Proximal gradient methods for learning

Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies algorithms for a general class of convex regularization problems where the regularization penalty may not be differentiable. One such example is ℓ 1 {\displaystyle \ell _{1}} regularization (also known as Lasso) of the form min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , where x i ∈ R d and y i ∈ R . {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},\quad {\text{ where }}x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} Proximal gradient methods offer a general framework for solving regularization problems from statistical learning theory with penalties that are tailored to a specific problem application. Such customized penalties can help to induce certain structure in problem solutions, such as sparsity (in the case of lasso) or group structure (in the case of group lasso). == Relevant background == Proximal gradient methods are applicable in a wide variety of scenarios for solving convex optimization problems of the form min x ∈ H F ( x ) + R ( x ) , {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x),} where F {\displaystyle F} is convex and differentiable with Lipschitz continuous gradient, R {\displaystyle R} is a convex, lower semicontinuous function which is possibly nondifferentiable, and H {\displaystyle {\mathcal {H}}} is some set, typically a Hilbert space. The usual criterion of x {\displaystyle x} minimizes F ( x ) + R ( x ) {\displaystyle F(x)+R(x)} if and only if ∇ ( F + R ) ( x ) = 0 {\displaystyle \nabla (F+R)(x)=0} in the convex, differentiable setting is now replaced by 0 ∈ ∂ ( F + R ) ( x ) , {\displaystyle 0\in \partial (F+R)(x),} where ∂ φ {\displaystyle \partial \varphi } denotes the subdifferential of a real-valued, convex function φ {\displaystyle \varphi } . Given a convex function φ : H → R {\displaystyle \varphi :{\mathcal {H}}\to \mathbb {R} } an important operator to consider is its proximal operator prox φ : H → H {\displaystyle \operatorname {prox} _{\varphi }:{\mathcal {H}}\to {\mathcal {H}}} defined by prox φ ⁡ ( u ) = arg ⁡ min x ∈ H φ ( x ) + 1 2 ‖ u − x ‖ 2 2 , {\displaystyle \operatorname {prox} _{\varphi }(u)=\operatorname {arg} \min _{x\in {\mathcal {H}}}\varphi (x)+{\frac {1}{2}}\|u-x\|_{2}^{2},} which is well-defined because of the strict convexity of the ℓ 2 {\displaystyle \ell _{2}} norm. The proximal operator can be seen as a generalization of a projection. We see that the proximity operator is important because x ∗ {\displaystyle x^{}} is a minimizer to the problem min x ∈ H F ( x ) + R ( x ) {\displaystyle \min _{x\in {\mathcal {H}}}F(x)+R(x)} if and only if x ∗ = prox γ R ⁡ ( x ∗ − γ ∇ F ( x ∗ ) ) , {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right),} where γ > 0 {\displaystyle \gamma >0} is any positive real number. === Moreau decomposition === One important technique related to proximal gradient methods is the Moreau decomposition, which decomposes the identity operator as the sum of two proximity operators. Namely, let φ : X → R {\displaystyle \varphi :{\mathcal {X}}\to \mathbb {R} } be a lower semicontinuous, convex function on a vector space X {\displaystyle {\mathcal {X}}} . We define its Fenchel conjugate φ ∗ : X → R {\displaystyle \varphi ^{}:{\mathcal {X}}\to \mathbb {R} } to be the function φ ∗ ( u ) := sup x ∈ X ⟨ x , u ⟩ − φ ( x ) . {\displaystyle \varphi ^{}(u):=\sup _{x\in {\mathcal {X}}}\langle x,u\rangle -\varphi (x).} The general form of Moreau's decomposition states that for any x ∈ X {\displaystyle x\in {\mathcal {X}}} and any γ > 0 {\displaystyle \gamma >0} that x = prox γ φ ⁡ ( x ) + γ prox φ ∗ / γ ⁡ ( x / γ ) , {\displaystyle x=\operatorname {prox} _{\gamma \varphi }(x)+\gamma \operatorname {prox} _{\varphi ^{}/\gamma }(x/\gamma ),} which for γ = 1 {\displaystyle \gamma =1} implies that x = prox φ ⁡ ( x ) + prox φ ∗ ⁡ ( x ) {\displaystyle x=\operatorname {prox} _{\varphi }(x)+\operatorname {prox} _{\varphi ^{}}(x)} . The Moreau decomposition can be seen to be a generalization of the usual orthogonal decomposition of a vector space, analogous with the fact that proximity operators are generalizations of projections. In certain situations it may be easier to compute the proximity operator for the conjugate φ ∗ {\displaystyle \varphi ^{}} instead of the function φ {\displaystyle \varphi } , and therefore the Moreau decomposition can be applied. This is the case for group lasso. == Lasso regularization == Consider the regularized empirical risk minimization problem with square loss and with the ℓ 1 {\displaystyle \ell _{1}} norm as the regularization penalty: min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{1},} where x i ∈ R d and y i ∈ R . {\displaystyle x_{i}\in \mathbb {R} ^{d}{\text{ and }}y_{i}\in \mathbb {R} .