---
title: 'AgML Collection: Graph ML & Domain Data Suite'
url: https://www.emergentmind.com/topics/agml-collection
type: topic
---

# AgML Collection: Graph ML & Domain Data Suite

AgML Collection is an aggregation of data sets and machine learning frameworks developed for mathematical, scientific, and domain-specific applications, with an emphasis on graph-based representations, formalized mathematics, and agriculture/environmental modeling. The collection extends across three principal areas: mathematical formalization using Agda libraries, environmental and agricultural data integration, and advanced graph ML methods for numerical analysis and indoor localization.

## 1. Constituent Data Sets and Libraries

### Agda MLFMF Libraries

The AgML Collection includes three Agda libraries from the MLFMF benchmark [2310.16005]:

- **Agda Standard Library:** 5,336 entries
- **Agda-unimath:** 50,120 entries
- **TypeTopology:** 3,650 entries

Each library is represented as a directed multigraph \(G=(V, E)\), where \(V\) encompasses definitions, datatypes, functions, lemmas, and postulates. Edge types encode declaration and body references, module structure, and definitional relations. Entry types are categorized as `:data`, `:constructor`, `:function`, `:record`, `:axiom`, `:primitive`, `:sort`, `:recursor`, `:abstract`.

- **Network statistics:**

  | Library            | |V|    | |E|      | avg deg | # modules |
  |--------------------|-------|----------|---------|-----------|
  | Agda Standard Lib  | 5,336 |  25,712  | 9.64    | 27        |
  | Agda-unimath       |50,120 | 482,310  |19.22    | 173       |
  | TypeTopology       | 3,650 |  29,810  |16.34    | 21        |

- **S-expression representation:** Each entry's computational graph is exported as a Lisp-style s-expression. For example:

  ```lisp
  (:entry
    (:name Agda.Builtin.Nat.id)
    (:type (Π (n : Nat) → Nat))
    (:data
      (:lambda n
        (:var n)))
  )
  ```
These formats are stored as `.lisp` (s-expressions), JSON (modules, entries), and CSV (edges).

### Agrimonia Environmental Data

Agrimonia [2210.10604] provides a harmonized dataset of daily air quality, meteorology, emissions, livestock, and land/soil use (2016–2021) for the Lombardy region. It is designed for direct ingestion into AgML workflows, supporting regression, classification, causal inference, and spatiotemporal modeling.

- **Core modalities:**
  - **Air Quality:** PM₁₀, PM₂.₅, NO₂, NOₓ, CO, SO₂, NH₃ (daily avg at 141 ground stations)
  - **Weather:** Temperature, humidity, wind speed/direction, precipitation, surface pressure, solar radiation (ERA5 reanalysis)
  - **Emissions:** NH₃, NOₓ, SO₂ (CAMS anthropogenic inventory, monthly 0.1° grid, interpolated to daily/station via PCHIP)
  - **Livestock:** Swine and bovine densities (biannual municipal, harmonized via PCHIP)
  - **Land/Soil:** High/low vegetation indices, CORINE land cover (44 categories), SIARL soil/cultivation (21 categories)

- **Data harmonization:** Inverse-distance weighting (IDW) used for gridding; temporal interpolation (PCHIP); air quality imputed by Kalman smoothing over state-space models.

- **Metadata:** All outputs are on a unified spatiotemporal grid (daily × station), SI units, ISO 8601 timestamps, WGS84 coordinates.

## 2. Graph- and ML-Based Methodologies

### Heterogeneous Network Analysis and Embedding

Each AgML library can be parsed as a graph. Edges are weighted by reference type:

- Unweighted adjacency: \(A_{ij} = 1\) if entry \(i\) refers to \(j\)
- Weighted: \(W_{ij}\) is the sum over edge types, e.g. \(w_{ij} = \alpha\,\#(\text{REF_DECL}(i, j)) + \beta\,\#(\text{REF_BODY}(i, j))\) (typically \(\alpha=\beta=1\)).

The s-expressions facilitate AST-level parsing for ML; streaming Lisp parsers (e.g., sexpdata) are recommended.

### GL-Coarsener: ML-Driven AMG Coarsening

The GL-Coarsener framework [2011.09994] exemplifies entity-level graph representation learning for efficient algebraic multi-grid (AMG) construction:

- **Graph definition:** From an SPD matrix \(A\), define graph \(G = (V, E, W)\) with edge weights \(w_{ij}=|A_{ij}|\).
- **Embedding:** node2vec, skip-gram construction; \(\mathbf{z}_i \in \mathbb{R}^{128}\), random walks with \(p=0.1, q=1\).
- **Clustering:** Mini-batch \(K\)-means, \(K \approx n/5\).
- **Transfer operators:** "Rough" prolongation matrix \(\hat{P}_{ij}\) assigns nodes to aggregates; optional smoothing; restriction \(R=P^T\).
- **Efficiency:** All stages parallelizable; AGML embedding overhead scales as
  \[
  T_{\mathrm{coarsen}}(P) \approx \frac{c_1|V| + c_2|E|}{P} + O(\log P)
  \]
- **Convergence:** Comparable iteration counts to Vaněk aggregation AMG; significant improvement over Beck classical coarsener.

