Intrapixel and Interpixel processing

Intrapixel and Interpixel processing

Intrapixel and Interpixel processing is used in the processing of computers graphics, as well as sensors and images in equipment such as cameras. For computer graphics, CMOS sensor processing is done in pixel level. This process includes two general categories: intrapixel processing, where the processing is performed on the individual pixel signals, and interpixel processing, where the processing is performed locally or globally on signals from several pixels. The purpose of interpixel processing is to perform early vision processing, not merely to capture images. Intrapixel and Interpixel processing is an integral part of spatial processing within the earth Mixed Spatial Attraction Model. This also includes use within hyperspectral image processing.

Tensor (machine learning)

In machine learning, the term tensor informally refers to two different concepts: (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data may be organized in a multidimensional array (M-way array), informally referred to as a "data tensor"; however, in the strict mathematical sense, a tensor is a multilinear mapping over a set of domain vector spaces to a range vector space. Observations, such as images, movies, volumes, sounds, and relationships among words and concepts, stored in an M-way array ("data tensor"), may be analyzed either by artificial neural networks or tensor methods. Tensor decomposition factors data tensors into smaller tensors. Operations on data tensors can be expressed in terms of matrix multiplication and the Kronecker product. The computation of gradients, a crucial aspect of backpropagation, can be performed using software libraries such as PyTorch and TensorFlow. Computations are often performed on graphics processing units (GPUs) using CUDA, and on dedicated hardware such as Google's Tensor Processing Unit or Nvidia's Tensor core. These developments have greatly accelerated neural network architectures, and increased the size and complexity of models that can be trained. == History == A tensor is by definition a multilinear map. In mathematics, this may express a multilinear relationship between sets of algebraic objects. In physics, tensor fields, considered as tensors at each point in space, are useful in expressing mechanics such as stress or elasticity. In machine learning, the exact use of tensors depends on the statistical approach being used. In 2001, the field of signal processing and statistics were making use of tensor methods. Pierre Comon surveys the early adoption of tensor methods in the fields of telecommunications, radio surveillance, chemometrics and sensor processing. Linear tensor rank methods (such as, Parafac/CANDECOMP) analyzed M-way arrays ("data tensors") composed of higher order statistics that were employed in blind source separation problems to compute a linear model of the data. He noted several early limitations in determining the tensor rank and efficient tensor rank decomposition. In the early 2000s, multilinear tensor methods crossed over into computer vision, computer graphics and machine learning with papers by Vasilescu or in collaboration with Terzopoulos, such as Human Motion Signatures, TensorFaces TensorTextures and Multilinear Projection. Multilinear algebra, the algebra of higher-order tensors, is a suitable and transparent framework for analyzing the multifactor structure of an ensemble of observations and for addressing the difficult problem of disentangling the causal factors based on second order or higher order statistics associated with each causal factor. Tensor (multilinear) factor analysis disentangles and reduces the influence of different causal factors with multilinear subspace learning. When treating an image or a video as a 2- or 3-way array, i.e., "data matrix/tensor", tensor methods reduce spatial or time redundancies as demonstrated by Wang and Ahuja. Yoshua Bengio, Geoff Hinton and their collaborators briefly discuss the relationship between deep neural networks and tensor factor analysis beyond the use of M-way arrays ("data tensors") as inputs. One of the early uses of tensors for neural networks appeared in natural language processing. A single word can be expressed as a vector via Word2vec. Thus a relationship between two words can be encoded in a matrix. However, for more complex relationships such as subject-object-verb, it is necessary to build higher-dimensional networks. In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From 2014 to 2015, tensor methods become more common in convolutional neural networks (CNNs). Tensor methods organize neural network weights in a "data tensor", analyze and reduce the number of neural network weights. Lebedev et al. accelerated CNN networks for character classification (the recognition of letters and