Explanation-based learning (EBL) is a form of machine learning that exploits a very strong, or even perfect, domain theory (i.e. a formal theory of an application domain akin to a domain model in ontology engineering, not to be confused with Scott's domain theory) in order to make generalizations or form concepts from training examples. It is also linked with Encoding (memory) to help with Learning. == Details == An example of EBL using a perfect domain theory is a program that learns to play chess through example. A specific chess position that contains an important feature such as "Forced loss of black queen in two moves" includes many irrelevant features, such as the specific scattering of pawns on the board. EBL can take a single training example and determine what are the relevant features in order to form a generalization. A domain theory is perfect or complete if it contains, in principle, all information needed to decide any question about the domain. For example, the domain theory for chess is simply the rules of chess. Knowing the rules, in principle, it is possible to deduce the best move in any situation. However, actually making such a deduction is impossible in practice due to combinatoric explosion. EBL uses training examples to make searching for deductive consequences of a domain theory efficient in practice. In essence, an EBL system works by finding a way to deduce each training example from the system's existing database of domain theory. Having a short proof of the training example extends the domain-theory database, enabling the EBL system to find and classify future examples that are similar to the training example very quickly. The main drawback of the method—the cost of applying the learned proof macros, as these become numerous—was analyzed by Minton. === Basic formulation === EBL software takes four inputs: a hypothesis space (the set of all possible conclusions) a domain theory (axioms about a domain of interest) training examples (specific facts that rule out some possible hypothesis) operationality criteria (criteria for determining which features in the domain are efficiently recognizable, e.g. which features are directly detectable using sensors) == Application == An especially good application domain for an EBL is natural language processing (NLP). Here a rich domain theory, i.e., a natural language grammar—although neither perfect nor complete, is tuned to a particular application or particular language usage, using a treebank (training examples). Rayner pioneered this work. The first successful industrial application was to a commercial NL interface to relational databases. The method has been successfully applied to several large-scale natural language parsing systems, where the utility problem was solved by omitting the original grammar (domain theory) and using specialized LR-parsing techniques, resulting in huge speed-ups, at a cost in coverage, but with a gain in disambiguation. EBL-like techniques have also been applied to surface generation, the converse of parsing. When applying EBL to NLP, the operationality criteria can be hand-crafted, or can be inferred from the treebank using either the entropy of its or-nodes or a target coverage/disambiguation trade-off (= recall/precision trade-off = f-score). EBL can also be used to compile grammar-based language models for speech recognition, from general unification grammars. Note how the utility problem, first exposed by Minton, was solved by discarding the original grammar/domain theory, and that the quoted articles tend to contain the phrase grammar specialization—quite the opposite of the original term explanation-based generalization. Perhaps the best name for this technique would be data-driven search space reduction. Other people who worked on EBL for NLP include Guenther Neumann, Aravind Joshi, Srinivas Bangalore, and Khalil Sima'an.
Piranesi (software)
Piranesi is an interactive paint system that enables the user to create artistic images from 3D scenes created using conventional modeling applications. == Image format == Piranesi uses the proprietary EPix file format. For every pixel, additional information is stored, such as distance from the viewer and material settings. EPix files can be rendered from 3D scenes using a fixed viewpoint by Piranesi's companion software, Vedute.
Ashish Vaswani
Ashish Vaswani is an Indian computer scientist and entrepreneur. He conducted research at Google Brain, co-founded Adept AI, and, as of 2025, was co-founder and chief executive officer of Essential AI. Vaswani is a co-author of the 2017 paper "Attention Is All You Need", which introduced the Transformer neural network architecture. The Transformer model has been used in the development of subsequent NLP models BERT, ChatGPT, and their successors. == Career == Vaswani completed his engineering in Computer Science from Birla Institute of Technology, Mesra (BIT Mesra) in 2002. In 2004, he enrolled at the University of Southern California for graduate studies. He earned his PhD in Computer Science at the University of Southern California supervised by David Chiang. During his research career at Google, Vaswani was part of the Google Brain team, where he conducted the work leading to the 'Attention Is All You Need' publication. Prior to joining Google, he was affiliated with the Information Sciences Institute at the University of Southern California. After Google, Vaswani co-founded Adept AI, a machine learning-focused startup that developed AI agents and tools for software automation. He has since left the company. He later co-founded Essential AI with Niki Parmar. As of 2025, he was chief executive officer of Essential AI. == Notable works == Vaswani's most notable paper, "Attention Is All You Need", was published in 2017. The paper introduced the Transformer model, which uses self-attention mechanisms instead of recurrence for sequence-to-sequence tasks. The Transformer architecture has become foundational to modern language models and NLP systems, including BERT (2018), GPT-2, GPT-3 (2019–2020) and many more recent models. The "Attention Is All You Need" paper is among the most cited papers in machine learning.
