AionFM

A Hybrid Continuous-Discrete Temporal Foundation Model for Probabilistic, Regime-Aware Time-Series Forecasting

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Overview

AionFM is a proposed time-series foundation model built around a central thesis: effective forecasting requires both numerical precision and behavioral abstraction. Rather than choosing between continuous value representations (which preserve accuracy but lack structural reasoning) and discrete tokenization (which enables transfer but loses precision), AionFM operates both simultaneously through a dual-stream decoder-only architecture.

The model processes temporal data through two synchronized representational streams:

• Continuous Value Patch Stream — segments normalized observations into subseries-level patches projected into dense embeddings, preserving full numerical resolution throughout the forecasting pipeline.
• Discrete Regime Token Stream — computes behavioral feature vectors from local temporal summaries and quantizes them into a learned vocabulary of residual regime tokens encoding trend, volatility, seasonality, discontinuities, missingness, and cross-variable structural states.

AionFM simultaneously serves as a point forecaster, probabilistic forecaster, scenario generator, regime detector, missing-data imputer, synthetic trajectory generator, and domain-adaptable forecasting engine — all within a single set of shared parameters.

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Key Contribution: The Residual Temporal Language

The defining innovation of AionFM is the Residual Temporal Language — a domain-independent behavioral vocabulary learned from normalized residuals rather than raw observations.

Instead of tokenizing raw values (which are inherently domain-specific), AionFM:

1. Estimates a local baseline b_t = f_baseline(x_{1:t}) capturing level, trend, and dominant seasonality
2. Computes a normalized residual e_t = (x_t - b_t) / (s_t + ε) that is scale-free and domain-independent
3. Summarizes residuals into behavioral descriptors (direction, curvature, volatility, shock magnitude, recovery rate, seasonality phase, cross-variable divergence, etc.)
4. Maps descriptors to discrete regime tokens via learned vector quantization

A regime token does not encode "the value is 17.2" — it encodes behavioral states such as "stable upward drift," "high-volatility expansion," "negative shock with partial recovery," or "mean-reverting residual compression."

This abstraction enables cross-domain transfer because concepts like "volatility expansion" or "shock recovery" recur across finance, energy, retail, traffic, climate, and operations data — even when raw magnitudes differ by orders of magnitude.

Behavioral Pattern Vocabulary

Pattern	Token Semantics	Description
Drift	Stable directional movement	Sustained positive/negative slope with low curvature
Reversal	Direction change	Sign change in local slope with high curvature
Shock	Abrupt deviation	Large standardized residual exceeding local volatility band
Recovery	Return toward baseline	Post-shock trajectory with exponential/linear decay
Compression	Volatility contraction	Declining local variance and narrowing range
Expansion	Volatility increase	Rising local variance and widening range
Saturation	Flattening near bound	Declining slope near a local max/min
Seasonality Peak/Trough	Cyclic extremum	Residual phase aligned with seasonal cycle at extremum
Regime Break	Structural discontinuity	Persistent change in statistical properties
Coupling	Cross-variable alignment	Increasing correlation among previously independent variables
Decoupling	Cross-variable divergence	Decreasing correlation among previously co-moving variables
Missing Burst	Observation gap cluster	Concentrated missing values (sensor failure, outage)
Anomalous Spike	Isolated extreme value	Single-observation deviation without sustained regime change