digits in images) by using 4D kernel tensors. == Definition == Let F {\displaystyle \mathbb {F} } be a field (such as the real numbers R {\displaystyle \mathbb {R} } or the complex numbers C {\displaystyle \mathbb {C} } ). A tensor T ∈ F I 1 × I 2 × … × I C {\displaystyle {\mathcal {T}}\in {\mathbb {F} }^{I_{1}\times I_{2}\times \ldots \times I_{C}}} is a multilinear transformation from a set of domain vector spaces to a range vector space: T : { F I 1 × F I 2 × … F I C } ↦ F I 0 {\displaystyle {\mathcal {T}}:\{{\mathbb {F} }^{I_{1}}\times {\mathbb {F} }^{I_{2}}\times \ldots {\mathbb {F} }^{I_{C}}\}\mapsto {\mathbb {F} }^{I_{0}}} Here, C {\displaystyle C} and I 0 , I 1 , … , I C {\displaystyle I_{0},I_{1},\ldots ,I_{C}} are positive integers, and ( C + 1 ) {\displaystyle (C+1)} is the number of modes of a tensor (also known as the number of ways of a multi-way array). The dimensionality of mode c {\displaystyle c} is I c {\displaystyle I_{c}} , for 0 ≤ c ≤ C {\displaystyle 0\leq c\leq C} . In statistics and machine learning, an image is vectorized when viewed as a single observation, and a collection of vectorized images is organized as a "data tensor". For example, a set of facial images { d i p , i e , i l , i v ∈ R I X } {\displaystyle \{{\mathbb {d} }_{i_{p},i_{e},i_{l},i_{v}}\in {\mathbb {R} }^{I_{X}}\}} with I X {\displaystyle I_{X}} pixels that are the consequences of multiple causal factors, such as a facial geometry i p ( 1 ≤ i p ≤ I P ) {\displaystyle i_{p}(1\leq i_{p}\leq I_{P})} , an expression i e ( 1 ≤ i e ≤ I E ) {\displaystyle i_{e}(1\leq i_{e}\leq I_{E})} , an illumination condition i l ( 1 ≤ i l ≤ I L ) {\displaystyle i_{l}(1\leq i_{l}\leq I_{L})} , and a viewing condition i v ( 1 ≤ i v ≤ I V ) {\displaystyle i_{v}(1\leq i_{v}\leq I_{V})} may be organized into a data tensor (ie. multiway array) D ∈ R I X × I P × I E × I L × V {\displaystyle {\mathcal {D}}\in {\mathbb {R} }^{I_{X}\times I_{P}\times I_{E}\times I_{L}\times V}} where I P {\displaystyle I_{P}} are the total number of facial geometries, I E {\displaystyle I_{E}} are the total number of expressions, I L {\displaystyle I_{L}} are the total number of illumination conditions, and I V {\displaystyle I_{V}} are the total number of viewing conditions. Tensor factorizations methods such as TensorFaces and multilinear (tensor) independent component analysis factorizes the data tensor into a set of vector spaces that span the causal factor representations, where an image is the result of tensor transformation T {\displaystyle {\mathcal {T}}} that maps a set of causal factor representations to the pixel space. Another approach to using tensors in machine learning is to embed various data types directly. For example, a grayscale image, commonly represented as a discrete 2-way array D ∈ R I R X × I C X {\displaystyle {\mathbf {D} }\in {\mathbb {R} }^{I_{RX}\times I_{CX}}} with dimensionality I R X × I C X {\displaystyle I_{RX}\times I_{CX}} where I R X {\displaystyle I_{RX}} are the number of rows and I C X {\displaystyle I_{CX}} are the number of columns. When an image is treated as 2-way array or 2nd order tensor (i.e. as a collection of column/row observations), tensor factorization methods compute the image column space, the image row space and the normalized PCA coefficients or the ICA coefficients. Similarly, a color image with RGB channels, D ∈ R N × M × 3 . {\displaystyle {\mathcal {D}}\in \mathbb {R} ^{N\times M\times 3}.} may be viewed as a 3rd order data tensor or 3-way array.-------- In natural language processing, a word might be expressed as a vector v {\displaystyle v} via the Word2vec algorithm. Thus v {\displaystyle v} becomes a mode-1 tensor v ↦ A ∈ R N . {\displaystyle v\mapsto {\mathcal {A}}\in \mathbb {R} ^{N}.} The embedding of subject-object-verb semantics requires embedding relationships among three words. Because a word is itself a vector, subject-object-verb semantics could be expressed using mode-3 tensors v a × v b × v c ↦ A ∈ R N × N × N . {\displaystyle v_{a}\times v_{b}\times v_{c}\mapsto {\mathcal {A}}\in \mathbb {R} ^{N\times N\times N}.} In practice the neural network designer is primarily concerned with the specification of embeddings, the connection of tensor layers, and the operations performed on them in a network. Modern machine learning frameworks manage the optimization, tensor factorization and backpropagation automatically. === As unit values === Tensors may be used as the unit values of neural networks which extend the concept of scalar, vector and matrix values to multiple dimensions. The output value of single layer unit y m {\displaystyle y_{m}} is the sum-product of its input units and the connection weights filtered through the activation function f {\displaystyle f} : y m = f ( ∑ n x n u m , n ) , {\displaystyle y_{m}=f\left(\sum _{n}x_{n}u_{m,n}\right),} where y m ∈ R .

