In the fields of information technology (IT) and systems management, IT operations analytics (ITOA) is an approach or method to retrieve, analyze, and report data for IT operations. ITOA may apply big data analytics to large datasets to produce business insights. In 2014, Gartner predicted its use might increase revenue or reduce costs. By 2017, it predicted that 15% of enterprises will use IT operations analytics technologies. == Definition == IT operations analytics (ITOA) (also known as advanced operational analytics, or IT data analytics) technologies are primarily used to discover complex patterns in high volumes of often "noisy" IT system availability and performance data. Forrester Research defined IT analytics as "The use of mathematical algorithms and other innovations to extract meaningful information from the sea of raw data collected by management and monitoring technologies." Note, ITOA is different than AIOps, which focuses on applying artificial intelligence and machine learning to the applications of ITOA. == History == Operations research as a discipline emerged from the Second World War to improve military efficiency and decision-making on the battlefield. However, only with the emergence of machine learning tech in the early 2000s could an artificially intelligent operational analytics platform actually begin to engage in the high-level pattern recognition that could adequately serve business needs. A critical catalyst towards ITOA development was the rise of Google, which pioneered a predictive analytics model that represented the first attempt to read into patterns of human behavior on the Internet. IT specialists then applied predictive analytics to the IT Industry, coming forward with platforms that can sift through data to generate insights without the need for human intervention. Due to the mainstream embrace of cloud computing and the increasing desire for businesses to adopt more big data practices, the ITOA industry has grown significantly since 2010. A 2016 ExtraHop survey of large and mid-size corporations indicates that 65 percent of the businesses surveyed will seek to integrate their data silos either this year or the next. The current goals of ITOA platforms are to improve the accuracy of their APM services, facilitate better integration with the data, and to enhance their predictive analytics capabilities. == Applications == ITOA systems tend to be used by IT operations teams, and Gartner describes seven applications of ITOA systems: Root cause analysis: The models, structures and pattern descriptions of IT infrastructure or application stack being monitored can help users pinpoint fine-grained and previously unknown root causes of overall system behavior pathologies. Proactive control of service performance and availability: Predicts future system states and the impact of those states on performance. Problem assignment: Determines how problems may be resolved or, at least, direct the results of inferences to the most appropriate individuals, or communities in the enterprise for problem resolution. Service impact analysis: When multiple root causes are known, the analytics system's output is used to determine and rank the relative impact, so that resources can be devoted to correcting the fault in the most timely and cost-effective way possible. Complement best-of-breed technology: The models, structures and pattern descriptions of IT infrastructure or application stack being monitored are used to correct or extend the outputs of other discovery-oriented tools to improve the fidelity of information used in operational tasks (e.g., service dependency maps, application runtime architecture topologies, network topologies). Real time application behavior learning: Learns & correlates the behavior of Application based on user pattern and underlying Infrastructure on various application patterns, create metrics of such correlated patterns and store it for further analysis. Dynamically baselines threshold: Learns behavior of Infrastructure on various application user patterns and determines the Optimal behavior of the Infra and technological components, bench marks and baselines the low and high water mark for the specific environments and dynamically changes the bench mark baselines with the changing infra and user patterns without any manual intervention. == Types == In their Data Growth Demands a Single, Architected IT Operations Analytics Platform, Gartner Research describes five types of analytics technologies: Log analysis Unstructured text indexing, search and inference (UTISI) Topological analysis (TA) Multidimensional database search and analysis (MDSA) Complex operations event processing (COEP) Statistical pattern discovery and recognition (SPDR) == Tools and ITOA platforms == A number of vendors operate in the ITOA space:
C-RAN
