econ-sae lifecycle walkthrough

(a) The substrate: agents as vectors in R^23

Each economic agent (household, firm, government, bank) is a point in R²³. The coordinates split into a conserved block (indices 0–13: stocks and per-period flows that obey exact accounting identities at every transaction) and a side block (indices 14–22: agent parameters that drive dynamics).

Coordinate layout

Three example agent rows (default economy, seed=0)

Column headers truncated to 6 chars; hover for full name. Cells shaded by block (conserved — blue; side — gray).

Household cohorts

Three cohorts split the 12 households into behavioral classes. Cohort drives MPC, productivity, reservation wage, sector preferences (CES weights over food / services / durables), and credit access (max debt-to-income).

Firm sectors

Three firm sectors with distinct production technology, pricing flexibility, and cyclicality.

Input-output network (Phase 3.4)

With io_network=True, each firm purchases intermediate goods from each sector before producing. IO_MATRIX[row][col] entries are the units of col's good needed per unit of row's output. A productivity shock to durables (the row that supplies all three columns) propagates through goods flows to every other sector.

Nine transaction kinds (vertices)

Every transaction is a double-entry vertex that updates two agents' vectors with opposite signs on the conserved block. The kinds:

wage purchase b2b_purchase tax transfer loan_origination loan_repayment interest deposit_interest dividend

All nine fire under stochastic shocks; b2b_purchase is conditional on the I-O network being enabled.

Conservation laws (the ground-truth axes)

For every period t and every trajectory:

• sum_i money[i] = M_initial (closed economy)
• sum_i (debt_liab - debt_asset)[i] = 0 (every loan two-sided)
• sum_i labor_supply[i] = sum_i labor_demand[i]
• sum_i goods_in_food[i] = sum_i goods_out_food[i] (and services, durables)

These six identities form a constructive ground truth: every trained model can be graded against them without post-hoc interpretation. The simulator preserves them to ~1e-13 (machine precision) across every trajectory in every experiment.

(b) Running the simulator: one trajectory of 40 periods

This is the baseline (no shocks, no Phase 3 features) trajectory of the default 12 HH + 3 firm + 1 gov + 1 bank economy. The simulator runs each period through a deterministic sequence of transaction steps (interest payments, production, wages, taxes, transfers, consumption, repayment, dividends, sticky-price update, expectations update). Every flow is a double-entry transaction; conservation holds at machine precision.

Transaction-kind occurrence

Conservation residuals (should all be ~1e-13)

These six identities are the constructive ground truth for the SAE benchmark. The simulator preserves them exactly under every combination of shocks and Phase 3 features.

(c) SAE: per-tier alignment and the multi-decoder recipe

The ground-truth feature vocabulary spans four tiers of difficulty (categorical, bucketed, conjunctive, regime). Each tier has a different recovery recipe; no single (substrate, SAE) pair recovers everything.

Experiments aggregated below:

• Phase 1 baseline
• Phase 1.5 scale
• Phase 1.6 attention
• Phase 1.7 temporal
• Phase 1.9 macro-feed v1
• Phase 2.0 macro-feed v2
• Phase 3.2 GatedSAE
• Phase 4.1 macro-feed v3
• Phase 4.2 full features
• Phase 5.1 regime-sup

Best-in-class per-tier recovery

categorical — 20/31 at AUC≥0.95, mean = 0.865

showing best 6 + worst 6 of 31 categorical features.

bucketed — 3/7 at AUC≥0.95, mean = 0.902

conjunctive — 6/8 at AUC≥0.95, mean = 0.980

regime — 4/6 at AUC≥0.95, mean = 0.976

(d) Polygram bridge

The polygram bridge encodes econ-sae's full 51-feature vocabulary as a polygram Dictionary using HEA_Rung2 with n_qubits = 6 (64 feature slots, no truncation). Per-feature beta = best-recovered AUC minus 0.5, so the "interpretability strength" of each feature appears as the scalar on the Dictionary slot.

Encoding-capacity diagnostics

Compression-style diagnostics mirroring sae-forge's ParetoFrontierRow.polygram_* fields. Headroom = capacity − n_features; positive means under-utilised substrate. utilisation = how much of the encoding's 2^n_qubits slot space is occupied by real features.

Per-tier beta spread

Interference sweep: rotate phase on a cross-tier pair

Target pair firm_sector_food / food_firm_low_inv, sweeping firm_sector_food.phi from 0 to 2π over 60 values.

Target-pair overlap range: 0.7704 to 1.0000 (mean 0.8870).

Cancellation experiments

For each pair, polygram searches for phase values that drive the inner product to zero. The "after" column is what phase tuning alone achieves under the HEA_Rung2 encoding's structural floor (~0.77 here, similar across pairs). Cross-tier and within-tier pairs converge to similar floors, which is informative about the encoding's geometry.

(e) Final benchmark scoreboard

Best-in-class per-tier results across all five experimental phases. The recipe column lists the (substrate, decoder) pair that achieved each tier's best mAUC: different tiers need different recipes. No single SAE / world-model combination recovers every tier; the multi-decoder recipe is the project's headline finding.

The recommended two-decoder recipe

1. Train an attention-enabled world model (cross-agent attention block + per-agent MLP head, optionally with cross-period GRU) on the multi-trajectory ensemble.
2. Train a per-agent SAE on its h1 activations to recover the categorical, bucketed, and conjunctive tiers.
3. Train a per-period macro-feed SAE on [macro + shock + GDP_window + impulse_flags + engineered ratios + mean-pooled h1] (z-scored) to recover the regime tier.
4. Optionally add a supervised regime head during world-model training to push the windowed-regime sub-features (expansion / contraction) toward AUC 0.95.

(f) Phase journey: how the ceiling moved at each step

Five lessons compound across the journey:

1. Substrate architecture sets the ceiling for per-agent features. Attention block was the single biggest unlock for conjunctive recovery.
2. Decoder granularity matters as much as substrate quality. Per-agent SAE for categorical / bucketed / conjunctive; per-period SAE for regime.
3. Input encoding matters as much as decoder choice. Impulse flags and engineered ratios each closed a different sub-tier of regime features.
4. Simulator dynamics drive what's recoverable. I-O cascades made one conjunctive feature cleanly recoverable for the first time.
5. Some labels need supervision. Threshold-on-ratio regime labels stalled at AUC 0.87 with unsupervised SAEs; supervised regime heads pushed them to 1.00 (for high_rate) and 0.92 (for expansion / contraction).