Semantic interpretation

Semantic interpretation is an important component in dialog systems. It is related to natural language understanding, but mostly it refers to the last stage of understanding. The goal of interpretation is binding the user utterance to concept, or something the system can understand. Typically it is creating a database query based on user utterance.

XLNet

The XLNet was an autoregressive Transformer designed as an improvement over BERT, with 340M parameters and trained on 33 billion words. It was released on 19 June 2019, under the Apache 2.0 license. It achieved state-of-the-art results on a variety of natural language processing tasks, including language modeling, question answering, and natural language inference. == Architecture == The main idea of XLNet is to model language autoregressively like the GPT models, but allow for all possible permutations of a sentence. Concretely, consider the following sentence:My dog is cute.In standard autoregressive language modeling, the model would be tasked with predicting the probability of each word, conditioned on the previous words as its context: We factorize the joint probability of a sequence of words x 1 , … , x T {\displaystyle x_{1},\ldots ,x_{T}} using the chain rule: Pr ( x 1 , … , x T ) = Pr ( x 1 ) Pr ( x 2 | x 1 ) Pr ( x 3 | x 1 , x 2 ) … Pr ( x T | x 1 , … , x T − 1 ) . {\displaystyle \Pr(x_{1},\ldots ,x_{T})=\Pr(x_{1})\Pr(x_{2}|x_{1})\Pr(x_{3}|x_{1},x_{2})\ldots \Pr(x_{T}|x_{1},\ldots ,x_{T-1}).} For example, the sentence "My dog is cute" is factorized as: Pr ( My , dog , is , cute ) = Pr ( My ) Pr ( dog | My ) Pr ( is | My , dog ) Pr ( cute | My , dog , is ) . {\displaystyle \Pr({\text{My}},{\text{dog}},{\text{is}},{\text{cute}})=\Pr({\text{My}})\Pr({\text{dog}}|{\text{My}})\Pr({\text{is}}|{\text{My}},{\text{dog}})\Pr({\text{cute}}|{\text{My}},{\text{dog}},{\text{is}}).} Schematically, we can write it as → My → My dog → My dog is → My dog is cute . {\displaystyle {\texttt {}}{\texttt {}}{\texttt {}}{\texttt {}}\to {\text{My }}{\texttt {}}{\texttt {}}{\texttt {}}\to {\text{My dog }}{\texttt {}}{\texttt {}}\to {\text{My dog is }}{\texttt {}}\to {\text{My dog is cute}}.} However, for XLNet, the model is required to predict the words in a randomly generated order. Suppose we have sampled a randomly generated order 3241, then schematically, the model is required to perform the following prediction task: is dog is dog is cute → My dog is cute {\displaystyle {\texttt {}}{\texttt {}}{\texttt {}}{\texttt {}}\to {\texttt {}}{\texttt {}}{\text{is }}{\texttt {}}\to {\texttt {}}{\text{dog is }}{\texttt {}}\to {\texttt {}}{\text{dog is cute}}\to {\text{My dog is cute}}} By considering all permutations, XLNet is able to capture longer-range dependencies and better model the bidirectional context of words. === Two-Stream Self-Attention === To implement permutation language modeling, XLNet uses a two-stream self-attention mechanism. The two streams are: Content stream: This stream encodes the content of each word, as in standard causally masked self-attention. Query stream: This stream encodes the content of each word in the context of what has gone before. In more detail, it is a masked cross-attention mechanism, where the queries are from the query stream, and the key-value pairs are from the content stream. The content stream uses the causal mask M causal = [ 0 − ∞ − ∞ … − ∞ 0 0 − ∞ … − ∞ 0 0 0 … − ∞ ⋮ ⋮ ⋮ ⋱ ⋮ 0 0 0 … 0 ] {\displaystyle M_{\text{causal}}={\begin{bmatrix}0&-\infty &-\infty &\dots &-\infty \\0&0&-\infty &\dots &-\infty \\0&0&0&\dots &-\infty \\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\dots &0\end{bmatrix}}} permuted by a random permutation matrix to P M causal P − 1 {\displaystyle PM_{\text{causal}}P^{-1}} . The query stream uses the cross-attention mask P ( M causal − ∞ I ) P − 1 {\displaystyle P(M_{\text{causal}}-\infty I)P^{-1}} , where the diagonal is subtracted away specifically to avoid the model "cheating" by looking at the content stream for what the current masked token is. Like the causal masking for GPT models, this two-stream masked architecture allows the model to train on all tokens in one forward pass. == Training == Two models were released: XLNet-Large, cased: 110M parameters, 24-layer, 1024-hidden, 16-heads XLNet-Base, cased: 340M parameters, 12-layer, 768-hidden, 12-heads. It was trained on a dataset that amounted to 32.89 billion tokens after tokenization with SentencePiece. The dataset was composed of BooksCorpus, and English Wikipedia, Giga5, ClueWeb 2012-B, and Common Crawl. It was trained on 512 TPU v3 chips, for 5.5 days. At the end of training, it still under-fitted the data, meaning it could have achieved lower loss with more training. It took 0.5 million steps with an Adam optimizer, linear learning rate decay, and a batch size of 8192.