### Attentional Graph Meta-Learning (AGML) for Localization

AGML [2504.04829] advances graph meta-learning for sparse fingerprint-based indoor localization:

- **Graph construction:** Nodes = fingerprints; adjacency \(A\) learned according to latent-space proximity and attention-derived pairwise scores.
- **Feature embedding:** Raw fingerprints \(x_i\) mapped via learned transforms to embedding \(l_i\).
- **Adjacency learning module (ALM):** Two-stage (coarse threshold \(T_h^0\); fine, attention-modulated threshold \(T_{ij}^A\)); differentiable adjacency via ReLU and tanh.
- **Message passing:** Multiple graph attention layers (MGALs) update node embeddings; output matches 2D coordinates on labeled data.
- **Meta-learning:** Model wrapped in MAML; tasks sampled from synthetic digital twin environments; adaptation via gradient-based inner and outer loops.
- **Data augmentation:** Unlabeled roaming measurements and synthetic digital twin fingerprints; feature-space distribution alignment between synthetic and real-world data.
- **Performance:** AGML yields RMSE reductions up to 2× versus AGNN/CNN/MLP baseline when labeled data are sparse. Ablation shows performance drop if ALM, meta-learning, or augmentation components are omitted.

## 3. Experimental Protocols, Metrics, and Baselines

### Link Prediction and Recommendation in Agda Libraries

All AgML libraries have associated link-prediction and recommendation baselines:

- **Splitting protocol:** 20% of function nodes held-out, 10% of proof-body edges retained.
- **Metrics:**
  - Accuracy@k: Fraction of queries with at least one correct reference in top-k.
  - Recall@k: Fraction of correct references recovered in top-k.
  - minRank: Mean minimal rank of true references.
- **Methods:** Dummy (max in-degree), BoW Jaccard, TFIDF, fastText BoW, analogies, node2vec + tree bagging.
- **Results:** node2vec+bagging achieves 96–98% acc@5; TFIDF and analogies yield 51–52%.

### Agrimonia Integration

Agrimonia is suited for ML tasks via AgML:

- Predictive regression (e.g. daily PM₂.₅ with Random Forest or neural nets)
- Spatial kriging or hierarchical modeling (Gaussian processes)
- Time-series forecasting (LSTM, TCN)
- Classification (threshold detection)
- Causal inference (difference-in-differences)
- Epidemiological modeling (exposure analytics)

All modalities are cross-compatible and statistical aggregation formulas adhere to documented standards (August–Roche–Magnus for RH, PCHIP for temporal interpolation).

## 4. Data Formats, Access, and Processing

- **Agda:** sexp/*.lisp (entries), modules.json, entries.json, edges.csv; recommended tools are streaming Lisp parsers and standard JSON/CSV libraries. High parentheses depth (O(100)) may require tailored parsing settings.
- **Agrimonia:** Agrimonia_Dataset.csv, MATLAB/R conversions, metadata files for full variable provenance.
- **GL-Coarsener:** Features extract directly from matrix coefficients; node2vec requires walk sampling parameters; K-means uses mini-batch size \(n/15\).
- **AGML:** Features and adjacency matrices learned with defined hyperparameters: α=10⁻⁴, β=10⁻³, ζ=10⁻²; λ₁=0.1, λ₂=0.01; hidden dims and attention parameters set per framework implementation.

## 5. Limitations and Prospects

- **Coverage:** AgML's formalized mathematics is currently restricted to Agda libraries; Agrimonia covers only EU rural scenes.
- **Generalizability:** Agricultural segmentation data are EU-centric, and depth estimation is monocular (no multispectral/LiDAR).
- **Evaluation:** High-level recommendation and human-aligned tasks require expert evaluation; subjective scoring (e.g., aesthetics via Q-Align) remains a challenge.
- **Parameter Tuning:** All major ML components require context-specific hyperparameter selection.
- **Extensions:** GL-Coarsener can be advanced to supervised graph neural network coarseners and energy-norm–optimized embeddings. AGML meta-learning may be adapted for continuous re-coarsening or time-sequenced inference.
- **Responsible AI:** Model fairness, bias, and explainability are open research axes.

## 6. Applications and Impact

AgML Collection underpins a wide array of ML and reasoning pipelines:

- **Mathematical formalization:** Accelerates automated theorem proving, type inference, and link recommendation in Agda/Lean.
- **Environmental modeling:** Integrates high-resolution air quality and agricultural emissions for causal and predictive analytics (Agrimonia).
- **Numerical solvers:** ML-driven coarsening yields scalable, parallelizable AMG cycles for PDE solvers (GL-Coarsener).
- **Indoor localization:** Fuses meta-learning and graph attention to deliver robust localization under data sparsity (AGML).

A plausible implication is that AgML Collection enables unified, graph-represented ML benchmarks for cross-domain learning, ranging from formal mathematics to environmental science and wireless localization, providing a foundation for both supervised and unsupervised graph-based ML research.

Source: https://www.emergentmind.com/topics/agml-collection