DeepSeek is a generative artificial intelligence chatbot developed by the Chinese company DeepSeek. Released on 20 January 2025, DeepSeek-R1 surpassed ChatGPT as the most downloaded freeware app on the iOS App Store in the United States by 27 January. DeepSeek's success against larger and more established rivals has been described as "upending AI" and initiating "a global AI space race". DeepSeek's compliance with Chinese government censorship policies and its data collection practices have also raised concerns over privacy and information control in the model, prompting regulatory scrutiny in multiple countries. However, it has also been praised for its open weights and infrastructure code, energy efficiency and contributions to open-source artificial intelligence. == History == On 10 January 2025, DeepSeek released the chatbot, based on the DeepSeek-R1 model, for iOS and Android. By 27 January, DeepSeek-R1 surpassed ChatGPT as the most-downloaded freeware app on the iOS App Store in the United States, which resulted in an 18% drop in Nvidia's share price. And after a "large-scale" cyberattack on the same day disrupted the proper functioning of its servers, DeepSeek had limited its new user registration to phone numbers from mainland China, email addresses, or Google account logins. On 3 April 2025, in collaboration with researchers at Tsinghua University, DeepSeek published a paper unveiling a new model that combines the techniques generative reward modeling (GRM) and self-principled critique tuning (SPCT). The resulting model is referred to as DeepSeek-GRM. The goal of using these techniques is to foster more effective inference-time scaling within their LLM and chatbot services. Notably, DeepSeek has said that these new models will be released and made open source. On 30 April 2025, Deepseek released its math-focused Artificial Intelligence Model named "DeepSeek-Prover-V2-671B". This model is useful for formal theorem proving and mathematical reasoning. On 24 April 2026, DeepSeek released DeepSeek V4 and V4-Pro. == Usage == DeepSeek can answer questions, solve logic problems, and write computer programs on par with other chatbots, according to benchmark tests used by American AI companies. Users can access the chatbot for free through the official DeepSeek website or mobile application, without limitation on the number of queries. DeepSeek only supports user-signup via a global email service, e.g. Gmail, Google or Yahoo. DeepSeek also offers access to the R1 and V3 models that power the chatbot via an API with a usage-based pricing model. This modality is primarily targeted towards developers and businesses. As of February 2025, API usage is priced at approximately $0.28 per million input tokens and $0.42 per million output tokens, making it less expensive than some competing services. Its web version is completely free, with 500 messages per hour cap limit to prevent bots from spamming. == Operation == DeepSeek-V3 uses significantly fewer resources compared to its peers. For example, whereas the world's leading AI companies train their chatbots with supercomputers using as many as 16,000 graphics processing units (GPUs), DeepSeek claims to have needed only about 2,000 GPUs—namely, the H800 series chips from Nvidia. It was trained in around 55 days at a cost of US$5.58 million, which is roughly one-tenth of what tech giant Meta spent building its latest AI technology. == Reactions == DeepSeek's success against larger and more established rivals has been described as "upending AI", constituting "the first shot at what is emerging as a global AI space race", and ushering in "a new era of AI brinkmanship". === Challenge to US AI dominance === DeepSeek's competitive performance at relatively minimal cost has been recognized as potentially challenging the global dominance of American AI models. Various publications and news media, such as The Hill and The Guardian, have described the release of the R1 chatbot as a "Sputnik moment" for American AI, echoing Marc Andreessen's view. OpenAI wrote a letter to the Office of Science and Technology Policy (OSTP), in March 2025, citing issues concerning a possibility that Deepseek could manipulate responses to cause harm. === Chinese perspective === DeepSeek's founder Liang Wenfeng has been compared to OpenAI CEO Sam Altman, with CNN calling him the Sam Altman of China and an evangelist for AI. Chinese state media widely praised DeepSeek as a national asset. On 20 January 2025, Chinese Premier Li Qiang invited Wenfeng to his symposium with experts and asked him to provide opinions and suggestions on a draft for comments of the annual 2024 government work report. On 20 February 2025, Wenfeng met with General Secretary of the Chinese Communist Party Xi Jinping, who encouraged party and state leaders to experiment with DeepSeek. Government officials responded to Xi's approval of the chatbot by reportedly using it to draft legal judgements, propose medical treatment plans, and analyze surveillance videos to search for missing persons. === Performance and success === Leading figures in the American AI sector had mixed reactions to DeepSeek's performance and success. Microsoft CEO Satya Nadella and OpenAI CEO Altman—whose companies are involved in the United States government-backed "Stargate Project" to develop American AI infrastructure—both called DeepSeek "super impressive". Various companies including Amazon Web Services, Toyota, and Stripe are seeking to use the model in their program. When American President Donald Trump announced The Stargate Project, he referred to DeepSeek as a wake-up call and a positive