Speech segmentation

Speech segmentation is the process of identifying the boundaries between words, syllables, or phonemes in spoken natural languages. The term applies both to the mental processes used by humans, and to artificial processes of natural language processing. In the field of automatic pronunciation assessment, the process of segmenting an utterance against expected word(s) is called forced alignment. Speech segmentation is a subfield of general speech perception and an important subproblem of the technologically focused field of speech recognition, and cannot be adequately solved in isolation. As in most natural language processing problems, one must take into account context, grammar, and semantics, and even so the result is often a probabilistic division (statistically based on likelihood) rather than a categorical one. Though it seems that coarticulation—a phenomenon which may happen between adjacent words just as easily as within a single word—presents the main challenge in speech segmentation across languages, some other problems and strategies employed in solving those problems can be seen in the following sections. This problem overlaps to some extent with the problem of text segmentation that occurs in some languages which are traditionally written without inter-word spaces, like Chinese and Japanese, compared to writing systems which indicate speech segmentation between words by a word divider, such as the space. However, even for those languages, text segmentation is often much easier than speech segmentation, because the written language usually has little interference between adjacent words, and often contains additional clues not present in speech (such as the use of Chinese characters for word stems in Japanese). == Lexical recognition == In natural languages, the meaning of a complex spoken sentence can be understood by decomposing it into smaller lexical segments (roughly, the words of the language), associating a meaning to each segment, and combining those meanings according to the grammar rules of the language. Though lexical recognition is not thought to be used by infants in their first year, due to their highly limited vocabularies, it is one of the major processes involved in speech segmentation for adults. Three main models of lexical recognition exist in current research: first, whole-word access, which argues that words have a whole-word representation in the lexicon; second, decomposition, which argues that morphologically complex words are broken down into their morphemes (roots, stems, inflections, etc.) and then interpreted and; third, the view that whole-word and decomposition models are both used, but that the whole-word model provides some computational advantages and is therefore dominant in lexical recognition. To give an example, in a whole-word model, the word "cats" might be stored and searched for by letter, first "c", then "ca", "cat", and finally "cats". The same word, in a decompositional model, would likely be stored under the root word "cat" and could be searched for after removing the "s" suffix. "Falling", similarly, would be stored as "fall" and suffixed with the "ing" inflection. Though proponents of the decompositional model recognize that a morpheme-by-morpheme analysis may require significantly more computation, they argue that the unpacking of morphological information is necessary for other processes (such as syntactic structure) which may occur parallel to lexical searches. As a whole, research into systems of human lexical recognition is limited due to little experimental evidence that fully discriminates between the three main models. In any case, lexical recognition likely contributes significantly to speech segmentation through the contextual clues it provides, given that it is a heavily probabilistic system—based on the statistical likelihood of certain words or constituents occurring together. For example, one can imagine a situation where a person might say "I bought my dog at a ____ shop" and the missing word's vowel is pronounced as in "net", "sweat", or "pet". While the probability of "netshop" is extremely low, since "netshop" isn't currently a compound or phrase in English, and "sweatshop" also seems contextually improbable, "pet shop" is a good fit because it is a common phrase and is also related to the word "dog". Moreover, an utterance can have different meanings depending on how it is split into words. A popular example, often quoted in the