Mathematical Function
MathematicalFunction AIO:MathematicalFunction NOT_REVIEWED
A mathematical rule that gives the value of a dependent variable corresponding to specified values of one or more independent variables.
Ontology IRI:
https://w3id.org/aio/MathematicalFunction
Ontology Structure & Relationships
Parent Classes
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owl:Thing
Branches
Annotations & Sources
Definition Sources:
Subsets:
https://w3id.org/aio/ClassSubset
Curated AIMech Concepts Grounded to this Class
15 Concepts| Curated Concept | Kind | Mapping Relation | Rationale |
|---|---|---|---|
Activation-Value Gaussian Pooling
AIMech:ActivationValueGaussianPooling |
Mathematical Methods | broad_match | For fixed parameters the unit defines a scalar mathematical function of a group of activations; the pinned mathematical-function class has broader scope. |
Active CMA covariance update
AIMech:ActiveCMACovarianceUpdate |
Mathematical Methods | related_match | Equations 5–6 define an explicit matrix-valued rule from the current covariance, supplied updated path, ranked mutation steps and scalar rates to a new symmetric matrix. This specific mathematical construction supports the relation, rather than generic computability of a whole optimizer. It asserts neither equivalence nor an upstream subclass edge, scalar activation semantics or universal positive-definite output. The host’s separate exponential step-size operation is not imported. |
CMA rank-mu covariance update
AIMech:CMARankMuCovarianceUpdate |
Mathematical Methods | related_match | The defining equations give an explicit matrix-valued mathematical rule: specified covariance, updated path, selected-step moment and scalar blend/rate inputs determine the new covariance. This is an informative relation to the broad pinned function definition, not merely the generic computability of a whole optimizer. It does not assert equivalence, an upstream subclass edge or a scalar activation, and does not import the host’s exponential step-size operation. |
Dispatch-dependent value functional
AIMech:DispatchDependentValueFunctional |
Mathematical Methods | broad_match | The proposed subject is the Section 3 mathematical rule itself: it maps a dispatch-prefix-conditioned planning context to a function of search start time. The target’s definition covers a rule assigning a dependent value from independent values and does not require a neural activation or a scalar codomain. This is a local broad-match inference for the functional only, not an exact match, an upstream axiom, a proof of probability calibration or a mapping of the complete planner. |
Dutch eligibility traces
AIMech:DutchEligibilityTraces |
Mathematical Methods | related_match | The component defines a deterministic vector-valued update from prior trace, current feature vector and scalar parameters. This supports a qualified mathematical-rule association with the pinned generic function class, without exact identity, an asserted subclass edge, a scalar-output restriction or a neural-activation claim. |
Expected improvement acquisition
AIMech:ExpectedImprovementAcquisition |
Mathematical Methods | related_match | EI assigns an expected gain to a candidate through a mathematical rule involving a predictive law and incumbent. This relates the specific acquisition rule to the pinned mathematical-function concept without equating it with that broad class, an activation function or a complete optimizer. It asserts no upstream subclass. |
Scaled Legendre HiPPO operator
AIMech:HiPPOLegS |
Mathematical Methods | broad_match | This specific scaled-Legendre projection maps signal history to a coefficient-valued function. It is a mathematical operator, not itself a complete neural network or external memory store. |
High-order polynomial projection operators
AIMech:HiPPOProjection |
Mathematical Methods | broad_match | Definition 1 and the coefficient/projection composition define operators mapping an input function to coefficient values through time. MathematicalFunction is broader than this specific family of mathematical rules; no complete neural-network identity is asserted. |
Learned-Norm Pooling Unit
AIMech:LearnedNormPoolingUnit |
Mathematical Methods | broad_match | For fixed learned parameters this unit supplies a defined scalar function of its inputs; the pinned mathematical-function class is broader. |
MEX Operator
AIMech:MEXOperator |
Mathematical Methods | broad_match | MEX is a parameterized scalar rule on a finite nonempty list, within the broader pinned mathematical-function class. |
Maxout Unit
AIMech:MaxoutUnit |
Mathematical Methods | broad_match | For fixed parameters the unit defines a scalar mathematical function of its input; the pinned mathematical-function class is broader. |
Natural gradient
AIMech:NaturalGradient |
Mathematical Methods | related_match | For a fixed objective and metric, the construction defines a mathematical rule from parameter values to tangent vectors. This broad relationship is not equivalence or an upstream subclass assertion, and does not identify the direction with a scalar activation, neural layer or complete optimizer. |
Noh–Rieger random-walk centrality
AIMech:NohRiegerRandomWalkCentrality |
Mathematical Methods | broad_match | The local concept is the precisely defined function (G,i) -> pi_i/sum_t((P^t)_ii-pi_i) on its stated graph domain. AIO MathematicalFunction is broader and defines a rule assigning a dependent value to specified independent variables. This record denotes the scoring functional rather than a particular numerical solver. |
Probability of improvement acquisition
AIMech:ProbabilityOfImprovementAcquisition |
Mathematical Methods | related_match | PI assigns a scalar probability through a mathematical rule involving a predictive law, threshold and event direction. This relates the specific acquisition criterion to the pinned mathematical-function concept without equating it with that broad class, a predictive model, a neural layer or a complete optimizer. No upstream subclass membership is asserted. |
Zhou random-walk distance-profile dissimilarity
AIMech:ZhouRandomWalkDissimilarity |
Mathematical Methods | broad_match | The local concept assigns a nonnegative number to a graph and an adjacent vertex pair using an explicit equation. AIO MathematicalFunction is the broader rule-to-value class; the local identity is a functional rather than a particular solver. |
Import Provenance & Upstream Synchronization
Source Repo: AIO GitHub
Release Version:
aio.jsonCommit:
397851c547…License: CC-BY-4.0
Imported At: 2026-10-10T07:34:10Z
SHA256:
8f741d71408c…
Source File:
data/aio/MathematicalFunction.yaml