CoDi
CoDi is a cellular automaton (CA) model for spiking neural networks (SNNs). CoDi is an acronym for Collect and Distribute, referring to the signals and spikes in a neural network. CoDi uses a von Neumann neighborhood modified for a three-dimensional space; each cell looks at the states of its six orthogonal neighbors and its own state. In a growth phase a neural network is grown in the CA-space based on an underlying chromosome. There are four types of cells: neuron body, axon, dendrite and blank. The growth phase is followed by a signaling- or processing-phase. Signals are distributed from the neuron bodies via their axon tree and collected from connection dendrites. These two basic interactions cover every case, and they can be expressed simply, using a small number of rules. == Cell interaction during signaling == The neuron body cells collect neural signals from the surrounding dendritic cells and apply an internally defined function to the collected data. In the CoDi model the neurons sum the incoming signal values and fire after a threshold is reached. This behavior of the neuron bodies can be modified easily to suit a given problem. The output of the neuron bodies is passed on to its surrounding axon cells. Axonal cells distribute data originating from the neuron body. Dendritic cells collect data and eventually pass it to the neuron body. These two types of cell-to-cell interaction cover all kinds of cell encounters. Every cell has a gate, which is interpreted differently depending on the type of the cell. A neuron cell uses this gate to store its orientation, i.e. the direction in which the axon is pointing. In an axon cell, the gate points to the neighbor from which the neural signals are received. An axon cell accepts input only from this neighbor, but makes its own output available to all its neighbors. In this way axon cells distribute information. The source of information is always a neuron cell. Dendritic cells collect information by accepting information from any neighbor. They give their output, (e.g. a Boolean OR operation on the binary inputs) only to the neighbor specified by their own gate. In this way, dendritic cells collect and sum neural signals, until the final sum of collected neural signals reaches the neuron cell. Each axonal and dendritic cell belongs to exactly one neuron cell. This configuration of the CA-space is guaranteed by the preceding growth phase. == Synapses == The CoDi model does not use explicit synapses, because dendrite cells that are in contact with an axonal trail (i.e. have an axon cell as neighbor) collect the neural signals directly from the axonal trail. This results from the behavior of axon cells, which distribute to every neighbor, and from the behavior of the dendrite cells, which collect from any neighbor. The strength of a neuron-neuron connection (a synapse) is represented by the number of their neighboring axon and dendrite cells. The exact structure of the network and the position of the axon-dendrite neighbor pairs determine the time delay and strength (weight) of a neuron-neuron connection. This principle infers that a single neuron-neuron connection can consist of several synapse with different time delays with independent weights. == Genetic encoding and growth of the network == The chromosome is initially distributed throughout the CA-space, so that every cell in the CA-space contains one instruction of the chromosome, i.e. one growth instruction, so that the chromosome belongs to the network as a whole. The distributed chromosome technique of the CoDi model makes maximum use of the available CA-space and enables the growth of any type of network connectivity. The local connection of the grown circuitry to its chromosome, allows local learning to be combined with the evolution of grown neural networks. Growth signals are passed to the direct neighbors of the neuron cell according to its chromosome information. The blank neighbors, which receive a neural growth signal, turn into either an axon cell or a dendrite cell. The growth signals include information containing the cell type of the cell that is to be grown from the signal. To decide in which directions axonal or dendritic trails should grow, the grown cells consult their chromosome information which encodes the growth instructions. These growth instructions can have an absolute or a relative directional encoding. An absolute encoding masks the six neighbors (i.e. directions) of a 3D cell with six bits. After a cell is grown, it accepts growth signals only