} The ℓ 1 {\displaystyle \ell _{1}} regularization problem is sometimes referred to as lasso (least absolute shrinkage and selection operator). Such ℓ 1 {\displaystyle \ell _{1}} regularization problems are interesting because they induce sparse solutions, that is, solutions w {\displaystyle w} to the minimization problem have relatively few nonzero components. Lasso can be seen to be a convex relaxation of the non-convex problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + λ ‖ w ‖ 0 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\lambda \|w\|_{0},} where ‖ w ‖ 0 {\displaystyle \|w\|_{0}} denotes the ℓ 0 {\displaystyle \ell _{0}} "norm", which is the number of nonzero entries of the vector w {\displaystyle w} . Sparse solutions are of particular interest in learning theory for interpretability of results: a sparse solution can identify a small number of important factors. === Solving for L1 proximity operator === For simplicity we restrict our attention to the problem where λ = 1 {\displaystyle \lambda =1} . To solve the problem min w ∈ R d 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 + ‖ w ‖ 1 , {\displaystyle \min _{w\in \mathbb {R} ^{d}}{\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}+\|w\|_{1},} we consider our objective function in two parts: a convex, differentiable term F ( w ) = 1 n ∑ i = 1 n ( y i − ⟨ w , x i ⟩ ) 2 {\displaystyle F(w)={\frac {1}{n}}\sum _{i=1}^{n}(y_{i}-\langle w,x_{i}\rangle )^{2}} and a convex function R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} . Note that R {\displaystyle R} is not strictly convex. Let us compute the proximity operator for R ( w ) {\displaystyle R(w)} . First we find an alternative characterization of the proximity operator prox R ⁡ ( x ) {\displaystyle \operatorname {prox} _{R}(x)} as follows: u = prox R ⁡ ( x ) ⟺ 0 ∈ ∂ ( R ( u ) + 1 2 ‖ u − x ‖ 2 2 ) ⟺ 0 ∈ ∂ R ( u ) + u − x ⟺ x − u ∈ ∂ R ( u ) . {\displaystyle {\begin{aligned}u=\operatorname {prox} _{R}(x)\iff &0\in \partial \left(R(u)+{\frac {1}{2}}\|u-x\|_{2}^{2}\right)\\\iff &0\in \partial R(u)+u-x\\\iff &x-u\in \partial R(u).\end{aligned}}} For R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} it is easy to compute ∂ R ( w ) {\displaystyle \partial R(w)} : the i {\displaystyle i} th entry of ∂ R ( w ) {\displaystyle \partial R(w)} is precisely ∂ | w i | = { 1 , w i > 0 − 1 , w i < 0 [ − 1 , 1 ] , w i = 0. {\displaystyle \partial |w_{i}|={\begin{cases}1,&w_{i}>0\\-1,&w_{i}<0\\\left[-1,1\right],&w_{i}=0.\end{cases}}} Using the recharacterization of the proximity operator given above, for the choice of R ( w ) = ‖ w ‖ 1 {\displaystyle R(w)=\|w\|_{1}} and γ > 0 {\displaystyle \gamma >0} we have that prox γ R ⁡ ( x ) {\displaystyle \operatorname {prox} _{\gamma R}(x)} is defined entrywise by ( prox γ R ⁡ ( x ) ) i = { x i − γ , x i > γ 0 , | x i | ≤ γ x i + γ , x i < − γ , {\displaystyle \left(\operatorname {prox} _{\gamma R}(x)\right)_{i}={\begin{cases}x_{i}-\gamma ,&x_{i}>\gamma \\0,&|x_{i}|\leq \gamma \\x_{i}+\gamma ,&x_{i}<-\gamma ,\end{cases}}} which is known as the soft thresholding operator S γ ( x ) = prox γ ‖ ⋅ ‖ 1 ⁡ ( x ) {\displaystyle S_{\gamma }(x)=\operatorname {prox} _{\gamma \|\cdot \|_{1}}(x)} . === Fixed point iterative schemes === To finally solve the lasso problem we consider the fixed point equation shown earlier: x ∗ = prox γ R ⁡ ( x ∗ − γ ∇ F ( x ∗ ) ) . {\displaystyle x^{}=\operatorname {prox} _{\gamma R}\left(x^{}-\gamma \nabla F(x^{})\right).} Given that we have computed the form of the proximity operator explicitly, then we can define a standard fixed point iteration procedure. Namely, fix some initial w 0 ∈ R d {\displaystyle w^{0}\in \mathbb {R} ^{d}} , and for k = 1 , 2 , … {\displaystyle k=1,2,\ldots } define w k + 1 = S γ ( w k − γ ∇ F ( w k ) ) . {\displaystyle w^{k+1}=S_{\gamma }\left(w^{k}-\gamma \nabla F\l

BERT (language model)

Bidirectional encoder representations from transformers (BERT) is a language model introduced in October 2018 by researchers at Google. It learns to represent text as a sequence of vectors using self-supervised learning. It uses the encoder-only transformer architecture. BERT dramatically improved the state of the art for large language models. As of 2020, BERT is a ubiquitous baseline in natural language processing (NLP) experiments. BERT is trained by masked token prediction and next sentence prediction. With this training, BERT learns contextual, latent representations of tokens in their context, similar to ELMo and GPT-2. It found applications for many natural language processing tasks, such as coreference resolution and polysemy resolution. It improved on ELMo and spawned the study of "BERTology", which attempts to interpret what is learned by BERT. BERT was originally implemented in the English language at two model sizes, BERTBASE (110 million parameters) and BERTLARGE (340 million parameters). Both were trained on the Toronto BookCorpus (800M words) and English Wikipedia (2,500M words). The weights were released on GitHub. On March 