field, is the phrase "How to wreck a nice beach", which sounds very similar to "How to recognize speech". As this example shows, proper lexical segmentation depends on context and semantics which draws on the whole of human knowledge and experience, and would thus require advanced pattern recognition and artificial intelligence technologies to be implemented on a computer. Lexical recognition is of particular value in the field of computer speech recognition, since the ability to build and search a network of semantically connected ideas would greatly increase the effectiveness of speech-recognition software. Statistical models can be used to segment and align recorded speech to words or phones. Applications include automatic lip-synch timing for cartoon animation, follow-the-bouncing-ball video sub-titling, and linguistic research. Automatic segmentation and alignment software is commercially available. == Phonotactic cues == For most spoken languages, the boundaries between lexical units are difficult to identify; phonotactics are one answer to this issue. One might expect that the inter-word spaces used by many written languages like English or Spanish would correspond to pauses in their spoken version, but that is true only in very slow speech, when the speaker deliberately inserts those pauses. In normal speech, one typically finds many consecutive words being said with no pauses between them, and often the final sounds of one word blend smoothly or fuse with the initial sounds of the next word. The notion that speech is produced like writing, as a sequence of distinct vowels and consonants, may be a relic of alphabetic heritage for some language communities. In fact, the way vowels are produced depends on the surrounding consonants just as consonants are affected by surrounding vowels; this is called coarticulation. For example, in the word "kit", the [k] is farther forward than when we say 'caught'. But also, the vowel in "kick" is phonetically different from the vowel in "kit", though we normally do not hear this. In addition, there are language-specific changes which occur in casual speech which makes it quite different from spelling. For example, in English, the phrase "hit you" could often be more appropriately spelled "hitcha". From a decompositional perspective, in many cases, phonotactics play a part in letting speakers know where to draw word boundaries. In English, the word "strawberry" is perceived by speakers as consisting (phonetically) of two parts: "straw" and "berry". Other interpretations such as "stra" and "wberry" are inhibited by English phonotactics, which does not allow the cluster "wb" word-initially. Other such examples are "day/dream" and "mile/stone" which are unlikely to be interpreted as "da/ydream" or "mil/estone" due to the phonotactic probability or improbability of certain clusters. The sentence "Five women left", which could be phonetically transcribed as [faɪvwɪmɘnlɛft], is marked since neither /vw/ in /faɪvwɪmɘn/ nor /nl/ in /wɪmɘnlɛft/ are allowed as syllable onsets or codas in English phonotactics. These phonotactic cues often allow speakers to easily distinguish the boundaries in words. Vowel harmony in languages like Finnish can also serve to provide phonotactic cues. While the system does not allow front vowels and back vowels to exist together within one morpheme, compounds allow two morphemes to maintain their own vowel harmony while coexisting in a word. Therefore, in compounds such as "selkä/ongelma" ('back problem') where vowel harmony is distinct between two constituents in a compound, the boundary will be wherever the switch in harmony takes place—between the "ä" and the "ö" in this case. Still, there are instances where phonotactics may not aid in segmentation. Words with unclear clusters or uncontrasted vowel harmony as in "opinto/uudistus" ('student reform') do not offer phonotactic clues as to how they are segmented. From the perspective of the whole-word model, however, these words are thought be stored as full words, so the constituent parts would not necessarily be relevant to lexical recognition. == In infants and non-natives == Infants are one major focus of research in speech segmentation. Since infants have not yet acquired a lexicon capable of providing extensive contextual clues or probability-based word searches within their first year, as mentioned above, they must often rely primarily upon phonotactic and rhythmic cues (with prosody being the dominant cue), all