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Architecture

  ┌──────────────────────────────────────────────────────────────────┐
  │                     INPUT TIME SERIES DATA                      │
  │  (targets, covariates, metadata, calendar, missingness masks)   │
  └────────────────────────────┬─────────────────────────────────────┘
                               │
                               ▼
  ┌──────────────────────────────────────────────────────────────────┐
  │            [1] INPUT NORMALIZATION & PREPARATION                │
  │  Reversible scaling, frequency detection, calendar encoding,    │
  │  missingness masking, entity/domain descriptors                 │
  └────────────────────────────┬─────────────────────────────────────┘
                               │
                  ┌────────────┴────────────┐
                  │                         │
                  ▼                         ▼
  ┌────────────────────────┐  ┌────────────────────────────┐
  │ [2] CONTINUOUS VALUE   │  │ [3] DISCRETE REGIME        │
  │ PATCH ENCODER          │  │ TOKENIZER                  │
  │ Patch segmentation,    │  │ Behavioral features,       │
  │ linear projection,     │  │ vector quantization,       │
  │ numerical embedding    │  │ macro/meso/micro tokens    │
  └──────────┬─────────────┘  └──────────────┬─────────────┘
             │                               │
             └───────────┬───────────────────┘
                         │ Gated Fusion
                         ▼
  ┌──────────────────────────────────────────────────────────────────┐
  │         [4] DUAL-STREAM CAUSAL TEMPORAL BACKBONE                │
  │  Decoder-only Transformer with causal masking                   │
  │  Patch attention + cross-variable attention + memory attention  │
  │  Temporal position encoding + frequency-aware positions         │
  │  Compressed long-context memory                                 │
  └────────────────────────────┬─────────────────────────────────────┘
                               │
                               ▼
  ┌──────────────────────────────────────────────────────────────────┐
  │      [5] PROBABILISTIC FORECAST & SCENARIO DECODER              │
  │  Point forecast │ Quantile │ Distribution │ Regime forecast     │
  │  Scenario generation │ Imputation                               │
  │  Inverse normalization & constraint projection                  │
  └──────────────────────────────────────────────────────────────────┘

Subsystem Summary

#	Subsystem	Role
1	Input Normalization	Reversible scaling (z-score, MAD, Box-Cox, return, seasonal residual), frequency detection, calendar encoding, missingness masking
2	Continuous Value Patch Encoder	Segments sequences into patches of length P with stride S; projects via h^v_k = W_v · p_k + b_v; preserves full numerical resolution
3	Discrete Regime Tokenizer	Computes behavioral feature vectors; maps to discrete codes via vector quantization; hierarchical macro/meso/micro token structure
4	Dual-Stream Causal Backbone	Decoder-only Transformer with gated fusion (α_k, β_k, γ_k); supports patch, cross-variable, regime-token, memory, and covariate-aware attention
5	Probabilistic Forecast & Scenario Decoder	Six output heads: point, quantile, distribution, regime, scenario, imputation

Hierarchical Regime Tokens

Level	Scope	Example States	Change Frequency
Macro	Multi-patch window	"upward trend," "stationary oscillation," "structural break"	Infrequent
Meso	Single/few-patch	"volatility expansion," "mean-reverting residual," "post-shock recovery"	Moderate
Micro	Within single patch	"positive residual spike," "residual compression," "noise-dominated"	Frequent

Compressed Temporal Memory

Tier	Scope	Resolution	Purpose
Active Window	Recent W patches	Full attention	Maximum-resolution processing
Recent Memory	Medium-term past	Learned compression	Key statistical properties preserved
Long-Term Memory	Distant past	High compression	Historical baselines, prior regimes, seasonal patterns

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Training Framework

7-Component Composite Objective

L_total = λ₁·L_patch + λ₂·L_mask + λ₃·L_regime + λ₄·L_quantile + λ₅·L_rollout + λ₆·L_contrastive + λ₇·L_calibration

#	Loss Component	Purpose	Key Reference
1	Next-Patch Prediction	Autoregressive temporal prediction; grounds model in numerical accuracy	—
2	Masked Temporal Reconstruction	Robustness, imputation capability, noise tolerance (15–40% masking)	—
3	Regime-Token Likelihood	Trains residual temporal language via cross-entropy over regime vocabulary	—
4	Quantile Loss	Calibrated uncertainty at τ ∈ {0.01, 0.05, 0.10, 0.25, 0.50, 0.75, 0.90, 0.95, 0.99}	Koenker & Bassett, 1978
5	Rollout Consistency	Multi-step coherence; reduces compounding error in long-horizon forecasts	—
6	Cross-Scale Contrastive Alignment	Connects local movements to broader regime context; separates noise from structure	van den Oord et al., 2018
7	Calibration Loss	Ensures empirical interval coverage matches nominal levels	Gneiting & Raftery, 2007

Pretraining Data

Real data spanning: retail sales, energy demand, web traffic, industrial sensors, weather/climate, transportation, healthcare operations, financial markets, economic indicators, manufacturing telemetry, and supply-chain flows.