development. Other leaders in the AI field, however—including Scale AI CEO Alexandr Wang, Anthropic cofounder and CEO Dario Amodei, and Elon Musk—have expressed skepticism of the app's performance or of the sustainability of its success. Wang in particularly referred to DeepSeek-V3 as "earth-shattering" and DeepSeek-R1 as "top performing, or roughly on par with the best American models", but speculated that China may possess more AI-powering Nvidia H100 GPUs than thought. === Stock market implications === DeepSeek's optimization of limited resources has highlighted potential limits of United States sanctions on China's AI development, including export restrictions on advanced AI chips to China. The success of the company's AI models consequently "sparked market turmoil" and caused shares in major global technology companies to plunge on 27 January 2025: Nvidia's stock fell by as much as 17–18%, as did the stock of rival Broadcom. Other tech firms also sank, including Microsoft (down 2.5%), Google's owner Alphabet (down over 4%), and Dutch chip equipment maker ASML (down over 7%). A global sell-off of technology stocks on Nasdaq, prompted by the release of the R1 model, led to record losses of about $593 billion in the market capitalizations of AI and computer hardware companies; and by the next day a total of $1 trillion of value was wiped from American stocks. == Concerns == === Distillation === DeepSeek has been reported to sometimes claim that it is ChatGPT. OpenAI said that DeepSeek may have "inappropriately" used outputs from its model as training data in a process called distillation. However, there is currently no method to prove this conclusively. === Censorship === DeepSeek's compliance with Chinese government censorship policies and its data collection practices have raised concerns over information control in the model, prompting regulatory scrutiny in multiple countries. Reports indicate that it applies content moderation in accordance with the government's "public opinion guidance" regulations, limiting responses on topics such as the Tiananmen Square massacre and Taiwan's political status. DeepSeek models that have been uncensored also display a bias towards Chinese government viewpoints on controversial topics such as Xi Jinping's human rights record and Taiwan's political status. However, users who have downloaded the models and hosted them on their own devices and servers have reported successfully removing this censorship. Some sources have observed that the official application programming interface (API) version of R1, which runs from servers located in mainland China, uses censorship mechanisms for topics considered politically sensitive for the government of China. For example, the model may initially generate answers to questions about the 1989 Tiananmen Square massacre, persecution of Uyghurs, comparisons between Xi Jinping and Winnie the Pooh, and human rights in China, but a censorship mechanism deletes the uncensored response afterwards and replaces it with a message such as:"Sorry, that's beyond my current scope. Let's talk about something else." The post hoc censorship mechanisms and restrictions added on top of the model's output can be removed in the open-source version of the R1 model. If the "core Socialist values" defined by the Chinese Internet regul
Albert One
Albert One is an artificial intelligence chatbot created by Robby Garner and designed to mimic the way humans make conversations using a multi-faceted approach in natural language programming. == History == In both 1998 and 1999, Albert One won the Loebner Prize Contest, a competition between chatterbots. Some parts of Albert were deployed on the internet beginning in 1995, to gather information about what kinds of things people would say to a chatterbot. Another element of Albert One involved the building of a large database of human statements, and associated replies. This portion of the project was tested at the 1994-1997 Loebner Prize contests. Albert was the first of Robby Garner's multifaceted bots. The Albert One system was composed of several subsystems. Among those were a version of Eliza, the therapist, Elivs, another Eliza-like bot, and several other helper applications working together in a hierarchical arrangement. As a continuation of the stimulus-response library, various other database queries and assertions were tested to arrive at each of Albert's responses. Robby went on to develop networked examples of this kind of hierarchical "glue" at The Turing Hub.
Blockmodeling linked networks
Blockmodeling linked networks is an approach in blockmodeling in analysing the linked networks. Such approach is based on the generalized multilevel blockmodeling approach. The main objective of this approach is to achieve clustering of the nodes from all involved sets, while at the same time using all available information. At the same time, all one-mode and two-node networks, that are connected, are blockmodeled, which results in obtaining only one clustering, using nodes from each sets. Each cluster ideally contains only nodes from one set, which also allows the modeling of the links among clusters from different sets (through two-mode networks). This approach was introduced by Aleš Žiberna in 2014. Blockmodeling linked networks can be done using: separate analysis: blockmodeling each level separately; conversion approach: converting all one-mode networks to the same level and joining with two-mode networks; a true multilevel approach: one-mode and two-mode networks are blockmodeled at the same time, resulting in one clustering for nodes from each level.