11, 2020, 24 smaller models were released, the smallest being BERTTINY with just 4 million parameters. == Architecture == BERT is an "encoder-only" transformer architecture. At a high level, BERT consists of 4 modules: Tokenizer: This module converts a piece of English text into a sequence of integers ("tokens"). Embedding: This module converts the sequence of tokens into an array of real-valued vectors representing the tokens. It represents the conversion of discrete token types into a lower-dimensional Euclidean space. Encoder: a stack of Transformer blocks with self-attention, but without causal masking. Task head: This module converts the final representation vectors into one-shot encoded tokens again by producing a predicted probability distribution over the token types. It can be viewed as a simple decoder, decoding the latent representation into token types, or as an "un-embedding layer". The task head is necessary for pre-training, but it is often unnecessary for so-called "downstream tasks," such as question answering or sentiment classification. Instead, one removes the task head and replaces it with a newly initialized module suited for the task, and finetune the new module. The latent vector representation of the model is directly fed into this new module, allowing for sample-efficient transfer learning. === Embedding === This section describes the embedding used by BERTBASE. The other one, BERTLARGE, is similar, just larger. The tokenizer of BERT is WordPiece, which is a sub-word strategy like byte-pair encoding. Its vocabulary size is 30,000, and any token not appearing in its vocabulary is replaced by [UNK] ("unknown"). The first layer is the embedding layer, which contains three components: token type embeddings, position embeddings, and segment type embeddings. Token type: The token type is a standard embedding layer, translating a one-hot vector into a dense vector based on its token type. Position: The position embeddings are based on a token's position in the sequence. BERT uses absolute position embeddings, where each position in a sequence is mapped to a real-valued vector. Each dimension of the vector consists of a sinusoidal function that takes the position in the sequence as input. Segment type: Using a vocabulary of just 0 or 1, this embedding layer produces a dense vector based on whether the token belongs to the first or second text segment in that input. In other words, type-1 tokens are all tokens that appear after the [SEP] special token. All prior tokens are type-0. The three embedding vectors are added together representing the initial token representation as a function of these three pieces of information. After embedding, the vector representation is normalized using a LayerNorm operation, outputting a 768-dimensional vector for each input token. After this, the representation vectors are passed forward through 12 Transformer encoder blocks, and are decoded back to 30,000-dimensional vocabulary space using a basic affine transformation layer. === Architectural family === The encoder stack of BERT has 2 free parameters: L {\displaystyle L} , the number of layers, and H {\displaystyle H} , the hidden size. There are always H / 64 {\displaystyle H/64} self-attention heads, and the feed-forward/filter size is always 4 H {\displaystyle 4H} . By varying these two numbers, one obtains an entire family of BERT models. For BERT: the feed-forward size and filter size are synonymous. Both of them denote the number of dimensions in the middle layer of the feed-forward network. the hidden size and embedding size are synonymous. Both of them denote the number of real numbers used to represent a token. The notation for encoder stack is written as L/H. For example, BERTBASE is written as 12L/768H, BERTLARGE as 24L/1024H, and BERTTINY as 2L/128H. == Training == === Pre-training === BERT was pre-trained simultaneously on two tasks: Masked language modeling (MLM): In this task, BERT ingests a sequence of words, where one word may be randomly changed ("masked"), and BERT tries to predict the original words that had been changed. For example, in the sentence "The cat sat on the [MASK]," BERT would need to predict "mat." This helps BERT learn bidirectional context, meaning it understands the relationships between words not just from left to right or right to left but from both directions at the same time. Next sentence prediction (NSP): In this task, BERT is trained to predict whether one sentence logically follows another. For example, given two sentences, "The cat sat on the mat" and "It was a sunny day", BERT has to decide if the second sentence is a valid continuation of the first one. This helps BERT understand relationships between sentences, which is important for tasks like question answering or document classification. ==== Masked language modeling ==== In masked language modeling, 15% of tokens would be randomly