Synthetic data from a configurable trajectory generator:

x_t = T_t + S_t + C_t + E_t + R_t + ε_t
      ───   ───   ───   ───   ───   ───
     trend  seas  cycle event regime noise

Simulates: piecewise/exponential/logistic trends, multiple seasonalities, random shocks, step changes, mean reversion, heteroskedasticity, autoregressive noise, sparse demand, irregular sampling, sensor drift, and correlated multivariate systems — with latent regime labels retained for direct supervision.

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Probabilistic Forecasting & Scenario Generation

Six Output Heads

Head	Output	Use Case
Point Forecast	Deterministic mean/median	Planning, benchmarking
Quantile Forecast	Calibrated quantiles at multiple levels	Prediction intervals, safety stock
Distribution	Parametric distribution parameters (Gaussian, Student-t, negative binomial, mixture, zero-inflated)	Likelihood evaluation, sampling
Regime Forecast	Future behavioral token sequence	Interpretable trajectory characterization
Scenario Generation	Multiple coherent future trajectories	Risk simulation, stress testing, capacity planning
Imputation	Reconstructed missing historical values	Data quality, gap-filling

Two-Stage Scenario Generation

1. Stage 1 — Regime Path Sampling: Sample plausible future regime token sequences from the conditional distribution (e.g., "continued growth," "shock at step 3 with recovery," "volatility expansion with reversal")
2. Stage 2 — Value Decoding: Generate numerical forecasts conditioned on each sampled regime path

Scenario types: conservative · median · optimistic · tail-risk · stress · regime-specific

Example Output Schema

{
  "model_version": "AionFM-M v1.0",
  "forecast_origin": "2026-05-01T00:00:00Z",
  "forecast_horizon": 14,
  "frequency": "daily",
  "target": "store_42_sku_1087_units",
  "point_forecast": [142, 138, 155, 161, 170, 168, 152, 145, 140, 158, 164, 173, 171, 155],
  "quantiles": {
    "q05": [112, 107, 119, 124, 131, 128, 117, 111, 107, 121, 126, 133, 131, 119],
    "q50": [142, 138, 155, 161, 170, 168, 152, 145, 140, 158, 164, 173, 171, 155],
    "q95": [176, 172, 194, 202, 213, 210, 190, 181, 175, 198, 206, 217, 214, 194]
  },
  "scenario_paths": {
    "continued_growth": [145, 142, 160, 168, 178, 176, 160, 153, 148, 166, 172, 182, 180, 164],
    "shock_recovery":   [142, 138, 118, 105, 120, 135, 148, 145, 140, 158, 164, 173, 171, 155],
    "seasonal_decline":  [142, 135, 128, 122, 118, 115, 112, 110, 108, 112, 118, 125, 130, 135]
  },
  "regime_probabilities": {
    "stable_growth": 0.42,
    "seasonal_peak": 0.27,
    "shock_recovery": 0.18,
    "reversal": 0.13
  },
  "explanation": {
    "current_regime": "stable_upward_drift with seasonal_approach",
    "uncertainty_driver": "seasonal_phase_transition at horizon 7-9",
    "change_point_probability": 0.23
  }
}