Generalized blockmodeling of valued networks
Generalized blockmodeling of valued networks is an approach of the generalized blockmodeling, dealing with valued networks (e.g., non-binary). While the generalized blockmodeling signifies a "formal and integrated approach for the study of the underlying functional anatomies of virtually any set of relational data", it is in principle used for binary networks. This is evident from the set of ideal blocks, which are used to interpret blockmodels, that are binary, based on the characteristic link patterns. Because of this, such templates are "not readily comparable with valued empirical blocks". To allow generalized blockmodeling of valued directional (one-mode) networks (e.g. allowing the direct comparisons of empirical valued blocks with ideal binary blocks), a non–parametric approach is used. With this, "an optional parameter determines the prominence of valued ties as a minimum percentile deviation between observed and expected flows". Such two–sided application of parameter then introduces "the possibility of non–determined ties, i.e. valued relations that are deemed neither prominent (1) nor non–prominent (0)." Resulted occurrences of links then motivate the modification of the calculation of inconsistencies between empirical and ideal blocks. At the same time, such links also give a possibility to measure the interpretational certainty, which is specific to each ideal block. Such maximum two–sided deviation threshold, holding the aggregate uncertainty score at zero or near–zero levels, is then proposed as "a measure of interpretational certainty for valued blockmodels, in effect transforming the optional parameter into an outgoing state". Problem with blockmodeling is the standard set of ideal block, as they are all specified using binary link (tie) patters; this results in "a non–trivial exercise to match and count inconsistencies between such ideal binary ties and empirical valued ties". One approach to solve this is by using dichotomization to transform the network into a binary version. The other two approaches were first proposed by Aleš Žiberna in 2007 by introducing valued (generalized) blockmodeling and also homogeneity blockmodeling. The basic idea of the latter is "that the inconsistency of an empirical block with its ideal block can be measured by within block variability of appropriate values". The newly–formed ideal blocks, which are appropriate for blockmodeling of valued networks, are then presented together with the definitions of their block inconsistencies. Two other approaches were later suggested by Carl Nordlund in 2019: deviational approach and correlation-based generalized approach. Both Nordlund's approaches are based on the idea, that valued networks can be compared with the ideal block without values. With this approach, more information is retained for analysis, which also means, that there are fewer partitions having identical values of the criterion function. This means, that the generalized blockmodeling of valued networks measures the inconsistencies more precisely. Usually, only one optimal partition is found in this approach, especially when it is used by homogeneity blockmodeling. Contrary, while using binary blockmodeling on the same sample, usually more than one optimal partition had occurred on several occasions.
Multilayer perceptron
In deep learning, a multilayer perceptron (MLP) is a kind of modern feedforward neural network consisting of fully connected neurons with nonlinear activation functions, organized in layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks are trained using backpropagation and are colloquially referred to as "vanilla" networks. MLPs grew out of an effort to improve on single-layer perceptrons, which could only be applied to linearly separable data. A perceptron traditionally used a Heaviside step function as its nonlinear activation function. However, the backpropagation algorithm requires that modern MLPs use continuous activation functions such as sigmoid or ReLU. Multilayer perceptrons form the basis of deep learning, and are applicable across a vast set of diverse domains. == Timeline == In 1943, Warren McCulloch and Walter Pitts proposed the binary artificial neuron as a logical model of biological neural networks. In 1958, Frank Rosenblatt proposed the multilayered perceptron model, consisting of an input layer, a hidden layer with randomized weights that did not learn, and an output layer with learnable connections. In 1962, Rosenblatt published many variants and experiments on perceptrons in his book Principles of Neurodynamics, including up to 2 trainable layers by "back-propagating errors". However, it was not the backpropagation algorithm, and he did not have a general method for training multiple layers. In 1965, Alexey Grigorevich Ivakhnenko and Valentin Lapa published Group Method of Data Handling. It was one of the first deep learning methods, used to train an eight-layer neural net in 1971. In 1967, Shun'ichi Amari reported the first multilayered neural network trained by stochastic gradient descent, was able to classify non-linearily separable pattern classes. Amari's student Saito conducted the computer experiments, using a five-layered feedforward network with two learning layers. Backpropagation was independently developed multiple times in early 1970s. The earliest published instance was Seppo Linnainmaa's master thesis (1970). Paul Werbos developed it independently in 1971, but had difficulty