The joint objective
A central pattern compares desired design with modeled behavior and adds operating cost, state regularization and design regularization. The notes restrict this same loss to environments, devices, layers, neurons and task instances. Sharing the objective form is intended to make the measurements consistent across those levels.
Seven environment layers
The model borrows physical, link, network, transport, session, presentation and application layers. Each receives its own environment view and metrics such as bit error, signal-to-noise ratio, frame loss, latency, retransmission, session retention, compression ratio and application response time. The loss formulations and exchange messages are design proposals; an OSI label does not establish a causal neural layer.
The 80-neuron template
All 80 U/V/dK rows have been expanded into explicitly labeled cost instances. Their r_min values and algebraic costs can be read individually. Task behavior remains source-incomplete because the raw notes themselves identify missing domain operators and state-change functions.
Conflicts preserved
One routing form selects minimal cost, while another selects argmax(C_i−dx). When dx is common to all candidates, subtracting it cannot change the ranking. Both variants are preserved for comparison. The record also distinguishes the outer Epona aggregator Φ from a loop integral, the unity score, the golden-ratio constant and IIT Φ.
Equations in this build
138 linked mathematical records. Each opens its notation, interpretation and source.
Rhiannon neuron 1: system and device cost
This is the documented cost template instantiated for neuron 1 in the system and device group. The source provides U=4, V=3 and dK=2, so the maximum structural requirement is 4.…
Rhiannon neuron 2: system and device cost
This is the documented cost template instantiated for neuron 2 in the system and device group. The source provides U=5, V=4 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 3: system and device cost
This is the documented cost template instantiated for neuron 3 in the system and device group. The source provides U=6, V=5 and dK=3, so the maximum structural requirement is 6.…
Rhiannon neuron 4: system and device cost
This is the documented cost template instantiated for neuron 4 in the system and device group. The source provides U=4, V=4 and dK=2, so the maximum structural requirement is 4.…
Rhiannon neuron 5: system and device cost
This is the documented cost template instantiated for neuron 5 in the system and device group. The source provides U=3, V=5 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 6: system and device cost
This is the documented cost template instantiated for neuron 6 in the system and device group. The source provides U=4, V=3 and dK=3, so the maximum structural requirement is 4.…
Rhiannon neuron 7: system and device cost
This is the documented cost template instantiated for neuron 7 in the system and device group. The source provides U=6, V=2 and dK=3, so the maximum structural requirement is 6.…
Rhiannon neuron 8: system and device cost
This is the documented cost template instantiated for neuron 8 in the system and device group. The source provides U=3, V=4 and dK=2, so the maximum structural requirement is 4.…
Rhiannon neuron 9: system and device cost
This is the documented cost template instantiated for neuron 9 in the system and device group. The source provides U=5, V=3 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 10: system and device cost
This is the documented cost template instantiated for neuron 10 in the system and device group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement is 4.…
Rhiannon neuron 11: network and I/O cost
This is the documented cost template instantiated for neuron 11 in the network and I/O group. The source provides U=3, V=3 and dK=2, so the maximum structural requirement is 3.…
Rhiannon neuron 12: network and I/O cost
This is the documented cost template instantiated for neuron 12 in the network and I/O group. The source provides U=3, V=4 and dK=2, so the maximum structural requirement is 4.…
Rhiannon neuron 13: network and I/O cost
This is the documented cost template instantiated for neuron 13 in the network and I/O group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement is 4.…
Rhiannon neuron 14: network and I/O cost
This is the documented cost template instantiated for neuron 14 in the network and I/O group. The source provides U=5, V=5 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 15: network and I/O cost
This is the documented cost template instantiated for neuron 15 in the network and I/O group. The source provides U=3, V=4 and dK=3, so the maximum structural requirement is 4.…
Rhiannon neuron 16: network and I/O cost
