AIMech AI

Pi-model

Algorithms AIMech:PiModel DRAFT
Aliases: Π-model
A semi-supervised classifier-training procedure that combines labeled cross-entropy with squared disagreement between two stochastic predictions of the same input from a shared-parameter network, propagating gradients through both predictions.
Identity Notes & Concept Scope The Greek Π notation is an identity alias for the Pi-model in Laine and Aila, not the generic AIO Model class. Its two contemporaneous stochastic predictions and two-sided gradient differ from temporal ensembling’s stored predictions, Mean Teacher’s weight-averaged stopped-gradient teacher, and SimSiam’s asymmetric stopped-gradient representation targets. This record describes a training algorithm, not a trained checkpoint or fixed network architecture. The inspected AIO SemiSupervisedLLM class specifically combines LLM pretraining with supervised fine-tuning; its related synonym self-training is not an exact identity for this method. AIO SelfsupervisedLearning excludes human-annotated labels, Distillation describes large-to-small compression, and RegularizationLayer is a layer: none supplies an equivalent class for this algorithm. No normalized identity match was found across all 442 pinned AIO labels/scoped synonyms and 230 preceding native IDs/names/aliases. Full-checkout fixed-string searches included ignored and hidden files in both worktree and main checkout; matches concern prior discovery leads and the Pi-model normalization regression. Ten exact AIO CLASS nodes, their scoped synonyms and outgoing edges, plus five neighboring native records were inspected. The corrected Unicode-aware normalizer preserves Π; the previous Pi-model/Model collision was a lexical defect, not semantic identity (review issue #58).

Claims & Grounded Evidence

1 Claim
Mechanism #method
For each minibatch B, run each input twice through the same classifier parameters with independently sampled input augmentation and network noise, producing C-class probability vectors z_i and z_tilde_i. Minimize −(1/|B|) sum over labeled i in B of log z_i[y_i], plus w(t)/(C|B|) times sum over all i in B of ||z_i−z_tilde_i||². Algorithm 1 normalizes the labeled sum by the complete minibatch size, not the number of labeled examples. Both prediction branches contribute gradients to the shared parameters. Start the consistency weight at zero and ramp it up; the reported Gaussian schedule is an experimental choice. There is no persistent per-example target or separately EMA-updated teacher in this core procedure.

⚠️ Curated Limitations & Negative Results

Artificial Intelligence Ontology (AIO) Grounding

Mapped AIO Classes
AIO Target Class Mapping Relation Mapping Rationale
AIO:Classification
Classification
related_match This procedure learns class predictions from labeled and unlabeled examples. The pinned AIO target describes a classification task under SupervisedLearning, not this semi-supervised training algorithm; this is an algorithm-to-task association, not equivalence or an is-a assertion.
AIO:MachineLearningTask
Machine Learning Task
related_match The algorithm specifies how to train a predictor from data. The AIO target is the general learning task; this association does not identify an algorithm with that task or assert an ontology subclass edge.

Evidence Sources & Primary Literature

2 Sources
Source ID Publication / Document Type / Access Reference & Checksum
method-source
Samuli Laine, Timo Aila
primary paper
full_text
sha256:d19ea2ecc468…
additional-1
Antti Tarvainen, Harri Valpola
primary paper
full_text
sha256:86c2ad510ea2…

Curation Provenance

Curator: Codex
Method: ai_assisted
Model: GPT-6
Created: 2026-10-11T10:12:04Z
Updated: 2026-10-11T10:12:04Z
Source File: data/curated/PiModel.yaml