publishing it until 1982. In 1986, David E. Rumelhart et al. popularized backpropagation. In 2003, interest in backpropagation networks returned due to the successes of deep learning being applied to language modelling by Yoshua Bengio with co-authors. In 2021, a very simple NN architecture combining two deep MLPs with skip connections and layer normalizations was designed and called MLP-Mixer; its realizations featuring 19 to 431 millions of parameters were shown to be comparable to vision transformers of similar size on ImageNet and similar image classification tasks. == Mathematical foundations == === Activation function === If a multilayer perceptron has a linear activation function in all neurons, that is, a linear function that maps the weighted inputs to the output of each neuron, then linear algebra shows that any number of layers can be reduced to a two-layer input-output model. In MLPs some neurons use a nonlinear activation function that was developed to model the frequency of action potentials, or firing, of biological neurons. The two historically common activation functions are both sigmoids, and are described by y ( v i ) = tanh ( v i ) and y ( v i ) = ( 1 + e − v i ) − 1 {\displaystyle y(v_{i})=\tanh(v_{i})~~{\textrm {and}}~~y(v_{i})=(1+e^{-v_{i}})^{-1}} . The first is a hyperbolic tangent that ranges from −1 to 1, while the other is the logistic function, which is similar in shape but ranges from 0 to 1. Here y i {\displaystyle y_{i}} is the output of the i {\displaystyle i} th node (neuron) and v i {\displaystyle v_{i}} is the weighted sum of the input connections. Alternative activation functions have been proposed, including the rectifier and softplus functions. More specialized activation functions include radial basis functions (used in radial basis networks, another class of supervised neural network models). In recent developments of deep learning the rectified linear unit (ReLU) is more frequently used as one of the possible ways to overcome the numerical problems related to the sigmoids. === Layers === The MLP consists of three or more layers (an input and an output layer with one or more hidden layers) of nonlinearly-activating nodes. Since MLPs are fully connected, each node in one layer connects with a certain weight w i j {\displaystyle w_{ij}} to every node in the following layer. === Learning === Learning occurs in the perceptron by changing connection weights after each piece of data is processed, based on the amount of error in the output compared to the expected result. This is an example of supervised learning, and is carried out through backpropagation, a generalization of the least mean squares algorithm in the linear perceptron. We can represent the degree of error in an output node j {\displaystyle j} in the n {\displaystyle n} th data point (training example) by e j ( n ) = d j ( n ) − y j ( n ) {\displaystyle e_{j}(n)=d_{j}(n)-y_{j}(n)} , where d j ( n ) {\displaystyle d_{j}(n)} is the desired target value for n {\displaystyle n} th data point at node j {\displaystyle j} , and y j ( n ) {\displaystyle y_{j}(n)} is the value produced by the perceptron at node j {\displaystyle j} when the n {\displaystyle n} th data point is given as an input. The node weights can then be adjusted based on corrections that minimize the error in the entire output for the n {\displaystyle n} th data point, given by E ( n ) = 1 2 ∑ output node j e j 2 ( n ) {\displaystyle {\mathcal {E}}(n)={\frac {1}{2}}\sum _{{\text{output node }}j}e_{j}^{2}(n)} . Using gradient descent, the change in each weight w i j {\displaystyle w_{ij}} is Δ w j i ( n ) = − η ∂ E ( n ) ∂ v j ( n ) y i ( n ) {\displaystyle \Delta w_{ji}(n)=-\eta {\frac {\partial {\mathcal {E}}(n)}{\partial v_{j}(n)}}y_{i}(n)} where y i ( n ) {\displaystyle y_{i}(n)} is the output of the previous neuron i {\displaystyle i} , and η {\displaystyle \eta } is the learning rate, which is selected to ensure that the weights quickly converge to a response, without oscillations. In the previous expression, ∂ E ( n ) ∂ v j ( n ) {\displaystyle {\frac {\partial {\mathcal {E}}(n)}{\partial v_{j}(n)}}} denotes the partial derivate of the error E ( n ) {\displaystyle {\mathcal {E}}(n)} according to the weighted sum v j ( n ) {\displaystyle v_{j}(n)} of the input connections of neuron i {\displaystyle i} . The derivative to be calculated depends on the induced local field v j {\displaystyle v_{j}} , which itself varies. It is easy to prove that for an output node this derivative can be simplified to − ∂ E ( n ) ∂ v j ( n ) = e j ( n ) ϕ ′ ( v j ( n ) ) {\displaystyle -{\frac {\partial {\mathcal {E}}(n)}{\partial v_{j}(n)}}=e_{j}(n)\phi ^{\prime }(v_{j}(n))} where ϕ ′ {\displaystyle \phi ^{\prime }} is the derivative of the activation function described above, which itself does not vary. The analysis is more difficult for the change in weights to a hidden node, but it can be shown that the relevant derivative is − ∂ E ( n ) ∂ v j ( n ) = ϕ ′ ( v j ( n ) ) ∑ k − ∂ E ( n ) ∂ v k ( n ) w k j ( n ) {\displaystyle -{\frac {\partial {\mathcal {E}}(n)}{\partial v_{j}(n)}}=\phi ^{\prime }(v_{j}(n))\sum _{k}-{\frac {\partial {\mathcal {E}}(n)}{\partial v_{k}(n)}}w_{kj}(n)} . This depends on the change in weights of the k {\displaystyle k} th nodes, which represent the output layer. So to change the hidden layer weights, the output layer weights change according to the derivative of the activation function, and so this algorithm represents a backpropagation of the activation function.