This is the documented cost template instantiated for neuron 16 in the network and I/O group. The source provides U=4, V=4 and dK=2, so the maximum structural requirement is 4.…
Rhiannon neuron 17: network and I/O cost
This is the documented cost template instantiated for neuron 17 in the network and I/O group. The source provides U=3, V=5 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 18: network and I/O cost
This is the documented cost template instantiated for neuron 18 in the network and I/O group. The source provides U=3, V=3 and dK=2, so the maximum structural requirement is 3.…
Rhiannon neuron 19: network and I/O cost
This is the documented cost template instantiated for neuron 19 in the network and I/O group. The source provides U=4, V=3 and dK=3, so the maximum structural requirement is 4.…
Rhiannon neuron 20: network and I/O cost
This is the documented cost template instantiated for neuron 20 in the network and I/O group. The source provides U=5, V=4 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 21: network and I/O cost
This is the documented cost template instantiated for neuron 21 in the network and I/O group. The source provides U=4, V=4 and dK=2, so the maximum structural requirement is 4.…
Rhiannon neuron 22: network and I/O cost
This is the documented cost template instantiated for neuron 22 in the network and I/O group. The source provides U=3, V=4 and dK=2, so the maximum structural requirement is 4.…
Rhiannon neuron 23: network and I/O cost
This is the documented cost template instantiated for neuron 23 in the network and I/O group. The source provides U=4, V=5 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 24: network and I/O cost
This is the documented cost template instantiated for neuron 24 in the network and I/O group. The source provides U=3, V=3 and dK=3, so the maximum structural requirement is 3.…
Rhiannon neuron 25: network and I/O cost
This is the documented cost template instantiated for neuron 25 in the network and I/O group. The source provides U=4, V=3 and dK=2, so the maximum structural requirement is 4.…
Rhiannon neuron 26: website, UI and render cost
This is the documented cost template instantiated for neuron 26 in the website, UI and render group. The source provides U=4, V=5 and dK=3, so the maximum structural requirement…
Rhiannon neuron 27: website, UI and render cost
This is the documented cost template instantiated for neuron 27 in the website, UI and render group. The source provides U=4, V=6 and dK=3, so the maximum structural requirement…
Rhiannon neuron 28: website, UI and render cost
This is the documented cost template instantiated for neuron 28 in the website, UI and render group. The source provides U=5, V=5 and dK=4, so the maximum structural requirement…
Rhiannon neuron 29: website, UI and render cost
This is the documented cost template instantiated for neuron 29 in the website, UI and render group. The source provides U=3, V=5 and dK=3, so the maximum structural requirement…
Rhiannon neuron 30: website, UI and render cost
This is the documented cost template instantiated for neuron 30 in the website, UI and render group. The source provides U=4, V=5 and dK=4, so the maximum structural requirement…
Rhiannon neuron 31: website, UI and render cost
This is the documented cost template instantiated for neuron 31 in the website, UI and render group. The source provides U=3, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 32: website, UI and render cost
This is the documented cost template instantiated for neuron 32 in the website, UI and render group. The source provides U=5, V=4 and dK=4, so the maximum structural requirement…
Rhiannon neuron 33: website, UI and render cost
This is the documented cost template instantiated for neuron 33 in the website, UI and render group. The source provides U=4, V=4 and dK=2, so the maximum structural requirement…
Rhiannon neuron 34: website, UI and render cost
This is the documented cost template instantiated for neuron 34 in the website, UI and render group. The source provides U=3, V=3 and dK=2, so the maximum structural requirement…
Rhiannon neuron 35: website, UI and render cost
This is the documented cost template instantiated for neuron 35 in the website, UI and render group. The source provides U=5, V=6 and dK=4, so the maximum structural requirement…
Rhiannon neuron 36: website, UI and render cost
This is the documented cost template instantiated for neuron 36 in the website, UI and render group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 37: website, UI and render cost
This is the documented cost template instantiated for neuron 37 in the website, UI and render group. The source provides U=3, V=5 and dK=2, so the maximum structural requirement…
Rhiannon neuron 38: website, UI and render cost
This is the documented cost template instantiated for neuron 38 in the website, UI and render group. The source provides U=5, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 39: website, UI and render cost