C-RAN (Cloud-RAN), also referred to as Centralized-RAN, is an architecture for cellular networks. C-RAN is a centralized, cloud computing-based architecture for radio access networks that supports 2G, 3G, 4G, 5G and future wireless communication standards. Its name comes from the four 'C's in the main characteristics of C-RAN system, "Clean, Centralized processing, Collaborative radio, and a real-time Cloud Radio Access Network". == Background == Traditional cellular, or Radio Access Networks (RAN), consist of many stand-alone base stations (BTS). Each BTS covers a small area, whereas a group BTS provides coverage over a continuous area. Each BTS processes and transmits its own signal to and from the mobile terminal, and forwards the data payload to and from the mobile terminal and out to the core network via the backhaul. Each BTS has its own cooling, back haul transportation, backup battery, monitoring system, and so on. Because of limited spectral resources, network operators 'reuse' the frequency among different base stations, which can cause interference between neighboring cells. There are several limitations in the traditional cellular architecture. First, each BTS is costly to build and operate. Moore's law helps reduce the size and power of an electrical system, but the supporting facilities of the BTS are not improved quite as well. Second, when more BTS are added to a system to improve its capacity, interference among BTS is more severe as BTS are closer to each other and more of them are using the same frequency. Third, because users are mobile, the traffic of each BTS fluctuates (called 'tide effect'), and as a result, the average utilization rate of individual BTS is pretty low. However, these processing resources cannot be shared with other BTS. Therefore, all BTS are designed to handle the maximum traffic, not average traffic, resulting in a waste of processing resources and power at idle times. == Evolution of base station architecture == === All-in-one macro base station === In the 1G and 2G cellular networks, base stations had an all-in-one architecture. Analog, digital, and power functions were housed in a single cabinet as large as a refrigerator. Usually the base station cabinet was placed in a dedicated room along with all necessary supporting facilitates such as power, backup battery, air conditioning, environment surveillance, and backhaul transmission equipment. The RF signal is generated by the base station RF unit and propagates through pairs of RF cables up to the antennas on the top of a base station tower or other mounting points. This all-in-one architecture was mostly found in macro cell deployments. === Distributed base station === For 3G, a distributed base station architecture was introduced by Ericsson, Nokia, Huawei, and other leading telecom equipment vendors. In this architecture the radio function unit, also known as the remote radio head (RRH), is separated from the digital function unit, or baseband unit (BBU) by fiber. Digital baseband signals are carried over fiber, using the Open Base Station Architecture Initiative (OBSAI) or Common Public Radio Interface (CPRI) standard. The RRH can be installed on the top of tower close to the antenna, reducing the loss compared to the traditional base station where the RF signal has to travel through a long cable from the base station cabinet to the antenna at the top of the tower. The fiber link between RRH and BBU also allows more flexibility in network planning and deployment as they can be placed a few hundred meters or a few kilometers away. Most modern base stations now use this decoupled architecture. === C-RAN/Cloud-RAN === C-RAN may be viewed as an architectural evolution of the above distributed base station system. It takes advantage of many technological advances in wireless, optical and IT communications systems. For example, it uses the latest CPRI standard, low cost Coarse or Dense Wavelength Division Multiplexing (CWDM/ DWDM) technology, and mmWave to allow transmission of baseband signal over long distance thus achieving large scale centralised base station deployment. It applies recent Data Centre Network technology to allow a low cost, high reliability, low latency and high bandwidth interconnect network in the BBU pool. It utilizes open platforms and real-time virtualization technology rooted in cloud computing to achieve dynamic shared resource allocation and support multi-vendor, multi-technology environments. == Architecture overview == C-RAN architecture has the following characteristics that are distinct from other cellular architectures: Large scale centralized deployment: Allows many RRHs to connect to a centralized BBU pool. The maximum distance can be 20km in fiber link for 4G (LTE/LTE-A) systems, and even longer distances (40~80km) for 3G (WCDMA/TD-SCDMA) and 2G (GSM/CDMA) systems. Native support to Collaborative Radio technologies: Any BBU can talk with any other BBU within the BBU pool with very high bandwidth (10 Gbit/s and above) and low latency (10 μs level). This is enabled by the interconnection of BBUs in the pool. This is one major difference from BBU Hotelling, or base station Hotelling; in the latter case, the BBUs of different base stations are simply stacked together and have no direct link between them to allow physical layer co-ordination. Real-time virtualization capability based on open platform: This is different from traditional base stations built on proprietary hardware, where the software and hardware are close-sourced and provided by single vendors. In contrast, a C-RAN BBU pool is built on open hardware, like x86/ARM CPU based servers, and interface cards that handle fiber links to RRHs and inter-connections in the pool. Real-time virtualization ensures that resources in the pool can be allocated dynamically to base station software stacks, say 4G/3G/2G function modules from different vendors, according to network load. However, to satisfy the strict timing requirements of wireless communication systems, the real-time performance for C-RAN is at the level of tens