selected for masked-prediction task, and the training objective was to predict the masked token given its context. In more detail, the selected token is: replaced with a [MASK] token with probability 80%, replaced with a random word token with probability 10%, not replaced with probability 10%. The reason not all selected tokens are masked is to avoid the dataset shift problem. The dataset shift problem arises when the distribution of inputs seen during training differs significantly from the distribution encountered during inference. A trained BERT model might be applied to word representation (like Word2Vec), where it would be run over sentences not containing any [MASK] tokens. It is later found that more diverse training objectives are generally better. As an illustrative example, consider the sentence "my dog is cute". It would first be divided into tokens like "my1 dog2 is3 cute4". Then a random token in the sentence would be picked. Let it be the 4th one "cute4". Next, there would be three possibilities: with probability 80%, the chosen token is masked, resulting in "my1 dog2 is3 [MASK]4"; with probability 10%, the chosen token is replaced by a uniformly sampled random token, such as "happy", resulting in "my1 dog2 is3 happy4"; with probability 10%, nothing is done, resulting in "my1 dog2 is3 cute4". After processing the input text, the model's 4th output vector is passed to its decoder layer, which outputs a probability distribution over its 30,000-dimensional vocabulary space. ==== Next sentence prediction ==== Given two sentences, the model predicts if they appear sequentially in the training corpus, outputting either [IsNext] or [NotNext]. During training, the algorithm sometimes samples two sentences from a single continuous span in the training corpus, while at other times, it samples two sentences from two discontinuous spans. The first sentence starts with a special token, [CLS] (for "classify"). The two sentences are separated by another special token, [SEP] (for "separate"). After processing the two sentences, the final vector for the [CLS] token is passed to a linear layer for binary classification into [IsNext] and [NotNext]. For example: Given "[CLS] my dog is cute [SEP] he likes playing [SEP]", the model should predict [IsNext]. Given "[CLS] my dog is cute [SEP] how do magnets work [SEP]", the model should predict [NotNext]. === Fine-tuning === BERT is meant as a general pretrained model for various applications in natural language processing. That is, after pre-training, BERT can be fine-tuned with fewer resources on smaller datasets to optimize its performance on specific tasks such as natural language inference and text classification, and sequence-to-sequence-based language generation tasks such as question answering and conversational response generation. The original BERT paper published results demonstrating that a small amount of fine

Richard S. Sutton

Richard Stuart Sutton (born 1957 or 1958) is a Canadian computer scientist. He is a professor of computing science at the University of Alberta, fellow & Chief Scientific Advisor at the Alberta Machine Intelligence Institute, and a research scientist at Keen Technologies. Sutton is considered one of the founders of modern computational reinforcement learning. In particular, he contributed to temporal difference learning and policy gradient methods. He received the 2024 Turing Award with Andrew Barto. == Education and early life == Richard Sutton was born in either 1957 or 1958 in Toledo, Ohio, and grew up in Oak Brook, Illinois, a suburb of Chicago, United States. Sutton received his Bachelor of Arts (BA) degree in psychology from Stanford University in 1978 before taking a Master of Science (1980) and PhD (1984) in computer science from the University of Massachusetts Amherst supervised by Andrew Barto. His doctoral dissertation introduced actor-critic architectures and temporal credit assignment. He was influenced by Harry Klopf's work in the 1970s, which proposed that supervised learning is insufficient for AI or explaining intelligent behavior, and trial-and-error learning, driven by "hedonic aspects of behavior", is necessary. This focused his interest to reinforcement learning. == Career and research == Sutton held a postdoctoral research position at the University of Massachusetts Amherst in 1984. He worked at GTE Laboratories in Waltham, Massachusetts as principal member of technical staff from 1985 to 1994, then returned to the University of Massachusetts Amherst as a senior research scientist. He joined AT&T Labs Shannon Laboratory in Florham Park, New Jersey as principal technical staff member from 1998 to 2002. He has been a professor of computing science at the University of Alberta since 2003, where he helped establish the Reinforcement Learning and Artificial Intelligence Laboratory. In 2017 he became a distinguished research scientist with Google DeepMind and helped launch DeepMind Alberta in Edmonton, a research office operated in close collaboration with the University of Alberta. 