This is the documented cost template instantiated for neuron 39 in the website, UI and render group. The source provides U=3, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 40: website, UI and render cost
This is the documented cost template instantiated for neuron 40 in the website, UI and render group. The source provides U=4, V=3 and dK=2, so the maximum structural requirement…
Rhiannon neuron 41: storage and filesystem cost
This is the documented cost template instantiated for neuron 41 in the storage and filesystem group. The source provides U=3, V=3 and dK=2, so the maximum structural requirement…
Rhiannon neuron 42: storage and filesystem cost
This is the documented cost template instantiated for neuron 42 in the storage and filesystem group. The source provides U=4, V=3 and dK=2, so the maximum structural requirement…
Rhiannon neuron 43: storage and filesystem cost
This is the documented cost template instantiated for neuron 43 in the storage and filesystem group. The source provides U=3, V=4 and dK=2, so the maximum structural requirement…
Rhiannon neuron 44: storage and filesystem cost
This is the documented cost template instantiated for neuron 44 in the storage and filesystem group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 45: storage and filesystem cost
This is the documented cost template instantiated for neuron 45 in the storage and filesystem group. The source provides U=5, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 46: storage and filesystem cost
This is the documented cost template instantiated for neuron 46 in the storage and filesystem group. The source provides U=4, V=3 and dK=3, so the maximum structural requirement…
Rhiannon neuron 47: storage and filesystem cost
This is the documented cost template instantiated for neuron 47 in the storage and filesystem group. The source provides U=3, V=5 and dK=3, so the maximum structural requirement…
Rhiannon neuron 48: storage and filesystem cost
This is the documented cost template instantiated for neuron 48 in the storage and filesystem group. The source provides U=4, V=4 and dK=2, so the maximum structural requirement…
Rhiannon neuron 49: storage and filesystem cost
This is the documented cost template instantiated for neuron 49 in the storage and filesystem group. The source provides U=5, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 50: storage and filesystem cost
This is the documented cost template instantiated for neuron 50 in the storage and filesystem group. The source provides U=3, V=3 and dK=2, so the maximum structural requirement…
Rhiannon neuron 51: calculation and optimization cost
This is the documented cost template instantiated for neuron 51 in the calculation and optimization group. The source provides U=5, V=5 and dK=4, so the maximum structural…
Rhiannon neuron 52: calculation and optimization cost
This is the documented cost template instantiated for neuron 52 in the calculation and optimization group. The source provides U=5, V=4 and dK=4, so the maximum structural…
Rhiannon neuron 53: calculation and optimization cost
This is the documented cost template instantiated for neuron 53 in the calculation and optimization group. The source provides U=4, V=5 and dK=4, so the maximum structural…
Rhiannon neuron 54: calculation and optimization cost
This is the documented cost template instantiated for neuron 54 in the calculation and optimization group. The source provides U=4, V=4 and dK=4, so the maximum structural…
Rhiannon neuron 55: calculation and optimization cost
This is the documented cost template instantiated for neuron 55 in the calculation and optimization group. The source provides U=6, V=5 and dK=4, so the maximum structural…
Rhiannon neuron 56: calculation and optimization cost
This is the documented cost template instantiated for neuron 56 in the calculation and optimization group. The source provides U=5, V=6 and dK=4, so the maximum structural…
Rhiannon neuron 57: calculation and optimization cost
This is the documented cost template instantiated for neuron 57 in the calculation and optimization group. The source provides U=6, V=6 and dK=5, so the maximum structural…
Rhiannon neuron 58: calculation and optimization cost
This is the documented cost template instantiated for neuron 58 in the calculation and optimization group. The source provides U=7, V=5 and dK=5, so the maximum structural…
Rhiannon neuron 59: calculation and optimization cost
This is the documented cost template instantiated for neuron 59 in the calculation and optimization group. The source provides U=6, V=6 and dK=4, so the maximum structural…
Rhiannon neuron 60: calculation and optimization cost