from the direction from which it received its first signal. This reception direction information is stored in the gate position of each cell's state. == Implementation as a partitioned CA == The states of our CAs have two parts, which are treated in different ways. The first part of the cell-state contains the cell's type and activity level and the second part serves as an interface to the cell's neighborhood by containing the input signals from the neighbors. Characteristic of our CA is that only part of the state of a cell is passed to its neighbors, namely the signal and then only to those neighbors specified in the fixed part of the cell state. This CA is called partitioned, because the state is partitioned into two parts, the first being fixed and the second is variable for each cell. The advantage of this partitioning-technique is that the amount of information that defines the new state of a CA cell is kept to a minimum, due to its avoidance of redundant information exchange. == Implementation in hardware == Since CAs are only locally connected, they are ideal for implementation on purely parallel hardware. When designing the CoDi CA-based neural networks model, the objective was to implement them directly in hardware (FPGAs). Therefore, the CA was kept as simple as possible, by having a small number of bits to specify the state, keeping the CA rules few in number, and having few cellular neighbors. The CoDi model was implemented in the FPGA based CAM-Brain Machine (CBM) by Korkin. == History == CoDi was introduced by Gers et al. in 1998. A specialized parallel machine based on FPGA Hardware (CAM) to run the CoDi model on a large scale was developed by Korkin et al. De Garis conducted a series of experiments on the CAM-machine evaluating the CoDi model. The original model, where learning is based on evolutionary algorithms, has been augmented with a local learning rule via feedback from dendritic spikes by Schwarzer.
Stanford Research Institute Problem Solver
The Stanford Research Institute Problem Solver, known by its acronym STRIPS, is an automated planner developed by Richard Fikes and Nils Nilsson in 1971 at SRI International. The same name was later used to refer to the formal language of the inputs to this planner. This language is the base for most of the languages for expressing automated planning problem instances in use today; such languages are commonly known as action languages. This article only describes the language, not the planner. == Definition == A STRIPS instance is composed of: An initial state; The specification of the goal states – situations that the planner is trying to reach; A set of actions. For each action, the following are included: preconditions (what must be established before the action is performed); postconditions (what is established after the action is performed). Mathematically, a STRIPS instance is a quadruple ⟨ P , O , I , G ⟩ {\displaystyle \langle P,O,I,G\rangle } , in which each component has the following meaning: P {\displaystyle P} is a set of conditions (i.e., propositional variables); O {\displaystyle O} is a set of operators (i.e., actions); each operator is itself a quadruple ⟨ α , β , γ , δ ⟩ {\displaystyle \langle \alpha ,\beta ,\gamma ,\delta \rangle } , each element being a set of conditions. These four sets specify, in order, which conditions must be true for the action to be executable, which ones must be false, which ones are made true by the action and which ones are made false; I {\displaystyle I} is the initial state, given as the set of conditions that are initially true (all others are assumed false); G {\displaystyle G} is the specification of the goal state; this is given as a pair ⟨ N , M ⟩ {\displaystyle \langle N,M\rangle } , which specify which conditions are true and false, respectively, in order for a state to be considered a goal state. A plan for such a planning instance is a sequence of operators that can be executed from the initial state and that leads to a goal state. Formally, a state is a set of conditions: a state is represented by the set of conditions that are true in it. Transitions between states are modeled by a transition function, which is a function mapping states into new states that result from the execution of actions. Since states are represented by sets of conditions, the transition function relative to the STRIPS instance ⟨ P , O , I , G ⟩ {\displaystyle \langle P,O,I,G\rangle } is a function succ : 2 P × O → 2 P , {\displaystyle \operatorname {succ} :2^{P}\times O\rightarrow 