1984: Postdoctoral researcher, University of Massachusetts Amherst (Amherst, Massachusetts) 1985–1994: Principal member of technical staff, Computer and Intelligent Systems Laboratory, GTE Laboratories (Waltham, Massachusetts) 1995–1998: Senior research scientist, University of Massachusetts Amherst (Amherst, Massachusetts) 1998–2002: Principal technical staff member, Artificial Intelligence Department, AT&T Labs Shannon Laboratory (Florham Park, New Jersey) 2003–present: Professor of computing science, University of Alberta (Edmonton, Alberta) 2017–2023: Distinguished research scientist, DeepMind Alberta, Google DeepMind (Edmonton, Alberta) 2024–Present: Research scientist, Keen Technologies === Reinforcement learning === Sutton joined Andrew Barto in the early 1980s at UMass, trying to explore the behavior of neurons in the human brain as the basis for human intelligence, a concept that had been advanced by computer scientist A. Harry Klopf. Sutton and Barto used mathematics toward furthering the concept and using it as the basis for artificial intelligence. This concept became known as reinforcement learning and went on to becoming a key part of artificial intelligence techniques. Barto and Sutton used Markov decision processes (MDP) as the mathematical foundation to explain how agents (algorithmic entities) made decisions when in a stochastic or random environment, receiving rewards at the end of every action. Traditional MDP theory assumed the agents knew all information about the MDPs in their attempt toward maximizing their cumulative rewards. Barto and Sutton's reinforcement learning techniques allowed for both the environment and the rewards to be unknown, and thus allowed for these category of algorithms to be applied to a wide array of problems. Sutton returned to Canada in the 2000s and continued working on the topic which continued to develop in academic circles until one of its first major real world applications saw Google's AlphaGo program built on this concept defeating the then prevailing human champion. Barto and Sutton have widely been credited and accepted as pioneers of modern reinforcement learning, with the technique itself being foundational to the AI boom. In a 2019 essay, Sutton proposed the "bitter lesson", which criticized the field of AI research for failing to learn that "building in how we think we think does not work in the long run", arguing that "70 years of AI research [had shown] that general methods that leverage computation are ultimately the most effective, and by a large margin", beating efforts building on human knowledge about specific fields like computer vision, speech recognition, chess or Go. Sutton argues that large language models aren’t capable of learning on-the-job, and so new model architectures are required to enable continual learning. Sutton further argues that a special training phase will be unnecessary — the agent will learn on-the-fly, rendering large language models obsolete. In 2023, Sutton and John Carmack announced a partnership for the development of artificial general intelligence (AGI). === Awards and honors === Sutton has been a Fellow of the Association for the Advancement of Artificial Intelligence (AAAI) since 2001; his nomination read: "For significant contributions to many topics in machine learning, including reinforcement learning, temporal difference techniques, and neural networks." In 2003, he received the President's Award from the International Neural Network Society and in 2013, the Outstanding Achievement in Research award from the University of Massachusetts Amherst. He received the 2024 Turing Award from the Association for Computing Machinery together with Andrew Barto; the citation of the award read: "For developing the conceptual and algorithmic foundations of reinforcement learning." In 2016, Sutton was elected Fellow of the Royal Society of Canada. In 2021, he was elected Fellow of the Royal Society (FRS) of London. === Research === Sutton introduced temporal-difference methods for prediction and control, establishing convergence properties and practical algorithms. He proposed integrated learning and planning through the Dyna architecture. He co-developed the options framework for temporal abstraction in reinforcement learning. He co-authored the first modern policy gradient formulation with function approximation. Sutton's essay The Bitter Lesson argued that general methods that scale with computation dominate domain-specific approaches in the long run. His former doctoral students include David Silver and Doina Precup. === Selected publications === His publications include: == Personal life == Sutton became a Canadian citizen in 2015, and his renunciation of US citizenship was reported in 2017.