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Model Family

Config	AionFM-S (Edge)	AionFM-M (Enterprise)	AionFM-L (High-Accuracy)	AionFM-X (Research)
Patch length P	16	32	64	64
Max context (patches)	128	512	1,024	2,048
Max forecast horizon	96	384	720	1,440
Max variables	16	128	512	2,048
Regime token vocab	256	1,024	4,096	8,192
Regime token levels	2 (macro/meso)	3 (macro/meso/micro)	3	3
Transformer depth	6	12	24	48
Attention width (d_model)	256	512	768	1,024
Memory compression	4:1	8:1	16:1	32:1
Quantile levels	5	9	9	19
Scenario count	10	50	100	500
Adapter size	32	64	128	256
Target use case	Edge, mobile, low-latency	General enterprise	High-accuracy batch	Research, high-value

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Domain Adaptation

AionFM supports four adaptation modes:

Mode	Data Required	What Updates	When to Use
Zero-shot	None	Nothing	Cold starts, rapid deployment, limited data
Few-shot calibration	50–500 obs	Scale, quantile coverage, seasonal phase, covariate effects	Limited domain data, fast adaptation
Adapter tuning	Domain dataset	Lightweight adapter modules (core frozen)	Domain-specific frequency, covariates, distributions
Full fine-tuning	Large domain dataset	All parameters	High-value, specialized applications

Covariate Support

• Known future: calendar, promotions, maintenance windows, holidays, price schedules, weather forecasts
• Historical: actual weather, prices, traffic, inventory, sensor readings, economic indicators
• Static metadata: store type, region, product category, sensor location, machine type
• Latent metadata: inferred entity descriptors from historical behavior

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Application Domains

Domain	Key Inputs	Key Outputs
Energy	Load history, temperature, calendar, weather forecasts, regional metadata	Peak demand intervals, extreme-load scenarios, regime detection, capacity-risk estimates
Retail	SKU sales, promotions, price changes, holidays, inventory constraints	Demand forecasts, safety stock recommendations, promotion uplift scenarios, hierarchical reconciliation
Industrial	Multi-sensor streams (temp, pressure, vibration), machine metadata	Predictive maintenance, drift detection, failure-regime probabilities, remaining useful life
Healthcare	ED arrivals, bed occupancy, procedure volume, staffing, calendar	Demand intervals, surge scenarios, capacity-risk flags, calendar-adjusted projections
Logistics	Shipment volume, congestion, delivery times, fleet utilization	Volume forecasts, delay-risk scenarios, disruption-sensitive capacity plans
Financial	Returns, volume, volatility, liquidity, cross-asset dependencies	Risk scenarios, volatility forecasts, regime probabilities, tail-risk estimates

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Advanced Capabilities

• Constraint-Aware Forecasting — projects raw forecasts into valid space respecting nonnegativity, capacity limits, conservation laws, market hours, monotonic cumulative quantities
• Hierarchical Forecasting — forecasts at multiple aggregation levels (Company → Region → Store → Category → SKU) with reconciliation consistency (Hyndman et al., 2011)
• Retrieval-Augmented Temporal Forecasting — retrieves historical windows with similar behavioral signatures to condition forecasts; improves rare-event forecasting, cold starts, and explainability
• Multivariate & Cross-Series Modeling — cross-variable attention, correlation-regime tokens, graph-aware adapters, metadata-conditioned attention; retrieval-based context selection for very large panels

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Evaluation Framework

Metrics

Category	Metrics
Point accuracy	MAE, RMSE, MAPE, sMAPE, MASE, WAPE
Probabilistic	Pinball loss, CRPS, prediction interval coverage & width, calibration error, weighted quantile loss
Scenario quality	Path coherence, distributional similarity, tail-event coverage, regime transition realism, multivariate dependency preservation
Robustness	Missing data degradation, corrupted observations, outliers, regime shifts, covariate dropout, scale shifts
Transfer	Zero-shot accuracy, few-shot adaptation speed, domain/frequency transfer, new-entity cold start
Interpretability	Regime-token stability, change-point alignment, regime explanation consistency, component attribution fidelity

Benchmarking Protocol

Five evaluation settings: zero-shot (unseen datasets) · fine-tuned (domain-specific) · few-shot (cold-start) · long-horizon (rollout stability) · stress (shocks, missing data, distribution shifts, rare regimes)