This is the documented cost template instantiated for neuron 60 in the calculation and optimization group. The source provides U=5, V=4 and dK=4, so the maximum structural…
Rhiannon neuron 61: calculation and optimization cost
This is the documented cost template instantiated for neuron 61 in the calculation and optimization group. The source provides U=4, V=5 and dK=3, so the maximum structural…
Rhiannon neuron 62: calculation and optimization cost
This is the documented cost template instantiated for neuron 62 in the calculation and optimization group. The source provides U=4, V=4 and dK=3, so the maximum structural…
Rhiannon neuron 63: calculation and optimization cost
This is the documented cost template instantiated for neuron 63 in the calculation and optimization group. The source provides U=3, V=4 and dK=3, so the maximum structural…
Rhiannon neuron 64: calculation and optimization cost
This is the documented cost template instantiated for neuron 64 in the calculation and optimization group. The source provides U=5, V=4 and dK=4, so the maximum structural…
Rhiannon neuron 65: calculation and optimization cost
This is the documented cost template instantiated for neuron 65 in the calculation and optimization group. The source provides U=6, V=5 and dK=4, so the maximum structural…
Rhiannon neuron 66: environment and pattern cost
This is the documented cost template instantiated for neuron 66 in the environment and pattern group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 67: environment and pattern cost
This is the documented cost template instantiated for neuron 67 in the environment and pattern group. The source provides U=4, V=5 and dK=3, so the maximum structural requirement…
Rhiannon neuron 68: environment and pattern cost
This is the documented cost template instantiated for neuron 68 in the environment and pattern group. The source provides U=3, V=5 and dK=3, so the maximum structural requirement…
Rhiannon neuron 69: environment and pattern cost
This is the documented cost template instantiated for neuron 69 in the environment and pattern group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 70: environment and pattern cost
This is the documented cost template instantiated for neuron 70 in the environment and pattern group. The source provides U=5, V=5 and dK=4, so the maximum structural requirement…
Rhiannon neuron 71: environment and pattern cost
This is the documented cost template instantiated for neuron 71 in the environment and pattern group. The source provides U=5, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 72: environment and pattern cost
This is the documented cost template instantiated for neuron 72 in the environment and pattern group. The source provides U=4, V=3 and dK=3, so the maximum structural requirement…
Rhiannon neuron 73: environment and pattern cost
This is the documented cost template instantiated for neuron 73 in the environment and pattern group. The source provides U=3, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 74: environment and pattern cost
This is the documented cost template instantiated for neuron 74 in the environment and pattern group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement…
Rhiannon neuron 75: environment and pattern cost
This is the documented cost template instantiated for neuron 75 in the environment and pattern group. The source provides U=5, V=3 and dK=3, so the maximum structural requirement…
Rhiannon neuron 76: internal math cost
This is the documented cost template instantiated for neuron 76 in the internal math group. The source provides U=3, V=3 and dK=3, so the maximum structural requirement is 3.…
Rhiannon neuron 77: internal math cost
This is the documented cost template instantiated for neuron 77 in the internal math group. The source provides U=4, V=4 and dK=3, so the maximum structural requirement is 4.…
Rhiannon neuron 78: internal math cost
This is the documented cost template instantiated for neuron 78 in the internal math group. The source provides U=5, V=4 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 79: internal math cost
This is the documented cost template instantiated for neuron 79 in the internal math group. The source provides U=4, V=5 and dK=3, so the maximum structural requirement is 5.…
Rhiannon neuron 80: internal math cost
This is the documented cost template instantiated for neuron 80 in the internal math group. The source provides U=3, V=4 and dK=2, so the maximum structural requirement is 4.…
Behavior–design loss for L_\ell
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
Combined model tuple
Packages DNA structure, gates, loop score, coherence driver, binary representation, seven layer losses, device loss and state/design/environment objects into one model tuple. A…
(S_\ell^\*,D_\ell^\*) relation
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
Behavior–design loss for L_{\ell,a}^\*