Minimum information standard

Minimum information standards are sets of guidelines and formats for reporting data derived by specific high-throughput methods. Their purpose is to ensure the data generated by these methods can be easily verified, analysed and interpreted by the wider scientific community. Ultimately, they facilitate the transfer of data from journal articles (unstructured data) into databases (structured data) in a form that enables data to be mined across multiple data sets. Minimal information standards are available for a vast variety of experiment types including microarray (MIAME), RNAseq (MINSEQE), metabolomics (MSI) and proteomics (MIAPE). Minimum information standards typically have two parts. Firstly, there is a set of reporting requirements – typically presented as a table or a checklist. Secondly, there is a data format. Information about an experiment needs to be converted into the appropriate data format for it to be submitted to the relevant database. In the case of MIAME, the data format is provided in spreadsheet format (MAGE-TAB). Some of the communities that maintain minimum information standards also provide tools to help experimental researchers to annotate their data. == MI Standards == The individual minimum information standards are brought by the communities of cross-disciplinary specialists focused on the problematic of the specific method used in experimental biology. The standards then provide specifications what information about the experiments (metadata) is crucial and important to be reported together with the resultant data to make it comprehensive. The need for this standardization is largely driven by the development of high-throughput experimental methods that provide tremendous amounts of data. The development of minimum information standards of different methods is since 2008 being harmonized by "Minimum Information about a Biomedical or Biological Investigation" (MIBBI) project. === MIAPPE, Minimum Information About a Plant Phenotyping Experiment === MIAPPE is an open, community driven project to harmonize data from plant phenotyping experiments. MIAPPE comprises both a conceptual checklist of metadata required to adequately describe a plant phenotyping experiment. === MIQE, Minimum Information for Publication of Quantitative Real-Time PCR Experiments === Published in 2009 these guidelines for the basis of requirements by many journals when submitting QPCR data, sadly they are not adhered to enough. === MIAME, gene expression microarray === Minimum Information About a Microarray Experiment (MIAME) describes the Minimum Information About a Microarray Experiment that is needed to enable the interpretation of the results of the experiment unambiguously and potentially to reproduce the experiment and is aimed at facilitating the dissemination of data from microarray experiments. It was published by the FGED Society in 2001 and was the first published minimum information standard for high-throughput experiments in the life sciences. MIAME contains a number of extensions to cover specific biological domains, including MIAME-env, MIAME-nut and MIAME-tox, covering environmental genomics, nutritional genomics and toxogenomics, respectively. === MINI: Minimum Information about a Neuroscience Investigation === ==== MINI: Electrophysiology ==== Electrophysiology is a technology used to study the electrical properties of biological cells and tissues. Electrophysiology typically involves the measurements of voltage change or electric current flow on a wide variety of scales from single ion channel proteins to whole tissues. This document is a single module, as part of the Minimum Information about a Neuroscience investigation (MINI) family of reporting guideline documents, produced by community consultation and continually available for public comment. A MINI module represents the minimum information that should be reported about a dataset to facilitate computational access and analysis to allow a reader to interpret and critically evaluate the processes performed and the conclusions reached, and to support their experimental corroboration. In practice a MINI module comprises a checklist of information that should be provided (for example about the protocols employed) when a data set is described for publication. The full specification of the MINI module can be found here. === MIARE, RNAi experiment === Minimum Information About an RNAi Experiment (MIARE) is a data reporting guideline which describes the minimum information that should be reported about an RNAi experiment to enable the unambiguous interpretation and reproduction of the results. === MIACA, cell based assay === Advances in genomics and functional genomics have enabled large-scale analyses of gene and protein function by means of high-throughput cell biological analyses. Thereby, cells in culture can be perturbed in vitro and the induced effects recorded and analyzed. Perturbations can be triggered in several ways, for instance with molecules (siRNAs, expression constructs, small chemical compounds, ligands for receptors, etc.), through environmental stresses (such as temperature shift, serum starvation, oxygen deprivation, etc.), or combinations thereof. The cellular responses to such perturbations are analyzed in order to identify molecular events in the biological processes addressed and understand biological principles. We propose the Minimum Information About a Cellular Assay (MIACA) for reporting a cellular assay, and CA-OM, the modular cellular assay object model, to facilitate exchange of data and accompanying information, and to compare and integrate data that originate from different, albeit complementary approaches, and to elucidate higher order principles. Documents describing MIACA are available and provide further information as well as the checklist of terms that should be reported. === MIAPE, proteomic experiments === The Minimum Information About a Proteomic Experiment documents describe information which should be given along with a proteomic experiment. The parent document describes the processes and principles underpinning the development of a series of domain specific documents which now cover all aspects of a MS-based proteomics workflow. === MIMIx, molecular interactions === This document has been developed and maintained by the Molecular Interaction worktrack of the HUPO-PSI (www.psidev.info) and describes the Minimum Information about a Molecular Interaction experiment. === MIAPAR, protein affinity reagents === The Minimum Information