Attention (machine learning)

In machine learning, attention is a method that determines the importance of each component in a sequence relative to the other components in that sequence. In natural language processing, importance is represented by "soft" weights assigned to each word in a sentence. More generally, attention encodes vectors called token embeddings across a fixed-width sequence that can range from tens to millions of tokens in size. Unlike "hard" weights, which are computed during the backwards training pass, "soft" weights exist only in the forward pass and therefore change with every step of the input. Earlier designs implemented the attention mechanism in a serial recurrent neural network (RNN) language translation system, but a more recent design, namely the transformer, removed the slower sequential RNN and relied more heavily on the faster parallel attention scheme. Inspired by ideas about attention in humans, the attention mechanism was developed to address the weaknesses of using information from the hidden layers of recurrent neural networks. Recurrent neural networks favor information contained in words at the end of a sentence and thus deemed more recent, thereby tending to attenuate the significance and associated predictive weight assigned to information earlier in the sentence. Attention allows a token equal access to any part of a sentence directly, rather than only through the previous state. == History == Additional surveys of the attention mechanism in deep learning are provided by Niu et al. and Soydaner. The major breakthrough came with self-attention, where each element in the input sequence attends to all others, enabling the model to capture global dependencies. This idea was central to the Transformer architecture, which replaced recurrence with attention mechanisms. As a result, Transformers became the foundation for models like BERT, T5 and generative pre-trained transformers (GPT). == Overview == The modern era of machine attention was revitalized by grafting an attention mechanism (Fig 1. orange) to an Encoder-Decoder. Figure 2 shows the internal step-by-step operation of the attention block (A) in Fig 1. === Interpreting attention weights === In translating between languages, alignment is the process of matching words from the source sentence to words of the translated sentence. Networks that perform verbatim translation without regard to word order would show the highest scores along the (dominant) diagonal of the matrix. The off-diagonal dominance shows that the attention mechanism is more nuanced. Consider an example of translating I love you to French. On the first pass through the decoder, 94% of the attention weight is on the first English word I, so the network offers the word je. On the second pass of the decoder, 88% of the attention weight is on the third English word you, so it offers t'. On the last pass, 95% of the attention weight is on the second English word love, so it offers aime. In the I love you example, the second word love is aligned with the third word aime. Stacking soft row vectors together for je, t', and aime yields an alignment matrix: Sometimes, alignment can be multiple-to-multiple. For example, the English phrase look it up corresponds to cherchez-le. Thus, "soft" attention weights work better than "hard" attention weights (setting one attention weight to 1, and the others to 0), as we would like the model to make a context vector consisting of a weighted sum of the hidden vectors, rather than "the best one", as there may not be a best hidden vector. == Variants == Many variants of attention implement soft weights, such as fast weight programmers, or fast weight controllers (1992). A "slow" neural network outputs the "fast" weights of another neural network through outer products. The slow network learns by gradient descent. It was later renamed as "linearized self-attention". Bahdanau-style attention, also referred to as additive attention, Luong-style attention, which is known as multiplicative attention, Early attention mechanisms similar to modern self-attention were proposed using recurrent neural networks. However, the highly parallelizable self-attention was introduced in 2017 and successfully used in the Transformer model, positional attention and factorized positional attention. For convolutional neural networks, attention mechanisms can be distinguished by the dimension on which they operate, namely: spatial attention, channel attention, or combinations. These variants recombine the encoder-side inputs to redistribute those effects to each target output. Often, a correlation-style matrix of dot products provides the re-weighting coefficients. In the figures below, W is the matrix of context attention weights, similar to the formula in Overview section above. == Optimizations == === Flash attention === The size of the attention matrix is proportional to the square of the number of input tokens. Therefore, when the input is long, calculating the attention matrix requires a lot of GPU memory. Flash attention is an implementation that reduces the memory needs and increases efficiency without sacrificing accuracy. It