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Mixture Of Experts
Mixture of experts (MoE) is a machine learning technique where multiple expert networks (learners) are used to divide a problem space into homogeneous regions. MoE represents a form of ensemble learning. They were also called committee machines. Basic theory MoE always has the following components, but they are implemented and combined differently according to the problem being solved: * Experts f_1, ..., f_n, each taking the same input x, and producing outputs f_1(x), ..., f_n(x). * A weighting function (also known as a gating function) w, which takes input x and produces a vector of outputs (w(x)_1, ..., w(x)_n). This may or may not be a probability distribution, but in both cases, its entries are non-negative. * \theta = (\theta_0, \theta_1, ..., \theta_n) is the set of parameters. The parameter \theta_0 is for the weighting function. The parameters \theta_1, \dots, \theta_n are for the experts. * Given an input x, the mixture of experts produces a single output by combinin ...
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Machine Learning
Machine learning (ML) is a field of study in artificial intelligence concerned with the development and study of Computational statistics, statistical algorithms that can learn from data and generalise to unseen data, and thus perform Task (computing), tasks without explicit Machine code, instructions. Within a subdiscipline in machine learning, advances in the field of deep learning have allowed Neural network (machine learning), neural networks, a class of statistical algorithms, to surpass many previous machine learning approaches in performance. ML finds application in many fields, including natural language processing, computer vision, speech recognition, email filtering, agriculture, and medicine. The application of ML to business problems is known as predictive analytics. Statistics and mathematical optimisation (mathematical programming) methods comprise the foundations of machine learning. Data mining is a related field of study, focusing on exploratory data analysi ...
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Student's T-distribution
In probability theory and statistics, Student's  distribution (or simply the  distribution) t_\nu is a continuous probability distribution that generalizes the Normal distribution#Standard normal distribution, standard normal distribution. Like the latter, it is symmetric around zero and bell-shaped. However, t_\nu has Heavy-tailed distribution, heavier tails, and the amount of probability mass in the tails is controlled by the parameter \nu. For \nu = 1 the Student's distribution t_\nu becomes the standard Cauchy distribution, which has very fat-tailed distribution, "fat" tails; whereas for \nu \to \infty it becomes the standard normal distribution \mathcal(0, 1), which has very "thin" tails. The name "Student" is a pseudonym used by William Sealy Gosset in his scientific paper publications during his work at the Guinness Brewery in Dublin, Ireland. The Student's  distribution plays a role in a number of widely used statistical analyses, including Student's t- ...
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Assignment Problem
The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: :The problem instance has a number of ''agents'' and a number of ''tasks''. Any agent can be assigned to perform any task, incurring some ''cost'' that may vary depending on the agent-task assignment. It is required to perform as many tasks as possible by assigning at most one agent to each task and at most one task to each agent, in such a way that the ''total cost'' of the assignment is minimized. Alternatively, describing the problem using graph theory: :The assignment problem consists of finding, in a weighted graph, weighted bipartite graph, a Matching (graph theory), matching of maximum size, in which the sum of weights of the edges is minimum. If the numbers of agents and tasks are equal, then the problem is called balanced assignment, and the graph-theoretic version is called minimum-cost perfect matching. Otherwise, it is called unbalanced assig ...
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DeepSeek
Hangzhou DeepSeek Artificial Intelligence Basic Technology Research Co., Ltd., Trade name, doing business as DeepSeek, is a Chinese artificial intelligence company that develops large language models (LLMs). Based in Hangzhou, Zhejiang, Deepseek is owned and funded by the Chinese hedge fund High-Flyer. DeepSeek was founded in July 2023 by Liang Wenfeng, the co-founder of High-Flyer, who also serves as the Chief executive officer, CEO for both companies. The company launched DeepSeek (chatbot), an eponymous chatbot alongside its DeepSeek-R1 model in January 2025. Released under the MIT License, DeepSeek-R1 provides responses comparable to other contemporary large language models, such as OpenAI's GPT-4 and OpenAI o1, o1. Its training cost was reported to be significantly lower than other LLMs. The company claims that it trained its V3 model for US$6 million—far less than the US$100 million cost for OpenAI's GPT-4 in 2023—and using approximately one-tenth the comput ...
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DeepSeek MoE And MLA (DeepSeek-V2)
Hangzhou DeepSeek Artificial Intelligence Basic Technology Research Co., Ltd., doing business as DeepSeek, is a Chinese artificial intelligence company that develops large language models (LLMs). Based in Hangzhou, Zhejiang, Deepseek is owned and funded by the Chinese hedge fund High-Flyer. DeepSeek was founded in July 2023 by Liang Wenfeng, the co-founder of High-Flyer, who also serves as the CEO for both companies. The company launched an eponymous chatbot alongside its DeepSeek-R1 model in January 2025. Released under the MIT License, DeepSeek-R1 provides responses comparable to other contemporary large language models, such as OpenAI's GPT-4 and o1. Its training cost was reported to be significantly lower than other LLMs. The company claims that it trained its V3 model for US$6 million—far less than the US$100 million cost for OpenAI's GPT-4 in 2023—and using approximately one-tenth the computing power consumed by Meta's comparable model, Llama 3.1. DeepS ...