About a Protein Affinity Reagent has been developed and maintained by the Molecular Interaction worktrack of the HUPO-PSI (www.psidev.info)in conjunction with the HUPO Antibody Initiative and a European consortium of binder producers and seeks to encourage users to improve their description of binding reagents, such as antibodies, used in the process of protein identification. === MIABE, bioactive entities === The Minimum Information About a Bioactive Entity was produced by representatives from both large pharma and academia who are looking to improve the description of usually small molecules which bind to, and potentially modulate the activity of, specific targets in a living organism. This document encompasses drug-like molecules as well as herbicides, pesticides and food additives. It is primarily maintained through the EMBL-EBI Industry program (www.ebi.ac.uk/industry). === MIGS/MIMS, genome/metagenome sequences === This specification is being developed by the Genomic Standards Consortium === MIFlowCyt, flow cytometry === === Minimum Information about a Flow Cytometry Experiment === The Minimum Information about a Flow Cytometry Experiment (MIFlowCyt) is a standard related to flow cytometry which establishes criteria to record information on experimental overview, samples, instrumentation and data analysis. It promotes consistent annotation of clinical, biological and technical issues surrounding a flow cytometry experiment. === MINDR, dual gene expression reporters === Requires (1) reporting absolute values of reporter readouts, (2) list of positive and negative controls, and (3) sequences of all reporter constructs. === MISFISHIE, In Situ Hybridization and Immunohistochemistry Experiments === === MIAPA, Phylogenetic Analysis === Criteria for Minimum Information About a Phylogenetic Analysis were described in 2006. === MIRAGE, Glycomics === The MIRAGE project is supported and coordinated by the Beilstein-Institut to establish guidelines for data handling and processing in glycomics research [1] === MIAO, ORF === === MIAMET, METabolomics experiment === === MIAFGE, Functional Genomics Experiment === === MIRIAM, Minimum Information Required in the Annotation of Models === The Minimal Information Required In the Annotation of Models (MIRIAM), is a set of rules for the curation and annotation of quantitative models of biological systems. === MIASE, Minimum Information About a Simulation Experiment =

4E cognition

4E cognition refers to a group of theories in (the philosophy of) cognitive science that challenge traditional views of the mind as something that happens only inside the brain. The four Es stand for: embodied, meaning that a brain is found in and, more importantly, vitally interconnected with a larger physical/biological body; embedded, which refers to the limitations placed on the body by the external environment and laws of nature; extended, which argues that the mind is supplemented and even enhanced by the exterior world (e.g., writing, a calculator, etc.); and enactive, which is the argument that without dynamic processes, actions that require reactions, the mind would be ineffectual. It could be argued that the four Es are compounding extensions of cognition or the mind, being part of a body that is, in turn, part of an environment which limits it but also allows for certain extensions, all of which require dynamic actions and reactions. == History == Ideas of embodied cognition, or rather the idea that our physical bodies play a crucial role in our decision making, can be traced back as far as Plato's dialogues and Aristotelian thought. It was, however, in the twentieth century that this debate began to resemble the current discussion, fueled by disagreements between cognitivists and behaviourists. Tensions within cognitivism, as well as the increasing popularity of neurobiology, led, on the one side, to a predominant focus on internal, cognitive processes while neglecting environmental factors, which in turn caused a push-back fuelling our modern understanding of embodied cognition. The term 4E cognition is hard to trace back to its first use, however, some sources attribute it to Shaun Gallagher and the conference on 4E cognition he organised in 2007, while others indicate the term to be first used in 2006 at an 'Embodied mind workshop' at Cardiff University that Gallagher attended. Embodiment or embodied cognition arguably presents the bridge between cognitivism and 4E cognition as the embodiment of cognitive function provides the necessary conditions for embeddedness, enactedness, and extendedness to connect to cognition. 4E cognition was and is heavily influenced by phenomenology. The ideas are still rather fragmented in nature due to their four main components, which can not be neatly divided, causing conceptual questions of internal boundary concepts. As a young field, it is held back both by its fragmented nature and a relative lack of critical evaluations. It is important to acknowledge that 4E cognition, though young, is a broad field containing and combining several different theoretical perspectives that conflict with one another to varying degrees. The somewhat convoluted and competing nature of the theories that can be grouped as 4E cognition, as well as the field's relative youth, make it difficult to put together an exhaustive history beyond the history of its four main theoretical pillars: embodiment, embeddedness, extendedness, and enactedness. == Importance and core tenets of 4E == If there are separate theories of cognition (e.g., embodied, extended, etc.), why group them under this umbrella, causing important epistemological and especially ontological dilemmas? Notably, other theories of 'non-traditional' cognition are not included under the 4E umbrella. The four E's in 4E cognition importantly all reject, or at a minimum draw into question, some of the core tenets of traditional cognitivism. Importantly, 4E cognition is seen as deindividualizing cognition to some extent, allowing for a broader examination of the interplay of personal, social, political, and ethical aspects that shape human cognition. This can be compared to advancements in the field of epigenetics, which have allowed for a broader examination of environmental (both natural and social) factors and their influence on what had previously only been subject to genetic theorizing. In a similar vein, 4E cognition might also help ground cognition in evolutionary theory by extending cognition to a biological account subject to development over time by means of