achieves this by partitioning the attention computation into smaller blocks that fit into the GPU's faster on-chip memory, reducing the need to store large intermediate matrices and thus lowering memory usage while increasing computational efficiency. === FlexAttention === FlexAttention is an attention kernel developed by Meta that allows users to modify attention scores prior to softmax and dynamically chooses the optimal attention algorithm. == Applications == Attention is widely used in natural language processing, computer vision, and speech recognition. In NLP, it improves context understanding in tasks like question answering and summarization. In vision, visual attention helps models focus on relevant image regions, enhancing object detection and image captioning. === Attention maps as explanations for vision transformers === From the original paper on vision transformers (ViT), visualizing attention scores as a heat map (called saliency maps or attention maps) has become an important and routine way to inspect the decision making process of ViT models. One can compute the attention maps with respect to any attention head at any layer, while the deeper layers tend to show more semantically meaningful visualization. Attention rollout is a recursive algorithm to combine attention scores across all layers, by computing the dot product of successive attention maps. Because vision transformers are typically trained in a self-supervised manner, attention maps are generally not class-sensitive. When a classification head is attached to the ViT backbone, class-discriminative attention maps (CDAM) combines attention maps and gradients with respect to the class [CLS] token. Some class-sensitive interpretability methods originally developed for convolutional neural networks can be also applied to ViT, such as GradCAM, which back-propagates the gradients to the outputs of the final attention layer. Using attention as basis of explanation for the transformers in language and vision is not without debate. While some pioneering papers analyzed and framed attention scores as explanations, higher attention scores do not always correlate with greater impact on model performances. == Mathematical representation == === Standard scaled dot-product attention === For matrices: Q ∈ R m × d k , K ∈ R n × d k {\displaystyle Q\in \mathbb {R} ^{m\times d_{k}},K\in \mathbb {R} ^{n\times d_{k}}} and V ∈ R n × d v {\displaystyle V\in \mathbb {R} ^{n\times d_{v}}} , the scaled dot-product, or QKV attention, is defined as: Attention ( Q , K , V ) = softmax ( Q K T d k ) V ∈ R m × d v {\displaystyle {\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{T}}{\sqrt {d_{k}}}}\right)V\in \mathbb {R} ^{m\times d_{v}}} where T {\displaystyle {}^{T}} denotes transpose and the softmax function is applied independently to every row of its argument. The matrix Q {\displaystyle Q} contains m {\displaystyle m} queries, while matrices K , V {\displaystyle K,V} jointly contain an unordered set of n {\displaystyle n} key-value pairs. Value vectors in matrix V {\displaystyle V} are weighted using the weights resulting from the softmax operation, so that the rows of the m {\displaystyle m} -by- d v {\displaystyle d_{v}} output matrix are confined to the convex hull of the points in R d v {\displaystyle \mathbb {R} ^{d_{v}}} given by the rows of V {\displaystyle V} . To understand the permutation invariance and permutation equivariance properties of QKV attention, let A ∈ R m × m {\displaystyle A\in \mathbb {R} ^{m\times m}} and B ∈ R n × n {\displaystyle B\in \mathbb {R} ^{n\times n}} be permutation matrices; and D ∈ R m × n {\displaystyle D\in \mathbb {R} ^{m\times n}} an arbitrary matrix. The softmax function is permutation equivariant in the sense that: softmax ( A D B ) = A softmax ( D ) B {\displays

DryvIQ

DryvIQ is a software application that enables businesses to migrate on-site system files and associated data across storage and content management platforms, as well as create synchronized hybrid storage systems. == History == Before it was DryvIQ, the software SkySync was released in 2013 by Ann Arbor, Michigan based company, Portal Architects, Inc. The company created SkySync, a back-end, administrative application designed to transfer content across storage platforms, after abandoning 18 months of development on a desktop application called SkyBrary in 2011. Between 2014 and 2015, Portal Architects established partnerships with the following companies: Autodesk, Box, Dropbox, Egnyte, EMC, Google, Syncplicity, Huddle, IBM, Microsoft, OpenText, Oracle, Citrix ShareFile, Hightail and Internet2. SkySync (currently DryvIQ) was named a "Cool Vendor in Content Management" by Gartner in 2015. In 2022, SkySync changed its name to DryvIQ, which is now what the company is currently known as. == Overview == DryvIQ is a software application that syncs, migrates or backs up files including their associated properties, metadata, versions, user accounts and permissions across on-premises and Cloud-based storage platforms. The software deploys on a server, virtual machine or within Microsoft Azure, Amazon Web Services or other cloud computing services.