AIMech AI

Rate-adapting Poisson model

Model Families AIMech:RateAdaptingPoissonModel DRAFT
Aliases: RAP
A harmonium model family coupling unbounded visible Poisson counts to finite binomial hidden variables through bilinear interactions that shift conditional log rates and binomial logits.
Identity Notes & Concept Scope Scoped to Gehler, Holub and Welling's ICML2006 RAP construction with fixed finite integer binomial trial counts. This differs from a Gaussian-hidden count harmonium, a two-unbounded-Poisson-layer construction, categorical word-bin EFH and replicated-token Softmax. Baseline Poisson rates and hidden logits are conditional parameters, not generally marginal means or independent hidden priors. The latent count model is distinct from its CD fitting algorithm or a trained retrieval system. No normalized identity matched four candidates against all 442 pinned AIO IDs, labels and scoped synonyms or 444 preceding native IDs, names and aliases. Full-checkout searches included ignored and hidden files in both checkouts; five matching lines per checkout came from two unique prior discovery-ledger contents, and all matching excerpts were read. All 205 semantic label/synonym hits were byte-verified against prior readings. Twenty-nine annotated AIO nodes and outgoing edges comprise 28 unchanged prior readings and one newly read multimodal-deep-learning node. Thirty-nine contextual YAMLs comprise 34 unchanged prior readings and five fully read current records. Three candidates are curated; the unbounded-count DWH specialization remains deferred because the inspected joint is not normalizable with nonzero count couplings. Absence is bounded to this pinned snapshot and maintained corpus.

Claims & Grounded Evidence

3 Claims
Mechanism #compatible-count-conditionals
With baseline log rates a_i, hidden thresholds beta_j, interaction weights W_ij and finite integer trial counts M_j, visible counts conditioned on h are independent Poisson with rates exp(a_i+sum_j W_ij h_j). Hidden variables conditioned on x are independent Binomial(M_j,sigmoid(sum_i W_ij x_i-beta_j)). The joint retains visible factorial and hidden binomial base measures. Summing all visible counts first leaves a finite sum over bounded hidden configurations, proving a finite joint normalizer for finite parameters without truncating visible counts.
Mechanism #marginal-and-complement-symmetry
Marginalizing hidden units gives visible log mass sum_i(a_i x_i-log(x_i!))+sum_j M_j softplus(sum_i W_ij x_i-beta_j), up to a global constant. The hard threshold interpretation is an approximation to softplus, not exact zero influence below a threshold. Complementing a hidden count to M_j-h_j, reversing its weight column and threshold, and adding M_j W_ij to each visible log baseline preserves the normalized visible law. This discrete symmetry does not establish arbitrary orthogonal rotation invariance or full parameter identifiability.
Mechanism #conditional-moment-learning-and-features
Likelihood gradients contrast observed and equilibrium sufficient statistics. Conditional hidden expectations M_j sigmoid(W_j^T x-beta_j) replace sampled hidden counts in the displayed gradient statistics. The reported CD1 procedure draws hidden counts from each observed vector, reconstructs visible counts and uses short-chain negative expectations, introducing approximation bias. Retrieval uses cosine similarity of the linear projection W^T x, which is distinct from the nonlinear conditional-binomial mean and from exact joint likelihood scoring.

⚠️ Curated Limitations & Negative Results

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes
AIO Target Class Mapping Relation Mapping Rationale
AIO:Model
Model
broad_match The source-defined probabilistic model family is narrower than the pinned Model class.
AIO:RestrictedBoltzmannMachine
Restricted Boltzmann Machine
related_match Bipartite conditional-independence structure is shared with harmoniums, but the pinned RBM class does not identify this exact observation, hidden-support and parameter-sharing construction.
AIO:ProbabilisticTopicModel
Probabilistic Topic Model
related_match The construction learns latent topic features for count data; the pinned target is a probabilistic-topic task rather than this particular joint law.

Evidence Sources & Primary Literature

1 Source
Source ID Publication / Document Type / Access Reference & Checksum
method-source
Peter V. Gehler, Alex D. Holub, Max Welling
primary paper
full_text
sha256:413a1ce4396a…

Curation Provenance

Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-12T01:13:01Z
Updated: 2026-10-12T01:16:06Z
Source File: data/curated/RateAdaptingPoissonModel.yaml