evolution. Overall, the importance of the extension that is 4E cognition aims to reexamine ideas of a self-centered view of cognition, advocating for a more holistic approach. Ideally, this would allow us to reconsider ideas of justice and individual rights and responsibilities that take into account a more nuanced understanding of the relations between people and their context, balancing self-agency with factors beyond it. === Conceptual differences from cognitive psychology === According to the traditional teachings of cognitive psychology, cognition is a type of information processing based on representational mental structures. This idea, as the name suggests, was heavily influenced by computer science. In this light, the brain is a kind of central processing unit that organises and directs all else. The classical cognitivist view draws a strong boundary between 'the internal' and 'the external', where cognition is solely a subject of 'the internal' realm. The four E's, however, break down this boundary. Cognition can not reside solely within the confines of our heads if it is also embodied, embedded, enacted, and extended. In a way, 4E cognition is interested in the extracranial processes affecting cognition. == From embodied cognition to 4E cognition == === The strong and the weak view === ==== Embodied cognition ==== Broadly speaking, there is a strong and a weak perspective of embodied cognition in 4E cognition. The weak understanding refers to mental processes being causally dependent on extracranial processes. This essentially means that there is a cause and effect or action-reaction relationship between the mind and the body and its environment, etc. The strong perspective views extracranial processes as a (partial) constitutive aspect of cognition. An example here could be using a calculator to solve math problems. The calculator is not part of your brain or mind, but it supports your cognitive processes. === Extracranial processes: bodily or extrabodily === In addition to the weak and the strong reading of 4E cognition, there is also the distinction between bodily and extrabodily extracranial processes. Bodily extracranial processes refer to processes within the body, e.g., sensory perception. Extrabodily extracranial processes refer to processes outside of the body, like the aforementioned calculator example. === Four claims of embodied cognition === ==== Embedded and extended cognition ==== When combining the weak/strong reading of embodied cognition and bodily/extrabodily extracranial process, four claims about embodied cognition emerge: strongly embodied and bodily processes strongly embodied and extrabodily processes weakly embodied and bodily processes weakly embodied and extrabodily processes The first and third claims signify a strong and a weak reading of embodied cognition in the more classical sense. The second claim fits almost perfectly with embedded cognition. Claim two is most compatible with extended cognition. ==== Enacted cognition ==== Finally, enacted cognition refers to cognition being connected to active interaction between a conscious agent and their environment. Here, too, there can be a weak and a strong reading. == Criticisms == Given the divided nature of the field, much criticism surrounding the lack of unity within the field has emerged. In particular, the claims of embodied cognition centering around the body appear to conflict with the tenets of extended cognition, which also appear to conflict with the body/environment distinction that is central to enactivism. Some theoreticians argue that the umbrella of 4E theories is still lacking a common language that might bridge the gaps between the theories that constitute it. There is also the concern that the grouping of such variable theories results in an important loss of nuance and complexity, which is a part of human cognition. Another concern raised is the "dogma of harmony". The criticism contained there regards the notion that within 4E theorizing, there is generally an optimistic and harmonic expectation of the extension between humans and their technologies, ignoring the possibility of those extensions detracting from cognition in some way rather than adding to it. Recent attempts to incorporate embodied cognitive neuroscience have been argued to hold the potential to resolve internal issues within 4E cognition. Overall, a concern often voiced regarding 4E cognition is that its proponents are at best only vaguely interested in cognition. More broadly, this concern reflects the arguably too distracted nature of this emerging field.

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_{

OpenVINO

OpenVINO is an open-source software toolkit developed by Intel for optimizing and deploying deep learning models. It supports several popular model formats and categories, such as large language models, computer vision, and generative AI. OpenVINO is optimized for Intel hardware, but offers support for ARM/ARM64 processors. It sees great use in AI Sound Processing drivers when tied with Intel's Gaussian & Neural Accelerator (GNA). Based in C++, it extends API support for C and Python, as well as Node.js (in early preview). OpenVINO is cross-platform and free for use under Apache License 2.0. == Workflow == The simplest OpenVINO usage involves obtaining a model and running it as is. Yet for the best results, a more complete workflow is suggested: obtain a model in one of supported frameworks, convert the model to OpenVINO IR using the OpenVINO Converter tool, optimize the model, using training-time or post-training options provided by OpenVINO's NNCF. execute inference, using OpenVINO Runtime by specifying one of several inference modes. == OpenVINO model format == OpenVINO IR is the default format used to run inference. It is saved as a set of two files, .bin and .xml, containing weights and topology, respectively. It is obtained by converting a model from one of the supported frameworks, using the application's API or a dedicated converter. Models of the supported formats may also be used for inference directly, without prior conversion to OpenVINO IR. Such an approach is more convenient but offers fewer optimization options and lower performance, since the conversion is performed automatically before inference. Some pre-converted models can be found in the Hugging Face repository. The supported model formats are: PyTorch TensorFlow TensorFlow Lite ONNX (including formats that may be serialized to ONNX) PaddlePaddle JAX/Flax == OS support == OpenVINO runs on Windows, Linux and MacOS.