of microseconds, which is two orders of magnitude better than the millisecond level 'real-time' performance usually seen in Cloud Computing environments. == Similar architecture and systems == KT, a telecom operator in the Republic of Korea, introduced a Cloud Computing Center (CCC) system in their 3G (WCDMA/HSPA) and 4G (LTE/LTE-A) network in 2011 and 2012. The concept of CCC is basically the same as C-RAN. SK Telecom has also deployed Smart Cloud Access Network (SCAN) and Advanced-SCAN in their 4G (LTE/LTE-A) network in Korea no later than 2012. In 2014, Airvana (now CommScope) introduced OneCell, a C-RAN-based small cell system designed for enterprises and public spaces. == Competing architectures in cellular network evolution == === All-in-one BTS === One major alternative solution that is addressing similar challenges of RAN, is the small size, all-in-one outdoor BTS. Thanks to the achievements in the semiconductor industry, all the functionality of a BTS, including RF, baseband processing, MAC processing and package level processing, can now be implemented in a volume of <50 liters. This makes the system small and weatherproof, reduces the difficulty of BTS site choice and construction, eliminates the air conditioning requirement, and thus reduces operational costs. However, because each BTS is still working on its own, it cannot readily make use of the collaboration algorithms to reduce the interference between neighboring BTSs. It is also relatively hard to upgrade or repair because the all-in-one BTS units are usually mounted near the antenna. More processing units in less-protected environments also implies a higher failure rate compared to C-RAN, which only has the RRU deployed outdoors. The advantage of Cloud RAN lies in its ability to implement LTE-Advanced features such as Coordinated MultiPoint (CoMP) with very low latency between multiple radio heads. However, the economic benefit of improvements such as CoMP can be negated by the higher backhaul costs for some operators. === Small cell === The main competition between small cell and C-RAN occurs in two deployment scenarios: outdoor hotspot coverage and indoor coverage. == Academic research and publications == As one of the promising evolution paths for future cellular network architecture, C-RAN has attracted high academic research interest. Meanwhile, because the native support of cooperative radio capability built into the C-RAN architecture, it also enables many advanced algorithms that were hard to implement in cellular networks, including Cooperative Multi-Point Transmission/Receiving, Network Coding, etc. In October 2011, Wireless World Research Forum 27 was hosted in Germany, when China Mobile was invited to give a C-RAN presentation. In August 2012, IEEE C-RAN 2012 workshop was hosted in Kunming, China. CRC Press published a book, "Green Communications: Theore
Sequence labeling
In machine learning, sequence labeling is a type of pattern recognition task that involves the algorithmic assignment of a categorical label to each member of a sequence of observed values. A common example of a sequence labeling task is part of speech tagging, which seeks to assign a part of speech to each word in an input sentence or document. Sequence labeling can be treated as a set of independent classification tasks, one per member of the sequence. However, accuracy is generally improved by making the optimal label for a given element dependent on the choices of nearby elements, using special algorithms to choose the globally best set of labels for the entire sequence at once. As an example of why finding the globally best label sequence might produce better results than labeling one item at a time, consider the part-of-speech tagging task just described. Frequently, many words are members of multiple parts of speech, and the correct label of such a word can often be deduced from the correct label of the word to the immediate left or right. For example, the word "sets" can be either a noun or verb. In a phrase like "he sets the books down", the word "he" is unambiguously a pronoun, and "the" unambiguously a determiner, and using either of these labels, "sets" can be deduced to be a verb, since nouns very rarely follow pronouns and are less likely to precede determiners than verbs are. But in other cases, only one of the adjacent words is similarly helpful. In "he sets and then knocks over the table", only the word "he" to the left is helpful (cf. "...picks up the sets and then knocks over..."). Conversely, in "... and also sets the table" only the word "the" to the right is helpful (cf. "... and also sets of books were ..."). An algorithm that proceeds from left to right, labeling one word at a time, can only use the tags of left-adjacent words and might fail in the second example above; vice versa for an algorithm that proceeds from right to left. Most sequence labeling algorithms are probabilistic in nature, relying on statistical inference to find the best sequence. The most common statistical models in use for sequence labeling make a Markov assumption, i.e. that the choice of label for a particular word is directly dependent only on the immediately adjacent labels; hence the set of labels forms a Markov chain. This leads naturally to the hidden Markov model (HMM), one of the most common statistical models used for sequence labeling. Other common models in use are the maximum entropy Markov model and conditional random field.
