}):=\mathbb {E} _{S\sim P^{m}}\left[\operatorname {Rad} _{S}({\mathcal {F}})\right]} where the above expectation is taken over an identically independently distributed (i.i.d.) sample S = ( z 1 , z 2 , … , z m ) {\displaystyle S=(z_{1},z_{2},\dots ,z_{m})} generated according to P {\displaystyle P} . == Intuition == The Rademacher complexity is typically applied on a function class of models that are used for classification, with the goal of measuring their ability to classify points drawn from a probability space under arbitrary labellings. When the function class is rich enough, it contains functions that can appropriately adapt for each arrangement of labels, simulated by the random draw of σ i {\displaystyle \sigma _{i}} under the expectation, so that this quantity in the sum is maximized. The Rademacher complexity of a set A {\displaystyle A} can be rewritten as Rad ⁡ ( A ) := 1 m E σ [ sup a ∈ A ∑ i = 1 m σ i a i ] = 1 m 2 m ∑ σ ∈ { − 1 / m , + 1 / m } m [ sup a ∈ A ⟨ σ , a ⟩ ] . {\displaystyle \operatorname {Rad} (A):={\frac {1}{m}}\mathbb {E} _{\sigma }\left[\sup _{a\in A}\sum _{i=1}^{m}\sigma _{i}a_{i}\right]={\frac {1}{{\sqrt {m}}2^{m}}}\sum _{\sigma \in \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}}\left[\sup _{a\in A}\langle \sigma ,a\rangle \right].} Each term in the summation is the farthest distance of the set A {\displaystyle A} from the origin, along a unit-length direction σ {\displaystyle \sigma } . The directions are along the vertices of a hypercube. Thus, we can also write it as Rad ⁡ ( A ) = 1 2 m 1 2 m − 1 ∑ σ ∈ { − 1 / m , + 1 / m } m / { − 1 , + 1 } [ sup a ∈ A ⟨ σ , a ⟩ − inf a ∈ A ⟨ σ , a ⟩ ] {\displaystyle \operatorname {Rad} (A)={\frac {1}{2{\sqrt {m}}}}{\frac {1}{2^{m-1}}}\sum _{\sigma \in \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}/\{-1,+1\}}\left[\sup _{a\in A}\langle \sigma ,a\rangle -\inf _{a\in A}\langle \sigma ,a\rangle \right]} Here, the set { − 1 / m , + 1 / m } m / { − 1 , + 1 } {\displaystyle \{-1/{\sqrt {m}},+1/{\sqrt {m}}\}^{m}/\{-1,+1\}} denotes half of the vertices of a hypercube, selected so that each diagonal has exactly one vertex selected. In words, this states that 2 m Rad ⁡ ( A ) {\displaystyle 2{\sqrt {m}}\operatorname {Rad} (A)} is precisely the average width of the set A {\displaystyle A} along all diagonal directions of a hypercube. == Examples == A singleton set has 0 width in any direction, so it has Rademacher complexity 0. The set A = { ( 1 , 1 ) , ( 1 , 2 ) } ⊆ R 2 {\displaystyle A=\{(1,1),(1,2)\}\subseteq \mathbb {R} ^{2}} has average width 1 / 2 {\displaystyle 1/{\sqrt {2}}} along the two diagonal directions of the square, so it has Rademacher complexity 1 / 4 {\displaystyle 1/4} . The unit cube [ 0 , 1 ] m {\displaystyle [0,1]^{m}} has constant width m {\displaystyle {\sqrt {m}}} along the diagonal directions, so it has Rademacher complexity 1 / 2 {\displaystyle 1/2} . Similarly, the unit cross-polytope { x ∈ R m : ‖ x ‖ 1 ≤ 1 } {\displaystyle \{x\in \mathbb {R} ^{m}:\|x\|_{1}\leq 1\}} has constant width 2 / m {\displaystyle 2/{\sqrt {m}}} along the diagonal directions, so it has Rademacher complexity 1 / m {\displaystyle 1/m} . == Using the Rademacher complexity == The Rademacher complexity can be used to derive data-dependent upper-bounds on the learnability of function classes. Intuitively, a function-class with smaller