2^{P},} where 2 P {\displaystyle 2^{P}} is the set of all subsets of P {\displaystyle P} , and is therefore the set of all possible states. The transition function succ {\displaystyle \operatorname {succ} } for a state C ⊆ P {\displaystyle C\subseteq P} , can be defined as follows, using the simplifying assumption that actions can always be executed but have no effect if their preconditions are not met: The function succ {\displaystyle \operatorname {succ} } can be extended to sequences of actions by the following recursive equations: succ ( C , [ ] ) = C {\displaystyle \operatorname {succ} (C,[\ ])=C} succ ( C , [ a 1 , a 2 , … , a n ] ) = succ ( succ ( C , a 1 ) , [ a 2 , … , a n ] ) {\displaystyle \operatorname {succ} (C,[a_{1},a_{2},\ldots ,a_{n}])=\operatorname {succ} (\operatorname {succ} (C,a_{1}),[a_{2},\ldots ,a_{n}])} A plan for a STRIPS instance is a sequence of actions such that the state that results from executing the actions in order from the initial state satisfies the goal conditions. Formally, [ a 1 , a 2 , … , a n ] {\displaystyle [a_{1},a_{2},\ldots ,a_{n}]} is a plan for G = ⟨ N , M ⟩ {\displaystyle G=\langle N,M\rangle } if F = succ ( I , [ a 1 , a 2 , … , a n ] ) {\displaystyle F=\operatorname {succ} (I,[a_{1},a_{2},\ldots ,a_{n}])} satisfies the following two conditions: N ⊆ F {\displaystyle N\subseteq F} M ∩ F = ∅ {\displaystyle M\cap F=\varnothing } == Extensions == The above language is actually the propositional version of STRIPS; in practice, conditions are often about objects: for example, that the position of a robot can be modeled by a predicate A t {\displaystyle At} , and A t ( r o o m 1 ) {\displaystyle At(room1)} means that the robot is in Room1. In this case, actions can have free variables, which are implicitly existentially quantified. In other words, an action represents all possible propositional actions that can be obtained by replacing each free variable with a value. The initial state is considered fully known in the language described above: conditions that are not in I {\displaystyle I} are all assumed false. This is often a limiting assumption, as there are natural examples of planning problems in which the initial state is not fully known. Extensions of STRIPS have been developed to deal with partially known initial states. == A sample STRIPS problem == A monkey is at location A in a lab. There is a box in location C. The monkey wants the bananas that are hanging from the ceiling in location B, but it needs to move the box and climb onto it in order to reach them. Initial state: At(A), Level(low), BoxAt(C), BananasAt(B) Goal state: Have(bananas) Actions: // move from X to Y _Move(X, Y)_ Preconditions: At(X), Level(low) Postconditions: not At(X), At(Y) // climb up on the box _ClimbUp(Location)_ Preconditions: At(Location), BoxAt(Location), Level(low) Postconditions: Level(high), not Level(low) // climb down from the box _ClimbDown(Location)_ Preconditions: At(Location), BoxAt(Location), Level(high) Postconditions: Level(low), not Level(high) // move monkey and box from X to Y _MoveBox(X, Y)_ Preconditions: At(X), BoxAt(X), Level(low) Postconditions: BoxAt(Y), not BoxAt(X), At(Y), not At(X) // take the bananas _TakeBananas(Location)_ Preconditions: At(Location), BananasAt(Location), Level(high) Postconditions: Have(bananas) == Complexity == Deciding whether any plan exists for a propositional STRIPS instance is PSPACE-complete. Various restrictions can be enforced in order to decide if a plan exists in polynomial time or at least make it an NP-complete problem. == Macro operator == In the monkey and banana problem, the robot monkey has to execute a sequence of actions to reach the banana at the ceiling. A single action provides a small change in the game. To simplify the planning process, it make sense to invent an abstract action, which isn't available in the normal rule description. The super-action consists of low level actions and can reach high-level goals. The advantage is that the computational complexity is lower, and longer tasks can be planned by the solver. Identifying new macro operators for a domain can be realized with genetic programming. The idea is, not to plan the domain itself, but in the pre-step, a heuristics is created that allows the domain to be solved much faster. In the context of reinforcement learning, a macro-operator is called an option. Similar to the definition within AI planning, the idea is, to provide a temporal abstraction (span over a longer period) and to modify the game state directly on a higher layer.