Anna Becker
Anna Becker is an Israeli researcher known in the field of artificial intelligence and computer science within the financial field. == Early life and education == Becker was born in Russia and immigrated to Israel at 16 after graduating from a school in Moscow. At 17, she began her studies at Technion – Israel Institute of Technology. During her master's degree in computer science, she taught first-year students of the same course, and at 27, Becker completed her PhD in Computer Science and Artificial Intelligence. == Career == While pursuing her PhD, Becker resolved an NP-complete approximation algorithm that had been unresolved for over twenty years. This made her a recognized scholar in the field. After completing her PhD, she developed an approximation technique by a factor of two. This technique is widely used today in operating systems, database systems, and VLSI chip designs. She then founded and sold Strategy Runner, a fintech software. After this, she founded EndoTech, an algorithmic trading platform based on artificial intelligence and machine learning. EndoTech's trading strategies have been operating in live cryptocurrency markets since 2017. The platform's BTC Alpha strategy has reported an average annual return of 163% on fixed capital over eight years of live operation, with a maximum drawdown of 14% and a trade accuracy rate of approximately 83%. In 2026, EndoTech entered a partnership with Bit1 Exchange to make its BTC Alpha and ETH Alpha copy trading strategies accessible to retail investors with no minimum deposit requirement, through a full-custody model in which user funds remain in their own exchange wallets at all times.As of 2023, Becker is working on Fianchetto Fund, an AI-based investing analysis platform. Becker has also co-authored a book on Bayesian networks, which has been published widely in the field of computer science and artificial intelligence.
Contrastive Language-Image Pre-training
Contrastive Language-Image Pre-training (CLIP) is a technique for training a pair of neural network models, one for image understanding and one for text understanding, using a contrastive objective. This method has enabled broad applications across multiple domains, including cross-modal retrieval, text-to-image generation, and aesthetic ranking. == Algorithm == The CLIP method trains a pair of models contrastively. One model takes in a piece of text as input and outputs a single vector representing its semantic content. The other model takes in an image and similarly outputs a single vector representing its visual content. The models are trained so that the vectors corresponding to semantically similar text-image pairs are close together in the shared vector space, while those corresponding to dissimilar pairs are far apart. To train a pair of CLIP models, one would start by preparing a large dataset of image-caption pairs. During training, the models are presented with batches of N {\displaystyle N} image-caption pairs. Let the outputs from the text and image models be respectively v 1 , . . . , v N , w 1 , . . . , w N {\displaystyle v_{1},...,v_{N},w_{1},...,w_{N}} . Two vectors are considered "similar" if their dot product is large. The loss incurred on this batch is the multi-class N-pair loss, which is a symmetric cross-entropy loss over similarity scores: − 1 N ∑ i ln e v i ⋅ w i / T ∑ j e v i ⋅ w j / T − 1 N ∑ j ln e v j ⋅ w j / T ∑ i e v i ⋅ w j / T {\displaystyle -{\frac {1}{N}}\sum _{i}\ln {\frac {e^{v_{i}\cdot w_{i}/T}}{\sum _{j}e^{v_{i}\cdot w_{j}/T}}}-{\frac {1}{N}}\sum _{j}\ln {\frac {e^{v_{j}\cdot w_{j}/T}}{\sum _{i}e^{v_{i}\cdot w_{j}/T}}}} In essence, this loss function encourages the dot product between matching image and text vectors ( v i ⋅ w i {\displaystyle v_{i}\cdot w_{i}} ) to be high, while discouraging high dot products between non-matching pairs. The parameter T > 0 {\displaystyle T>0} is the temperature, which is parameterized in the original CLIP model as T = e − τ {\displaystyle T=e^{-\tau }} where τ ∈ R {\displaystyle \tau \in \mathbb {R} } is a learned parameter. Other loss functions are possible. For example, Sigmoid CLIP (SigLIP) proposes the following loss function: L = 1 N ∑ i , j ∈ 1 : N f ( ( 2 δ i , j − 1 ) ( e τ w i ⋅ v j + b ) ) {\displaystyle L={\frac {1}{N}}\sum _{i,j\in 1:N}f((2\delta _{i,j}-1)(e^{\tau }w_{i}\cdot v_{j}+b))} where f ( x ) = ln ( 1 + e − x ) {\displaystyle f(x)=\ln(1+e^{-x})} is the negative log sigmoid loss, and the Dirac delta symbol δ i , j {\displaystyle \delta _{i,j}} is 1 if i = j {\displaystyle i=j} else 0. == CLIP models == While the original model was developed by OpenAI, subsequent models have been trained by other organizations as well. === Image model === The image encoding models used in CLIP are typically vision transformers (ViT). The naming convention for these models often reflects the specific ViT architecture used. For instance, "ViT-L/14" means a "vision transformer large" (compared to other models in the same series) with a patch size of 14, meaning that the image is divided into 14-by-14 pixel patches before being processed by the transformer. The size indicator ranges from B, L, H, G (base, large, huge, giant), in that order. Other than ViT, the image model is typically a convolutional neural network, such as ResNet (in the original series by OpenAI), or ConvNeXt (in the OpenCLIP model series by LAION). Since the output vectors of the image model and the text model must