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
Cross-layer or cross-device message
Constructs a message from differences between an optimized local state/design and the receiving state/design, together with a change signal. The coupling function or weight…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
Layer-neuron joint state–design minimization
For each layer, the selected state and design minimize behavior–design mismatch, weighted operating cost, state regularization and design regularization. The same environment is…
Cross-layer or cross-device message
Constructs a message from differences between an optimized local state/design and the receiving state/design, together with a change signal. The coupling function or weight…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Cross-layer or cross-device message
Constructs a message from differences between an optimized local state/design and the receiving state/design, together with a change signal. The coupling function or weight…
Environment-aspect loss aggregation
Adds the layer’s per-aspect losses with λ weights. Every aspect can contribute to the same layer objective, avoiding an implicit assumption that each layer observes only one…
2. Full equation applied to each aspect and layer · (S_\ell^\*, D_\ell^\*)
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
Layer sensitivity to an environment aspect
Uses a partial derivative of the layer loss with respect to an environment aspect as a sensitivity message. The derivative describes local effect on the objective; it does not…
Layer sensitivity to an environment aspect
Uses a partial derivative of the layer loss with respect to an environment aspect as a sensitivity message. The derivative describes local effect on the objective; it does not…
1. Define each layer as a macro-neuron · (S_\ell^\*, D_\ell^\*)
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
Layer or device behavior mapping
Defines the mapping from local inputs to behavior, an optimized state, or its associated minimized cost. The source-specific function and environment determine the returned value.
Layer or device behavior mapping
Defines the mapping from local inputs to behavior, an optimized state, or its associated minimized cost. The source-specific function and environment determine the returned value.
Behavior–design loss for L_\ell^\*
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
2. Add neuron-style metrics to each layer · \Phi_\ell
The relation accumulates its integrand over the stated interval or closed loop. The result depends on the integrand, integration variable, limits and trajectory. In the archived…
Cost-based neuron coupling
Forms a coupling weight from a weighted combination of the two neuron costs; some historical versions also add a coherence-driver contribution. These variants are retained…
2. Add neuron-style metrics to each layer · \rho(x)
This expression selects a state or parameter setting that minimizes the displayed objective. Its terms describe what is penalized or fitted; the feasible domain, term weights and…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Source symbol definition
This line gives the source-local meaning of the displayed symbol. It is a definition used by surrounding equations; the same Greek letter can have a different meaning in another…
Restriction of the global objective
Reuses the global loss with its environment restricted or projected to the named layer or neuron. This keeps the objective structure consistent while changing the variables and…
State or environment definition
Defines the collection of state coordinates or environment aspects available to the model. The listed components establish the representation used by later losses and update…
C. Layers now become “partial observers” of the same global truth · L_\ell^\*
This is a composition of operators. The rightmost operator receives the input first, and successive operators transform its output. The overall behavior depends on every…
Restriction of the global objective
Reuses the global loss with its environment restricted or projected to the named layer or neuron. This keeps the objective structure consistent while changing the variables and…
Epona input collections: seven layers and 80 neurons
Epona receives two indexed collections of optimized state–design pairs: seven layer results and 80 neuron results. This is a definition of the proposed aggregation inputs, rather…
Behavior–design loss for L_\ell^\*(S',D')
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
Neuron-specific restriction of a layer loss
The loss for neuron i in layer ℓ is the layer loss evaluated with that neuron’s structural/input parameter Uᵢ and the environment slice Eℓ. This specialization is intended to…
Behavior–design loss for L_{\ell,i}^\*(S',D')