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Long Short-term Memory
Long short-term memory (LSTM) is a type of recurrent neural network (RNN) aimed at mitigating the vanishing gradient problem commonly encountered by traditional RNNs. Its relative insensitivity to gap length is its advantage over other RNNs, hidden Markov models, and other sequence learning methods. It aims to provide a short-term memory for RNN that can last thousands of timesteps (thus "''long'' short-term memory"). The name is made in analogy with long-term memory and short-term memory and their relationship, studied by cognitive psychologists since the early 20th century. An LSTM unit is typically composed of a cell and three gates: an input gate, an output gate, and a forget gate. The cell remembers values over arbitrary time intervals, and the gates regulate the flow of information into and out of the cell. Forget gates decide what information to discard from the previous state, by mapping the previous state and the current input to a value between 0 and 1. A (rounded) ...
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T5 (language Model)
T5 (Text-to-Text Transfer Transformer) is a series of Large language model, large language models developed by Google AI introduced in 2019. Like the Attention Is All You Need, original Transformer model, T5 models are Transformer (deep learning architecture), encoder-decoder Transformers, where the encoder processes the input text, and the decoder generates the output text. T5 models are usually pretrained on a massive Text corpus, dataset of text and code, after which they can perform the text-based tasks that are similar to their pretrained tasks. They can also be finetuned to perform other tasks. T5 models have been employed in various applications, including chatbots, machine translation systems, text summarization tools, code generation, and robotics. Training The original T5 models are pre-trained on the Colossal Clean Crawled Corpus (C4), containing text and code Web crawler, scraped from the internet. This pre-training process enables the models to learn general langu ...
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Feedforward Neural Network
Feedforward refers to recognition-inference architecture of neural networks. Artificial neural network architectures are based on inputs multiplied by weights to obtain outputs (inputs-to-output): feedforward. Recurrent neural networks, or neural networks with loops allow information from later processing stages to feed back to earlier stages for sequence processing. However, at every stage of inference a feedforward multiplication remains the core, essential for backpropagationRumelhart, David E., Geoffrey E. Hinton, and R. J. Williams.Learning Internal Representations by Error Propagation. David E. Rumelhart, James L. McClelland, and the PDP research group. (editors), Parallel distributed processing: Explorations in the microstructure of cognition, Volume 1: Foundation. MIT Press, 1986. or backpropagation through time. Thus neural networks cannot contain feedback like negative feedback or positive feedback where the outputs feed back to the ''very same'' inputs and modify them, ...
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Google Brain
Google Brain was a deep learning artificial intelligence research team that served as the sole AI branch of Google before being incorporated under the newer umbrella of Google AI, a research division at Google dedicated to artificial intelligence. Formed in 2011, it combined open-ended machine learning research with information systems and large-scale computing resources. It created tools such as TensorFlow, which allow neural networks to be used by the public, and multiple internal AI research projects, and aimed to create research opportunities in machine learning and natural language processing. It was merged into former Google sister company DeepMind to form Google DeepMind in April 2023. History The Google Brain project began in 2011 as a part-time research collaboration between Google fellow Jeff Dean (computer scientist), Jeff Dean and Google Researcher Greg Corrado. Google Brain started as a Google X project and became so successful that it was graduated back to Google: As ...
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Sparse Matrix
In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of rows or columns. By contrast, if most of the elements are non-zero, the matrix is considered dense. The number of zero-valued elements divided by the total number of elements (e.g., ''m'' × ''n'' for an ''m'' × ''n'' matrix) is sometimes referred to as the sparsity of the matrix. Conceptually, sparsity corresponds to systems with few pairwise interactions. For example, consider a line of balls connected by springs from one to the next: this is a sparse system, as only adjacent balls are coupled. By contrast, if the same line of balls were to have springs connecting each ball to all other balls, the system would correspond to a dense matrix. ...
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Conditional Computation
Conditional (if then) may refer to: *Causal conditional, if X then Y, where X is a cause of Y *Conditional probability, the probability of an event A given that another event B *Conditional proof, in logic: a proof that asserts a conditional, and proves that the antecedent leads to the consequent *Material conditional, in propositional calculus, or logical calculus in mathematics *Relevance conditional, in relevance logic *Conditional (computer programming), a statement or expression in computer programming languages *A conditional expression in computer programming languages such as ?: *Conditions in a contract Grammar and linguistics *Conditional mood (or conditional tense), a verb form in many languages *Conditional sentence, a sentence type used to refer to hypothetical situations and their consequences **Indicative conditional, a conditional sentence expressing "if A then B" in a natural language **Counterfactual conditional, a conditional sentence indicating what would b ...
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Deep Learning
Deep learning is a subset of machine learning that focuses on utilizing multilayered neural networks to perform tasks such as classification, regression, and representation learning. The field takes inspiration from biological neuroscience and is centered around stacking artificial neurons into layers and "training" them to process data. The adjective "deep" refers to the use of multiple layers (ranging from three to several hundred or thousands) in the network. Methods used can be either supervised, semi-supervised or unsupervised. Some common deep learning network architectures include fully connected networks, deep belief networks, recurrent neural networks, convolutional neural networks, generative adversarial networks, transformers, and neural radiance fields. These architectures have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, c ...
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