have exactly the same length, both the image model and the text model have fixed-length vector outputs, which in the original report is called "embedding dimension". For example, in the original OpenAI model, the ResNet models have embedding dimensions ranging from 512 to 1024, and for the ViTs, from 512 to 768. Its implementation of ViT was the same as the original one, with one modification: after position embeddings are added to the initial patch embeddings, there is a LayerNorm. Its implementation of ResNet was the same as the original one, with 3 modifications: In the start of the CNN (the "stem"), they used three stacked 3x3 convolutions instead of a single 7x7 convolution, as suggested by. There is an average pooling of stride 2 at the start of each downsampling convolutional layer (they called it rect-2 blur pooling according to the terminology of ). This has the effect of blurring images before downsampling, for antialiasing. The final convolutional layer is followed by a multiheaded attention pooling. ALIGN a model with similar capabilities, trained by researchers from Google used EfficientNet, a kind of convolutional neural network. === Text model === The text encoding models used in CLIP are typically Transformers. In the original OpenAI report, they reported using a Transformer (63M-parameter, 12-layer, 512-wide, 8 attention heads) with lower-cased byte pair encoding (BPE) with 49152 vocabulary size. Context length was capped at 76 for efficiency. Like GPT, it was decoder-only, with only causally-masked self-attention. Its architecture is the same as GPT-2. Like BERT, the text sequence is bracketed by two special tokens [SOS] and [EOS] ("start of sequence" and "end of sequence"). Take the activations of the highest layer of the transformer on the [EOS], apply LayerNorm, then a final linear map. This is the text encoding of the input sequence. The final linear map has output dimension equal to the embedding dimension of whatever image encoder it is paired with. These models all had context length 77 and vocabulary size 49408. ALIGN used BERT of various sizes. == Dataset == === WebImageText === The CLIP models released by OpenAI were trained on a dataset called "WebImageText" (WIT) containing 400 million pairs of images and their corresponding captions scraped from the internet. The total number of words in this dataset is similar in scale to the WebText dataset used for training GPT-2, which contains about 40 gigabytes of text data. The dataset contains 500,000 text-queries, with up to 20,000 (image, text) pairs per query. The text-queries were generated by starting with all words occurring at least 100 times in English Wikipedia, then extended by bigrams with high mutual information, names of all Wikipedia articles above a certain search volume, and WordNet synsets. The dataset is private and has not been released to the public, and there is no further information on it. ==== Data preprocessing ==== For the CLIP image models, the input images are preprocessed by first dividing each of the R, G, B values of an image by the maximum possible value, so that these values fall between 0 and 1, then subtracting by [0.48145466, 0.4578275, 0.40821073], and dividing by [0.26862954, 0.26130258, 0.27577711]. The rationale was that these are the mean and standard deviations of the images in the WebImageText dataset, so this preprocessing step roughly whitens the image tensor. These numbers slightly differ from the standard preprocessing for ImageNet, which uses [0.485, 0.456, 0.406] and [0.229, 0.224, 0.225]. If the input image does not have the same resolution as the native resolution (224×224 for all except ViT-L/14@336px, which has 336×336 resolution), then the input image is first scaled by bicubic interpolation, so that its shorter side is the same as the native resolution, then the central square of the image is cropped out. === Others === ALIGN used over one billion image-text pairs, obtained by extracting images and their alt-tags from online crawling. The method was described as similar to how the Conceptual Captions dataset was constructed, but instead of complex filtering, they only applied a frequency-based filtering. Later models trained by other organizations had published datasets. For example, LAION trained OpenCLIP with published datasets LAION-400M, LAION-2B, and DataComp-1B. == Training == In the original OpenAI CLIP report, they reported training 5 ResNet and 3 ViT (ViT-B/32, ViT-B/16, ViT-L/14). Each was trained for 32 epochs. The largest ResNet model took 18 days to train on 592 V100 GPUs. The largest ViT model took 12 days on 256 V100 GPUs. All ViT models were trained on 224×224 image resolution. The ViT-L/14 was then boosted to 336×336 resolution by FixRes, resulting in a model. They found this was the best-performing model. In the OpenCLIP series, the ViT-L/14 model was trained on 384 A100 GPUs on the LAION-2B dataset, for 160 epochs for a total of 32B samples seen. == Applications == === Cross-modal retrieval === CLIP's cross-modal retrieval enables the alignment of visual and textual data in a shared latent space, allowing users to retrieve images based on text descriptions and vice versa, without the need for explicit image annotations. In text-to-image retrieval, users input descriptive text, and CLIP retrieves images with matching embeddings. In image-to-text retrieval, images are used to find related text content. CLIP’s ability to connect vis