Double descent
Double descent in statistics and machine learning is the phenomenon where a model's error rate on the test set initially decreases with the number of parameters, then peaks, then decreases again. This phenomenon has been considered surprising, as it contradicts assumptions about overfitting in classical machine learning. The increase usually occurs near the interpolation threshold, where the number of parameters is the same as the number of training data points (the model is just large enough to fit the training data). Or, more precisely, it is the maximum number of samples on which the model/training procedure achieves approximately on average 0 training error. == History == Early observations of what would later be called double descent in specific models date back to 1989. The term "double descent" was coined by Belkin et. al. in 2019, when the phenomenon gained popularity as a broader concept exhibited by many models. The latter development was prompted by a perceived contradiction between the conventional wisdom that too many parameters in the model result in a significant overfitting error (an extrapolation of the bias–variance tradeoff), and the empirical observations in the 2010s that some modern machine learning techniques tend to perform better with larger models. == Theoretical models == Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. A number of works have suggested that double descent can be explained using the concept of effective dimension: While a network may have a large number of parameters, in practice only a subset of those parameters are relevant for generalization performance, as measured by the local Hessian curvature. This explanation is formalized through PAC-Bayes compression-based generalization bounds, which show that less complex models are expected to generalize better under a Solomonoff prior.
Pax Silica
Pax Silica is a United States-led international initiative focused on strengthening and coordinating "trusted" supply chains for advanced technologies—especially semiconductors, artificial intelligence (AI) infrastructure, critical minerals, advanced manufacturing, logistics, and associated energy and data infrastructure. The initiative is coordinated by the US Department of State and was launched in December 2025 alongside the signing of the non-binding Pax Silica Declaration by an initial group of partner countries. The initiative describes itself as a "positive-sum" partnership intended to reduce "coercive dependencies" and improve resilience across the full technology stack, from mineral extraction and processing through chip manufacturing and computing infrastructure. US officials described Pax Silica as a framework for coordinating flagship projects and policy alignment across partner countries, including supply-chain mapping, investment and co-investment initiatives, and protection of critical infrastructure and sensitive technologies. Reuters reported discussions of projects linked to trade and logistics routes and an industrial park initiative in Israel. Gulf countries, such as the UAE and Qatar, are betting on attracting AI companies with cheap energy. Moreover, the UAE's potential to invest in Pax Silica's activities has been noted as a fundamental asset for the initiative. In early 2026, the U.S. announced plans to contribute $250M toward an investmest consortium that's intended to strengthen energy and critical mineral supply chains. == Launch and background == During the 2020s, governments increasingly treated supply-chain resilience in semiconductors, critical minerals, and AI-related computing infrastructure as a national-security priority, amid export controls, industrial policy measures, and geopolitical competition over the technologies underpinning advanced manufacturing and AI. Pax Silica was presented by US officials as an economic-security framework aimed at aligning policies and investment among "trusted partners" that host major technology firms and key industrial capacity. Pacific Forum's analyst Akhil Ramesh, writing for the National Interest magazine, described the initiative as understanding that: "economic security today is inseparable from control over energy, critical minerals, high-end manufacturing, and advanced models." On December 11, 2025, the US Department of State announced the inaugural Pax Silica Summit and a planned signing of the Pax Silica Declaration, describing Pax Silica as the Department's flagship effort on AI and supply-chain security. The initial summit was held in Washington, D.C. on December 12, 2025. The State Department fact sheet described cooperation areas including connectivity and data infrastructure, compute and semiconductors, advanced manufacturing, logistics, mineral refining and processing, and energy. == Membership == Pax Silica participation has been discussed in terms of (1) countries that have signed the declaration and (2) countries invited to summit discussions or publicly reported as prospective signatories but which had not (as of mid-January 2026) signed the declaration. === Countries that signed the Pax Silica Declaration === Seven countries signed the declaration at the December 12, 2025, summit in Washington, D.C.: Australia Israel Japan South Korea Singapore United Kingdom United States Some countries who attended the initial conversations did not immediately sign, while additional countries were invited to join after the discussions concluded. The following are the later signatory countries on the declaration: Greece Netherlands (joined December 17, 2025; "non-signing partner") Qatar (joined January 13, 2026) United Arab Emirates (joined January 14, 2026) India (joined February 20, 2026) Sweden (signed March 17, 2026) Finland (signed April 16, 2026) Philippines (signed April 17, 2026) Norway (signed May 6, 2026) === Countries invited / participating, but not yet signed === At launch, US materials and contemporaneous reporting described additional invited participants and observers, including: Canada – observer/participant in related discussions, per US briefing materials; not listed among signatories. Taiwan – participated in summit sessions according to a State Department briefing; not listed among signatories. The Organisation for Economic Co-operation and Development (OECD) and European Union were also noted by US officials as present in an observer capacity, but are not countries.