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Deployment Modes

Mode	Latency	Use Case
Batch forecasting	Minutes–hours	Daily/weekly/monthly planning, demand forecasting, capacity provisioning
Real-time inference	Sub-second (S) to sub-5s (M)	Monitoring, sensor anomaly detection, intraday demand, traffic
Interactive scenario engine	Seconds	Planning teams modify assumptions and receive updated forecasts in real time
Embedded API	Per-request	Integration into enterprise systems, dashboards, optimization engines

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Limitations

• Forecast quality depends on data quality; garbage in, garbage out
• Extreme regime shifts (geopolitical events, unprecedented policy changes) remain difficult for any historical model
• Long-horizon forecasts may become diffuse as uncertainty compounds
• Interpretability tokens are learned approximations, not ground-truth causal states
• Scenario generation requires careful validation — statistical plausibility ≠ operational plausibility
• Domain constraints must be explicitly encoded for high-stakes applications
• Calibration must be monitored post-deployment for distributional drift
• This is a conceptual specification — empirical validation across diverse benchmarks is needed

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Future Research Directions

1. Better Regime Vocabularies — hierarchical vector quantization, human-interpretable token labeling, domain-specific token adapters, causal regime discovery
2. Causal Forecasting — separating correlation from intervention; what-if questions (price changes, capacity reductions, promotion delays)
3. Agentic Planning Integration — AionFM as a component in planning systems that generate forecasts, simulate actions, compare scenarios, and optimize decisions
4. Physics-Aware Constraints — incorporating physical equations and conservation laws for industrial, climate, and engineering systems
5. Multimodal Temporal Modeling — integrating textual event descriptions, news, maintenance logs, images, geospatial data, and graph structures alongside the time-series backbone

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References

[1] Adams, R.P. and MacKay, D.J.C. (2007). Bayesian Online Changepoint Detection. arXiv preprint arXiv:0710.3742.

[2] Box, G.E.P., Jenkins, G.M., Reinsel, G.C., and Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control, 5th edition. John Wiley and Sons.

[3] Durbin, J. and Koopman, S.J. (2012). Time Series Analysis by State Space Methods, 2nd edition. Oxford University Press.

[4] Gneiting, T. and Raftery, A.E. (2007). Strictly Proper Scoring Rules, Prediction, and Estimation. Journal of the American Statistical Association, 102(477), 359–378.

[5] Hamilton, J.D. (1989). A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle. Econometrica, 57(2), 357–384.

[6] Hochreiter, S. and Schmidhuber, J. (1997). Long Short-Term Memory. Neural Computation, 9(8), 1735–1780.

[7] Hyndman, R.J. and Athanasopoulos, G. (2021). Forecasting: Principles and Practice, 3rd edition. OTexts, Melbourne, Australia.

[8] Hyndman, R.J., Ahmed, R.A., Athanasopoulos, G., and Shang, H.L. (2011). Optimal Combination Forecasts for Hierarchical Time Series. Computational Statistics and Data Analysis, 55(9), 2579–2589.

[9] Koenker, R. and Bassett, G. (1978). Regression Quantiles. Econometrica, 46(1), 33–50.

[10] van den Oord, A., Vinyals, O., and Kavukcuoglu, K. (2017). Neural Discrete Representation Learning. Advances in Neural Information Processing Systems, 30, 6306–6315.

[11] van den Oord, A., Li, Y., and Vinyals, O. (2018). Representation Learning with Contrastive Predictive Coding. arXiv preprint arXiv:1807.03748.

[12] Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A.N., Kaiser, L., and Polosukhin, I. (2017). Attention Is All You Need. Advances in Neural Information Processing Systems, 30, 5998–6008.

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License

This is an open technical specification released for community development. No empirical results are reported. The architecture and methods described are proposed designs intended to guide implementation and invite community contribution.

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license: other license_name: dosl-iie-1.0 license_link: LICENSE