Class activation mapping
Class activation mapping methods are explainable AI (XAI) techniques used to visualize the regions of an input image that are the most relevant for a particular task, especially image classification, in convolutional neural networks (CNNs). These methods generate heatmaps by weighting the feature maps from a convolutional layer according to their relevance to the target class. In the field of artificial intelligence, generically defined as "the effort to automate intellectual tasks normally performed by humans", machine learning and deep learning were created. They both use statistical and computational methods to learn patterns from data, reducing the need for manually coded rules. Machine learning models are trained on input data and the known respective answers, learning the underlying patterns or structures present in the data. Traditional Machine learning algorithms employ manually designed feature sets, posing a direct link between machine learning designers and employed features. Deep learning is a subfield of machine learning, based on the concept of successive layers of representation, in which the data is progressively unfolded in different ways, to extract relevant and informative patterns in data analysis. Deep learning algorithms are defined as feature learning algorithms automatically learning hierarchical feature representations from raw data, extracting increasingly abstract features through multiple layers. CNNs are a specific architecture of deep learning models, designed to process spatially structured data, such as images, exploiting a series of convolution, non-linear activation and pooling operations to extract relevant features, contained in the so-called feature maps from input data. CNNs have demonstrated to be highly effective in a variety of computer vision and image processing tasks. CNNs (and deep learning models more broadly) are described as black boxes due to their complex and non-transparent internal layers of representation. The need for clearer indications on its internal working and decision-making process gave birth to XAI techniques. Among the proposed XAI techniques for computer vision tasks, Class activation mapping methods can show which pixels in an input image are important to the predicted logit for a class of interest, in a classification task. Class activation mapping methods were originally developed for class-discriminative scenarios to visualize which parts of the input image influenced the classification decision, namely to visually highlight the regions of those feature maps that contribute most strongly to the prediction of a given class. More advanced versions of these methods are not limited to image classification tasks, but have been extended also to several vision-related tasks, such as object detection, image captioning, visual question answering and image segmentation. == Background == The following methods laid the groundwork for the class activation maps approaches, forming the conceptual basis of using gradients to highlight class-discriminative regions. === Class model visualization and saliency maps for convolutional neural networks === The class model visualization and image-specific saliency maps approaches have been presented in the foundational work "Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps" by Karen Simonyan, Andrea Vedaldi, and Andrew Zisserman and it generalizes the deconvnet method by Zeiler and Fergus. Class model visualization synthesizes an artificial input image that strongly activates the output neurons associated with a target class. Given a trained, fixed model, this method starts with a zero-initialized image, backpropagates the gradients from the class score to the image pixels, updates the image pixels increasing the specific class scores and it repeats the pixel updating process, showing an encoded (idealized version) prototype of the class of interest. Image-specific class saliency visualization method provides a visual explanation by highlighting the most relevant pixels in an image for predicting a certain class C of interest. This is done by computing the gradient of the class score with respect to the input image, I 0 , {\displaystyle I_{0},} w = ∂ S C ∂ I | I 0 {\displaystyle w=\left.{\frac {\partial S_{C}}{\partial I}}\right|_{I_{0}}} approximating the model locally (around I 0 {\displaystyle I_{0}} ) as linear, using a first-order Taylor expansion: S C ( I ) ≈ w C T I + b {\displaystyle S_{C}(I)\approx w_{C}^{T}I+b} . The magnitude of w C {\displaystyle w_{C}} , the gradient, indicates the importancy of the pixels: larger gradients suggest greater influence on the prediction. Once the gradient is known, the saliency map is defined as the maximum absolute gradient across the color channels: M i j = m a x C | ∂ S C ∂ I i j C | {\displaystyle M_{ij}=max_{C}\left|{\frac {\partial S_{C}}{\partial I_{ij}^{C}}}\right|} resulting in an saliency map (i.e. heatmap). === Guided backpropagation === The concept of guided backpropagation can be traced for the first time in the paper by Springenberg et al. "Striving For Simplicity: The All Convolutional Net" and also this method builds upon the work by Zeiler and Fergus "Visualizing and Understanding Convolutional Networks". Guided backpropagation core is to understand what a CNN is learning, by visualizing the patterns that activate more strongly individual neurons (or filters), in architectures which do not rely on