Measures mismatch between a desired design and modeled behavior, then adds operating cost and regularization. The subscripts restrict the same objective to a layer, device, neuron…
4. Chain rule view (symbolically) · L_{\ell,i}^{(k)}
This is a composition of operators. The rightmost operator receives the input first, and successive operators transform its output. The overall behavior depends on every…
Weighted objective across 80 Rhiannon neurons
Sums the 80 neuron-specific loss values with weights ω_i. The weights express the importance or contribution of each tool-neuron; the result is passed to the higher-level…
Epona orchestration objective
Aggregates the Rhiannon objective with device metrics and policy constraints. “Aggregate” is a placeholder for the orchestration rule; the expression identifies information passed…
Weighted objective across 80 Rhiannon neurons
Sums the 80 neuron-specific loss values with weights ω_i. The weights express the importance or contribution of each tool-neuron; the result is passed to the higher-level…
Epona aggregation of 80 neuron losses
Feeds the weighted sum of 80 neuron losses, device metrics and policy information into an outer aggregator Φ. Here Φ names an aggregation function; it must not be silently…
Local loss inherited from the global loss
This line states the intended relationship between a layer’s loss and the global objective. The right-hand side is descriptive text, so a numerical implementation still needs the…
Restriction of the global objective
Reuses the global loss with its environment restricted or projected to the named layer or neuron. This keeps the objective structure consistent while changing the variables and…
Device-conditioned global loss
Lᵢ is the shared objective evaluated on device i’s proposed state and design under its environment Eᵢ. The vertical bar records conditioning or context in this notation; it is not…
Optimization or reverse pathway
Describes choosing either an optimization operator or a reverse operator to transform an error quantity. The source leaves the pathway-selection condition and both operators to…
Maximum-score routing rule
Selects the neuron or family attaining the largest displayed score. In the Rhiannon C_i−dx variant, subtracting the same dx from every candidate does not change the winner. This…
Complex loop-phase representation
Places the real loop phase on the unit circle using a complex exponential. The magnitude is one, and the complex angle tracks the phase modulo 2π. This is a representation of a…
EPONA → RHIANNON EXTENDED SYSTEM (ASCII DIAGRAM) · ε
This relation uses a gradient: the vector of local changes in a scalar objective with respect to its variables. It supplies a local direction or stationarity condition; an…
ENVIRONMENT LAYERS (1–7) · \Lambda
The notes combine the named components with tensor-product or direct-sum-style notation. The expression records the proposed organization of the model. Concrete dimensions,…
5. Error gradient and its rate of change · \Lambda
The notes combine the named components with tensor-product or direct-sum-style notation. The expression records the proposed organization of the model. Concrete dimensions,…
1.4. Extended Rhiannon object (compact) · \boxed{ R_{\text{ext}}
The notes combine the named components with tensor-product or direct-sum-style notation. The expression records the proposed organization of the model. Concrete dimensions,…
Complex loop-phase representation
Places the real loop phase on the unit circle using a complex exponential. The magnitude is one, and the complex angle tracks the phase modulo 2π. This is a representation of a…
M2 device behavior mapping
The model maps performance-core, efficiency-core, GPU, neural-engine, memory-use and temperature variables into a modeled device response. The function f is a placeholder for this…
iPhone device behavior mapping
The behavior function g uses core and accelerator variables together with battery, temperature, radio and sensor state. It defines which device conditions the proposed optimizer…
Layer message added to receiver state
The receiver adds the message from layer ℓ to its existing state Yₘ. This is an additive state-update rule. Message and receiver must have compatible dimensions and scales, and…
Environment-aspect behavior–design loss
For one layer and one environment aspect, the loss combines design/behavior mismatch with weighted cost, state regularization and design regularization. This is the…
Layer loss by environment substitution
The layer objective is defined by substituting that layer’s environment Eℓ into the global loss. This is a restriction of a shared objective, intended to reuse the same logic…
Task-specific time-varying layer-neuron loss
The kth task uses the neuron’s loss function with a task-specific input and a layer environment that can vary over time. This separates the shared loss template from the…