Read the equation
The process state evolves through F, a readout H extracts the representation z, and a detector D uses the declared inputs to score a declaration. These are distinct operations even when they share model parameters. Reproduction requires their actual implementations, and the detector’s use of future information must be ruled out if it is meant to operate online.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| ell_t | Runtime process state |
| theta_t | Model parameters |
| m_t | Persistent memory |
| u_t | Input |
| z_t | Readout representation |
| D_t | Declaration score |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
Let ι denote an identity label for one experimental instance. Let st be its computational state, θt its parameters, mt its retained memory, ut its input, and ℓt its recurrent working state. An observable declaration event is Dt. A candidate internally generated representation is zt. A general implementation might be written ℓt+1=Fθtℓt,mt,ut, zt=Hθtℓt,mt, Dt=Dzt,ℓt. These are interfaces, not recovered fully specified equations. Until F, H, and D are defined, this notation names the desired operations without providing an executable theory. There are two different reference choices. An origin reference freezes the state declared at an initial time, r0=ztD. A current reference tracks a specified measurable property of the actual system, rt=ϕst. The latter requires a measurement map ϕ into the same representational space as zt. δtorigin=dzt,r0, δtcurrent=dzt,ϕst.
Exact original notation
{ℓ}_{t+1}={F}_{{\theta }_{t}}\left({ℓ}_{t},{m}_{t},{u}_{t}\right), {z}_{t}={H}_{{\theta }_{t}}\left({ℓ}_{t},{m}_{t}\right), {D}_{t}=D\left({z}_{t},{ℓ}_{t}\right).Sources & provenance
{ℓ}_{t+1}={F}_{{\theta }_{t}}\left({ℓ}_{t},{m}_{t},{u}_{t}\right), {z}_{t}={H}_{{\theta }_{t}}\left({ℓ}_{t},{m}_{t}\right), {D}_{t}=D\left({z}_{t},{ℓ}_{t}\right).
{ℓ}_{t+1}={F}_{{\theta }_{t}}\left({ℓ}_{t},{m}_{t},{u}_{t}\right), {z}_{t}={H}_{{\theta }_{t}}\left({ℓ}_{t},{m}_{t}\right), {D}_{t}=D\left({z}_{t},{ℓ}_{t}\right).