max-pooling layer. When propagating gradients back through a rectified linear unit (ReLU), guided backpropagation passes the gradient if and only if the input to the ReLU was positive (forward pass) and the output gradient is positive (backward signal), tackling both inactive neurons, negative gradients and suppressing the noise. The result displays sharper, high-resolution visualizations of what each neuron is responding to. Guided backpropagation represents a simple and practical method for model interpretability, helping understand how and where neural networks detect semantic concepts across layers. Moreover, it can be applied to any network architecture, due to its working principle. == Base versions == Class activation mapping and gradient-weighted class activation mapping are the original and most widely used methods for visual explanations in convolutional neural networks. These methods serve as the foundation for many later developments in explainable AI. Notation: In this article, the symbols i and j represent integer indices that disappear inside sums or averages, while x and y are the continuous (or up-sampled integer) coordinates of the final heat-map that is plotted. === Class activation mapping (CAM) === Class activation mapping (CAM) was the first, and the original, version of CAM methods, and it gave the name to the whole category. The approach was firstly introduced by Zhou et al. in their seminal work "Learning Deep Features for Discriminative Localization". This approach achieves class-specific heatmaps by modifying image classification CNN architectures, replacing fully-connected layers with convolutional layers and a final global average pooling layer. Its main scope is to localize and highlight discriminative regions of an input image that a CNN uses to identify a particular class, without needing explicit bounding box annotations. ==== Global average pooling (GAP) ==== Global average pooling (GAP) represents the key element in the original CAM approach. It is a dimensionality reduction technique and, similarly to other pooling layers, it allows the downsampling of the feature maps, calculating representative values for a specific region of the feature map. The particularity of GAP is that it calculates a single value for an entire feature map, significantly reducing the model dimensions. ==== Mathematical description ==== The mathematical description considers as its key the combination of convolutional and GAP layers. In CAM, it is mandatory to have the GAP layer after the last convolutional layer and before the final linear classifier layer. This last element of the architecture connects the output logits (the network predictions) y C {\displaystyle y^{C}} , to the GAP values, with its respective fine-tuned weights, w k C {\displaystyle w_{k}^{C}} . Considering A k {\displaystyle A^{k}} as the last feature maps of the last convolutional layer, GAP produces one value for each feature map, by averaging all the matrix elements (i, j) of the feature map: F k = 1 m n ∑ i = 1 m ∑ j = 1 n A i j k {\displaystyle F^{k}={\frac {1}{mn}}\sum _{i=1}^{m}\sum _{j=1}^{n}A_{ij}^{k}} with A k = [ A 11 k A 12 k ⋯ A 1 n k A 21 k A 22 k ⋯ A 2 n k ⋮ ⋮ ⋱ ⋮ A m 1 k A m 2 k ⋯ A m n k ] = { A i j k ∣ 1 ≤ i ≤ m , 1 ≤ j ≤ n } {\displaystyle A^{k}={\begin{bmatrix}A_{11}^{k}&A_{12}^{k}&\cdots &A_{1n}^{k}\\A_{21}^{k}&A_{22}^{k}&\cdots &A_{2n}^{k}\\\vdots &\vdots &\ddots &\vdots \\A_{m1}^{k}&A_{m2}^{k}&\cdots &A_{mn}^{k}\end{bmatrix}}=\left\{A_{
Inductive programming
Inductive programming (IP) is a special area of automatic programming, covering research from artificial intelligence and programming, which addresses learning of typically declarative (logic or functional) and often recursive programs from incomplete specifications, such as input/output examples or constraints. Depending on the programming language used, there are several kinds of inductive programming. Inductive functional programming, which uses functional programming languages such as Lisp or Haskell, and most especially inductive logic programming, which uses logic programming languages such as Prolog and other logical representations such as description logics, have been more prominent, but other (programming) language paradigms have also been used, such as constraint programming or probabilistic programming. == Definition == Inductive programming incorporates all approaches which are concerned with learning programs or algorithms from incomplete (formal) specifications. Possible inputs in an IP system are a set of training inputs and corresponding outputs or an output evaluation function, describing the desired behavior of the intended program, traces or action sequences which describe the process of calculating specific outputs, constraints for the program to be induced concerning its time efficiency or its complexity, various kinds of background knowledge such as standard data types, predefined functions to be used, program schemes or templates describing the data flow of the intended program, heuristics for guiding the search for a solution or other biases. Output of an IP system is a program in some arbitrary programming language containing conditionals and loop or recursive control structures, or any other kind of Turing-complete representation language. In many applications the output program must be correct with respect to the examples and partial specification, and this leads to the consideration of inductive