PaTAS Simulator — Parallel Trust Assessment System

Input Trust T_x

T_s — size feature

b d u

T_nr — # rooms feature

b d u

Adjust input trust opinions; b + d + u is renormalized as you drag.

Parameter Trust T_θ

T_θ₁ — weight on s (=10)

b d u

T_θ₂ — weight on n_r (=100)

b d u

Fusion Operator ⊕

Preset Scenarios

Apartment-rent perceptron with parallel Trust Nodes Network

y′ = θ₁ · s + θ₂ · n_r | T_y′ = (T_θ₁ ⊗ T_s) ⊕ (T_θ₂ ⊗ T_nr)

Step-by-step trace

Final output trust T_y′

—

Trust (belief)

—

Distrust

—

Uncertainty

—

Network Inputs x ∈ ℝ²

T_x₁

b d u

T_x₂

b d u

Parameter Trust Profile T_θ

All edges share one of these trust profiles; the architecture is 2 → 3 → 2.

IPTA Activation Mask ReLU

Pick which hidden neurons are activated for this specific inference. PaTAS' GenIPTA prunes the Trust Nodes Network to just the activated path.

h₁ h₂ h₃

Output Aggregation ⊕

Aggregates the two output-neuron trust opinions into a single consolidated network trust.

Trust Feedforward through a 2 → 3 → 2 network

T_{z^(l)_i} = ⋁_j ( T_{x^(l-1)_j} ⊗ T_{θ^(l)_ij} ) , T_x^(l+1) = T_f(T_z^(l))

Trust Feedforward & IPTA trace

Aggregated T_y

—

Trust

—

Distrust

—

Uncertainty

—

Algorithm 1 — ParameterTrustUpdate(g, T_y, ϵ)

Walks one mini-batch through the six steps that revise the trust of a single parameter T_{θ_i,j} given gradient evidence, label trust, input-feature trust, and learning-rate trust. Pick a neuron, edit the gradients, then step through.

Batch Label Trust {T_y}

Click any bar to expand sliders and edit (b, d, u) directly. T_{y_batch} = ⋁_{y∈y_batch} T_y (Line 4).

Target Neuron & Gradients N(i)

Edit gradients g_i,j per incoming edge:

ϵ 0.05

|g_i,j| < ϵ → weak (positive evidence r); ≥ ϵ → strong (negative evidence s).

Auxiliary Trust T_lr, T_x

T_lr — learning rate

b d u

T_{x_j} — input feature

b d u

Initial T_{θ_i,j} (before update) prior

current parameter trust

b d u

Step 0 / 6

Network view: target parameter and its evidence

T_{θ_i,j} ← Update(Revise(T_{θ_i,j}, T_{n_i‖Y}), T_lr, T_{x_j}, T_{y_batch})

Line 3–4 · Step 1 Aggregate label trust over the mini-batch

Cumulative fusion of all T_y in the batch:

T_{y_batch} = ⋁_{y∈y_batch} T_y

Result: —

—

Line 8 · Step 2 Gather gradients for the target neuron

g_i^(l) = { g_i,j^(l) | j ∈ N(i) }

Gradients for —: —

Line 10 · Step 3 NodeTrust — quantify gradient evidence

Count weak/strong gradients via ϵ, then apply Baseline-Prior Quantification (W = 2):

b = r/(W+r+s), d = s/(W+r+s), u = W/(W+r+s)

—

Result: — (T_{n_i|y_batch})

Line 12 · Step 4 DeduceTrust — combine conditionals over T_{y_batch}

T_{n_i|ȳ_batch} is set vacuous (0, 0, 1). Then apply the deduction operator ⊚:

T_{n_i‖Y_batch} = T_{y_batch} ⊚ ( T_{n_i|y_batch}, T_{n_i|ȳ_batch} )

Result: —

Line 14–15 · Step 5 Revise — fuse deduced neuron trust into T_θ

T_{θ_i,j} ← T_{θ_i,j} ⊖ T_{n_i‖Y_batch} (⊖ = cumulative fusion)

Before: —

After: —

Line 16–17 · Step 6 Update — multiply by (T_{x_j} ⊘ T_{y_batch})

Conservative division ⊘ takes min belief, max disbelief:

(b, d, u) = (min(b₁,b₂), max(d₁,d₂), 1−(b+d))

T_{x_j} ⊘ T_{y_batch} = —

T_{θ_i,j} ← T_{θ_i,j} ⊙ (T_{x_j} ⊘ T_{y_batch})

Final: —

—

Net change: ΔT_{θ_i,j}

—

Δ trust

—

Δ distrust

—

Δ uncertainty

—

Theorem 2 — Vacuous input ⇒ Vacuous output

If T_x = (0, 0, 1), then for any parameter trust profile T_θ, the PaTAS feedforward yields T_y′ = (0, 0, 1). The simulator empirically verifies this below. Re-roll random parameter trust to see it hold.

Theorem 3 — Symmetric inputs ⇒ Symmetric outputs

Given T_x = (b, d, u) and its symmetric counterpart T_x̄ = (d, b, u), the outputs satisfy b_y = d_ȳ, d_y = b_ȳ, u_y = u_ȳ. Also: full trust ⇒ d_y = 0, full distrust ⇒ b_y = 0.

Convergence Sanity (Trust mass under repeated Averaging fusion)

Cumulative fusion of n independent identical opinions concentrates trust by reducing uncertainty. This mirrors what PaTAS does across a batch when label-trust evidence accumulates. Try varying n and the per-source opinion.

batch n 10

Implementation notes: Trust discounting uses ω_θ ⊗ ω_x = (P·b_x, P·d_x, 1 − P(b_x+d_x)) with P = b_θ + a·u_θ. Cumulative fusion follows Jøsang's standard formulation; for the u=0 boundary an ε-stabilization is applied. The Parameter-Trust Update implements Algorithm 1 of the paper directly: Baseline-Prior Quantification (W=2) maps gradient counts to a binomial opinion, deduction ⊚ uses the binomial projection, revision ⊖ is realized as cumulative fusion (per Theorem 4 of the paper), and the auxiliary Update step composes binomial multiplication ⊙ with conservative division ⊘. T_lr enters via a final trust-discounting step that modulates the parameter trust by learning-rate reliability. Base rate a = 0.5 throughout. All numbers are recomputed live as inputs change.