Joint constraints
Joint constraints are rotational constraints on the joints of an artificial system. They are used in an inverse kinematics chain, in fields including 3D animation or robotics. Joint constraints can be implemented in a number of ways, but the most common method is to limit rotation about the X, Y and Z axis independently. An elbow, for instance, could be represented by limiting rotation on X and Z axis to 0 degrees, and constraining the Y-axis rotation to 130 degrees. To simulate joint constraints more accurately, dot-products can be used with an independent axis to repulse the child bones orientation from the unreachable axis. Limiting the orientation of the child bone to a border of vectors tangent to the surface of the joint, repulsing the child bone away from the border, can also be useful in the precise restriction of shoulder movement.
Quadratic classifier
In statistics, a quadratic classifier is a statistical classifier that uses a quadratic decision surface to separate measurements of two or more classes of objects or events. It is a more general version of the linear classifier. == The classification problem == Statistical classification considers a set of vectors of observations x of an object or event, each of which has a known type y. This set is referred to as the training set. The problem is then to determine, for a given new observation vector, what the best class should be. For a quadratic classifier, the correct solution is assumed to be quadratic in the measurements, so y will be decided based on x T A x + b T x + c {\displaystyle \mathbf {x^{T}Ax} +\mathbf {b^{T}x} +c} In the special case where each observation consists of two measurements, this means that the surfaces separating the classes will be conic sections (i.e., either a line, a circle or ellipse, a parabola or a hyperbola). In this sense, we can state that a quadratic model is a generalization of the linear model, and its use is justified by the desire to extend the classifier's ability to represent more complex separating surfaces. == Quadratic discriminant analysis == Quadratic discriminant analysis (QDA) is closely related to linear discriminant analysis (LDA), where it is assumed that the measurements from each class are normally distributed. Unlike LDA however, in QDA there is no assumption that the covariance of each of the classes is identical. When the normality assumption is true, the best possible test for the hypothesis that a given measurement is from a given class is the likelihood ratio test. Suppose there are only two groups, with means μ 0 , μ 1 {\displaystyle \mu _{0},\mu _{1}} and covariance matrices Σ 0 , Σ 1 {\displaystyle \Sigma _{0},\Sigma _{1}} corresponding to y = 0 {\displaystyle y=0} and y = 1 {\displaystyle y=1} respectively. Then the likelihood ratio is given by Likelihood ratio = | 2 π Σ 1 | − 1 exp ( − 1 2 ( x − μ 1 ) T Σ 1 − 1 ( x − μ 1 ) ) | 2 π Σ 0 | − 1 exp ( − 1 2 ( x − μ 0 ) T Σ 0 − 1 ( x − μ 0 ) ) < t {\displaystyle {\text{Likelihood ratio}}={\frac {{\sqrt {|2\pi \Sigma _{1}|}}^{-1}\exp \left(-{\frac {1}{2}}(\mathbf {x} -{\boldsymbol {\mu }}_{1})^{T}\Sigma _{1}^{-1}(\mathbf {x} -{\boldsymbol {\mu }}_{1})\right)}{{\sqrt {|2\pi \Sigma _{0}|}}^{-1}\exp \left(-{\frac {1}{2}}(\mathbf {x} -{\boldsymbol {\mu }}_{0})^{T}\Sigma _{0}^{-1}(\mathbf {x} -{\boldsymbol {\mu }}_{0})\right)}}