programming as a special area inside automatic programming or program synthesis, usually opposed to 'deductive' program synthesis, where the specification is usually complete. In other cases, inductive programming is seen as a more general area where any declarative programming or representation language can be used and we may even have some degree of error in the examples, as in general machine learning, the more specific area of structure mining or the area of symbolic artificial intelligence. A distinctive feature is the number of examples or partial specification needed. Typically, inductive programming techniques can learn from just a few examples. The diversity of inductive programming usually comes from the applications and the languages that are used: apart from logic programming and functional programming, other programming paradigms and representation languages have been used or suggested in inductive programming, such as functional logic programming, constraint programming, probabilistic programming, abductive logic programming, modal logic, action languages, agent languages and many types of imperative languages. == History == The early works of Plotkin, and his "relative least general generalization (rlgg)", had an enormous impact in inductive logic programming. There were some encouraging results on learning recursive Prolog programs such as quicksort from examples together with suitable background knowledge, for example with GOLEM. However, after initial success, the community got disappointed by limited progress about the induction of recursive programs with ILP less and less focusing on recursive programs and leaning more and more towards a machine learning setting with applications in relational data mining and knowledge discovery. In parallel to work in ILP, Koza proposed genetic programming in the early 1990s as a generate-and-test based approach to learning programs. The idea of genetic programming was further developed into the inductive programming system ADATE and the systematic-search-based system MagicHaskeller. Here again, functional programs are learned from sets of positive examples together with an output evaluation (fitness) function which specifies the desired input/output behavior of the program to be learned. The early work in grammar induction (also known as grammatical inference) is related to inductive programming, as rewriting systems or logic programs can be used to represent production rules. In fact, early works in inductive inference considered grammar induction and Lisp program inference as basically the same problem. The results in terms of learnability were related to classical concepts, such as identification-in-the-limit, as introduced in the seminal work of Gold. More recently, the language learning problem was addressed by the inductive programming community. In the recent years, the classical approaches have been resumed and advanced with great success. Therefore, the synthesis problem has been reformulated on the background of constructor-based term rewriting systems taking into account modern techniques of functional programming, as well as moderate use of search-based strategies and usage of background knowledge as well as automatic invention of subprograms. Many new and successful applications have recently appeared beyond program synthesis, most especially in the area of data manipulation, programming by example and cognitive modelling (see below). Other ideas have also been explored with the common characteristic of using declarative languages for the representation of hypotheses. For instance, the use of higher-order features, schemes or structured distances have been advocated for a better handling of recursive data types and structures; abstraction has also been explored as a more powerful approach to cumulative learning and function invention. One powerful paradigm that has been recently used for the representation of hypotheses in inductive programming (generally in the form of generative models) is probabilistic programming (and related paradigms, such as stochastic logic programs and Bayesian logic programming). == Application areas == The first workshop on Approaches and Applications of Inductive Programming (AAIP) Archived 2016-03-03 at the Wayback Machine held in conjunction with ICML 2005 identified all applications where "learning of programs or recursive rules are called for, [...] first in the domain of software engineering where structural learning, software assistants and software agents can help to relieve programmers from routine tasks, give programming support for end users, or support of novice programmers and programming tutor systems. Further areas of application are language learning, learning recursive control rules for AI-planning, learning recursive concepts in web-mining or for data-format transformations". Since then, these and many other areas have shown to be successful application niches for inductive programming, such as end-user programming, the related areas of programming by example and programming by demonstration, and intelligent tutoring systems. Other areas where inductive inference has been recently applied are knowledge acquisition, artificial general intelligence, reinforcement learning and theory evaluation, and cognitive science in general. There may also be prospective applications in intelligent agents, games, robotics, personalisation, ambient intelligence and human interfaces.