Sigmoid belief network
Architectures AIMech:SigmoidBeliefNetwork DRAFT
Aliases: SBN
A directed acyclic probabilistic network of binary variables whose forward conditional probabilities are logistic functions of weighted parent states and a bias.
Identity Notes & Concept Scope
This is the sigmoid conditional family defined by Neal, including equivalent zero/one and minus-one/plus-one encodings. It is not a symmetric Boltzmann machine, a sigmoid activation function alone, or an arbitrary neural network containing sigmoid units. Hidden variables are permitted but not required; the fully visible autoregressive specialization is not treated as an alias for the whole family. Wake-sleep and other inference or learning procedures do not define the model identity. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 343 preceding native IDs/names/aliases. Full-checkout fixed-string searches included ignored and hidden files in worktree and main, returning 7 and 7 lines respectively. All 6 unique matched line contents were inspected in full: RWS component-model distinctions, its saved review and the carried sigmoid/autoregressive discovery lead, not existing candidate records. Exact checkout counts and differences are retained in the ledger. Thirteen exact AIO CLASS nodes with scoped synonyms/comments and outgoing edges and six full native neighboring records were inspected. Absence is bounded to this snapshot and semantic neighborhood.
Claims & Grounded Evidence
1 Claim
Mechanism
#method
Choose a topological ordering of binary nodes and directed connections from earlier parents to later nodes. In zero/one encoding let a_i=b_i+sum_j w_ij s_j over parents; then P(s_i=1|parents)=sigmoid(a_i) and P(s_i=0|parents)=1-sigmoid(a_i). Multiplying these locally normalized factors gives the joint distribution without an undirected global partition function. Ancestral sampling visits nodes in topological order. For the equivalent minus-one/plus-one encoding, divide each non-bias weight by two and add half the original incoming-weight sum to the original bias. Marginalizing hidden variables still requires a sum over their configurations, and a Gibbs full conditional uses both the node factor and factors of its children, rather than merely its forward conditional. In the inspected maximum-likelihood learning derivation, gradients of a visible-data log likelihood are posterior expectations of joint log-probability scores; Gibbs sampling is one approximation for those expectations, not a mandatory part of the architecture.
⚠️ Curated Limitations & Negative Results
- Local normalization and exact ancestral draws do not make arbitrary posterior inference or hidden-variable marginal likelihood tractable. Clamping later observed nodes and using only forward conditionals does not generally sample the desired posterior.
- The two binary encodings require the stated weight and bias transformation; copying identical numerical parameters between them changes the distribution.
- The gradient identity requires appropriate posterior expectations. A finite Gibbs run need not provide exact equilibrium samples, rapid mixing or an unbiased implemented learning update.
- Acyclic probabilistic dependence is not by itself evidence for intervention-level causal interpretation, and the learned units need not represent human-interpretable propositions.
- No global training optimum, biological implementation or benchmark ranking is asserted. Only the declared portions of the 43-page source were inspected.
Artificial Intelligence Ontology (AIO) Grounding
Mapped AIO Classes
| AIO Target Class | Mapping Relation | Mapping Rationale |
|---|---|---|
AIO:BayesianNetwork
Bayesian Network
|
broad_match | The pinned AIO target is broader: a directed acyclic probabilistic conditional-dependence network. This native family additionally requires binary nodes and logistic weighted-parent forward conditionals. The mapping is from the narrower native architecture to the broader AIO class, not an equivalence or an assertion of causal semantics. |
Evidence Sources & Primary Literature
1 Source| Source ID | Publication / Document | Type / Access | Reference & Checksum |
|---|---|---|---|
method-source
|
Radford M. Neal
|
primary paper
full_text
|
ID: doi:10.1016/0004-3702(92)90065-6
sha256:4e4f40a92dce…
|
Curation Provenance
Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T17:27:17Z
Updated: 2026-10-11T17:27:17Z
Source File:
data/curated/SigmoidBeliefNetwork.yaml