Rademacher complexity is easier to learn. === Bounding the representativeness === In machine learning, it is desired to have a training set that represents the true distribution of some sample data S {\displaystyle S} . This can be quantified using the notion of representativeness. Denote by P {\displaystyle P} the probability distribution from which the samples are drawn. Denote by H {\displaystyle H} the set of hypotheses (potential classifiers) and denote by F {\displaystyle {\mathcal {F}}} the corresponding set of error functions, i.e., for every hypothesis h ∈ H {\displaystyle h\in H} , there is a function f h ∈ F {\displaystyle f_{h}\in F} , that maps each training sample (features,label) to the error of the classifier h {\displaystyle h} (note in this case hypothesis and classifier are used interchangeably). For example, in the case that h {\displaystyle h} represents a binary classifier, the error function is a 0–1 loss function, i.e. the error function f h {\displaystyle f_{h}} returns 0 if h {\displaystyle h} correctly classifies a sample and 1 else. We omit the index and write f {\displaystyle f} instead of f h {\displaystyle f_{h}} when the underlying hypothesis is irrelevant. Define: L P ( f ) := E z ∼ P [ f ( z ) ] {\displaystyle L_{P}(f):=\mathbb {E} _{z\sim P}[f(z)]} – the expected error of some error function f ∈ F {\displaystyle f\in {\mathcal {F}}} on the real distribution P {\displaystyle P} ; L S ( f ) := 1 m ∑ i = 1 m f ( z i ) {\displaystyle L_{S}(f):={1 \over m}\sum _{i=1}^{m}f(z_{i})} – the estimated error of some error function f ∈ F {\displaystyle f\in {\mathcal {F}}} on the sample S {\displaystyle S} . The representativeness of the sample S {\displaystyle S} , with respect to P {\displaystyle P} and F {\displaystyle {\mathcal {F}}} , is defined as: Rep P ⁡ ( F , S ) := sup f ∈ F ( L P ( f ) − L S ( f ) ) {\displaystyle \operatorname {Rep} _{P}({\mathcal {F}},S):=\sup _{f\in F}(L_{P}(f)-L_{S}(f))} Smaller representativeness is better, since it provides a way to avoid overfitting: it means that the true error of a classifier is not much higher than its estimated error, and so selecting a classifier that has low estimated error will ensure that the true error is also low. Note however that the concept of representativeness is relative and hence can not be compared across distinct samples. The expected representativeness of a sample can be bounded above by the Rademacher complexity of the function class: If F {\displaystyle {\mathcal {F}}} is a set of functions with range within [ 0 , 1 ] {\displaystyle [0,1]} , then Rad P , m ⁡ ( F ) − ln ⁡ 2 2 m ≤ E S ∼ P m [ Rep P ⁡ ( F , S ) ] ≤ 2 Rad P , m ⁡ ( F ) {\displaystyle \operatorname {Rad} _{P,m}({\mathcal {F}})-{\sqrt {\frac {\ln 2}{2m}}}\leq \mathbb {E} _{S\sim P^{m}}[\operatorname {Rep} _{P}({\

Hidden layer

In artificial neural networks, a hidden layer is a layer of artificial neurons that is neither an input layer nor an output layer. The simplest examples appear in multilayer perceptrons (MLP), as illustrated in the diagram. An MLP without any hidden layer is essentially just a linear model. With hidden layers and activation functions, however, nonlinearity is introduced into the model. In typical machine learning practice, the weights and biases are initialized, then iteratively updated during training via backpropagation.

Fluency Voice Technology

Fluency Voice Technology was a company that developed and sold packaged speech recognition solutions for use in call centers. Fluency's Speech Recognition solutions are used by call centers worldwide to improve customer service and significantly reduce costs and are available on-premises and hosted. == History == 1998 – Fluency was created as a spin-off from the Voice Research & Development team of a company called netdecisions. This R&D operation was established in Cambridge UK. The focus of the development was speech recognition systems based on the VXML standard. 2001 – Fluency became a separate entity in May 2001. Fluency began the creation of a software development platform specifically aimed at automating call center activities. This platform became Fluency's VoiceRunner. 2002 to 2004 – Fluency establishes accomplishes many successful deployments in customer sites such as National Express and Barclaycard. 2003 – Fluency expanded into the USA. Fluency also acquires Vocalis of Cambridge, UK in August 2003. 2004 – Fluency receives £6 million investment from leading European Venture Capitalists and establishes a global OEM partnership with Avaya, and the acquisition of SRC Telecom. 2008 – Fluency is acquired by Syntellect Ltd == Customers == Call Centers around the world use Fluency to improve service and reduce costs. They include Travelodge, Standard Life Bank, Sutton and East Surrey Water, Pizza Hut, CWT, Barclays, Powergen, First Choice, OutRight, J D Williams, Capital Blue Cross, Chelsea Building Society, EDF, bss, TV Licensing and Capita Software Services.

Embodied cognitive science

Embodied cognitive science is an interdisciplinary field of research, the aim of which is to explain the mechanisms underlying intelligent behavior. It comprises three main methodologies: the modeling of psychological and biological systems in a holistic manner that considers the mind and body as a single entity; the formation of a common set of general principles of intelligent behavior; and the experimental use of robotic agents in controlled environments. == Contributors == Embodied cognitive science borrows heavily from embodied philosophy and the related research fields of cognitive science, psychology, neuroscience and artificial intelligence. Contributors to the field include: From the perspective of neuroscience, Gerald Edelman of the Neurosciences Institute at La Jolla, Francisco Varela of CNRS in France, and J. A. Scott Kelso of Florida Atlantic University From the perspective of psychology, Lawrence Barsalou, Michael Turvey, Vittorio Guidano and Eleanor Rosch From the perspective of linguistics, Gilles Fauconnier, George Lakoff, Mark Johnson, Leonard Talmy and Mark Turner From the perspective of language acquisition, Eric Lenneberg and Philip Rubin at Haskins Laboratories From the perspective of anthropology, Edwin Hutchins, Bradd Shore, James Wertsch and Merlin Donald. From the perspective of autonomous agent design, early work is sometimes attributed to Rodney Brooks or Valentino Braitenberg From the perspective of artificial intelligence, Understanding Intelligence by Rolf Pfeifer and Christian Scheier or How the Body Shapes the Way We Think, by Rolf Pfeifer and Josh C. Bongard From the perspective of philosophy, Andy Clark, Dan Zahavi, Shaun Gallagher, and Evan Thompson In 1950, Alan Turing proposed that a machine may need a human-like body to think and speak: It can also be maintained that it is best to provide the machine with the best sense organs that money can buy, and then teach it to understand and speak English. That process could follow the normal teaching of a child. Things would be pointed out and named, etc. Again, I do not know what the right answer is, but I think both approaches should be tried. == Traditional cognitive theory == Embodied cognitive science is an alternative theory to cognition in which it minimizes appeals to computational theory of mind in favor of greater emphasis on how an organism's body determines how and what it thinks. Traditional cognitive theory is based mainly around symbol manipulation, in which certain inputs are fed into a processing unit that produces an output. These inputs follow certain rules of syntax, from which the processing unit finds semantic meaning. Thus, an appropriate output is produced. For example, a human's sensory organs are its input devices, and the stimuli obtained from the external environment are fed into the nervous system which serves as the processing unit. From here, the nervous system is able to read the sensory information because it follows a syntactic structure, thus an output is created. This output then creates bodily motions and brings forth behavior and cognition. Of particular note is that cognition is sealed away in the brain, meaning that mental cognition is cut off from the external world and is only possible by the input of sensory information. == The embodied cognitive approach == Embodied cognitive science differs from the traditionalist approach in that it denies the input-output system. This is chiefly due to the problems presented by the Homunculus argument, which concluded that semantic meaning could not be derived from symbols without some kind of inner interpretation. If some little man in a person's head interpreted incoming symbols, then who would interpret the little man's inputs? Because of the specter of an infinite regress, the traditionalist model began to seem less plausible. Thus, embodied cognitive science aims to avoid this problem by defining cognition in three ways. === Physical attributes of the body === The first aspect of embodied cognition examines the role of the physical body, particularly how its properties affect its ability to think. This part attempts to overcome the symbol manipulation component that is a feature of the traditionalist model. Depth perception, for instance, can be better explained under the embodied approach due to the sheer complexity of the action. Depth perception requires that the brain detect the disparate retinal images obtained by the distance of the two eyes. In addition, body and head cues complicate this further. When the head is turned in a given direction, objects in the foreground will appear to move against objects in the background. From this, it is said that some kind of visual processing is occurring without the need of any kind of symbol manipulation. This is because the objects appearing to move the foreground are simply appearing to move. This observation concludes then that depth can be perceived with no intermediate symbol manipulation necessary. A more poignant example exists through examining auditory perception. Generally speaking the greater the distance between the ears, the greater the possible auditory acuity. Also relevant is the amount of density in between the ears, for the strength of the frequency wave alters as it passes through a given medium. The brain's auditory system takes these factors into account as it process information, but again without any need for a symbolic manipulation system. This is because the distance between the ears for example does not need symbols to represent it. The distance itself creates the necessary opportunity for greater auditory acuity. The amount of density between the ears is similar, in that it is the actual amount itself that simply forms the opportunity for frequency alteration. Thus under consideration of the physical properties of the body, a symbolic system is unnecessary and an unhelpful metaphor. === The body's role in the cognitive process === The second aspect draws heavily from George Lakoff's and Mark Johnson's work on concepts. They argued that humans use metaphors whenever possible to better explain their external world. Humans also have a basic stock of concepts in which other concepts can be derived from. These basic concepts include spatial orientations such as up, down, front, and back. Humans can understand what these concepts mean because they can directly experience them from their own bodies. For example, because human movement revolves around standing erect and moving the body in an up-down motion, humans innately have these concepts of up and down. Lakoff and Johnson contend this is similar with other spatial orientations such as front and back too. As mentioned earlier, these basic stocks of spatial concepts are the basis in which other concepts are constructed. Happy and sad for instance are seen now as being up or down respectively. When someone says they are feeling down, what they are really saying is that they feel sad for example. Thus the point here is that true understanding of these concepts is contingent on whether one can have an understanding of the human body. So the argument goes that if one lacked a human body, they could not possibly know what up or down could mean, or how it could relate to emotional states. [I]magine a spherical being living outside of any gravitational field, with no knowledge or imagination of any other kind of experience. What could UP possibly mean to such a being? While this does not mean that such beings would be incapable of expressing emotions in other words, it does mean that they would express emotions differently from humans. Human concepts of happiness and sadness would be different because human would have different bodies. So then an organism's body directly affects how it can think, because it uses metaphors related to its body as the basis of concepts. === Interaction of local environment === A third component of the embodied approach looks at how agents use their immediate environment in cognitive processing. Meaning, the local environment is seen as an actual extension of the body's cognitive process. The example of a personal digital assistant (PDA) is used to better imagine this. Echoing functionalism (philosophy of mind), this point claims that mental states are individuated by their role in a much larger system. So under this premise, the information on a PDA is similar to the information stored in the brain. So then if one thinks information in the brain constitutes mental states, then it must follow that information in the PDA is a cognitive state too. Consider also the role of pen and paper in a complex multiplication problem. The pen and paper are so involved in the cognitive process of solving the problem that it seems ridiculous to say they are somehow different from the process, in very much the same way the PDA is used for information like the brain. Another example examines how humans control and manipulate their environment