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arxiv: 2606.31804 · v1 · pith:TIQXKC7Vnew · submitted 2026-06-30 · 💻 cs.LG · stat.ML

Relational and Sequential Conformal Inference for Energy Time Series over Graphs via Foundation Models

Keivan Faghih Niresi , Alice Cicirello , Olga Fink This is my paper

Pith reviewed 2026-07-01 06:46 UTC · model grok-4.3

classification 💻 cs.LG stat.ML
keywords conformal predictionspatial-temporal graph neural networksenergy demand forecastingfoundation modelsin-context learninguncertainty quantificationgraph-structured time series
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The pith

STOIC reformulates graph forecast residuals into tabular form so foundation models can calibrate conformal prediction intervals without retraining.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces STOIC, a method that first produces point forecasts for energy demand using spatial-temporal graph neural networks and then converts the resulting residuals into a tabular format. A tabular foundation model then performs zero-shot calibration of prediction intervals via in-context learning. This targets the need for statistically valid uncertainty estimates in interconnected energy systems where both time dynamics and node relations matter. A sympathetic reader would see value in obtaining coverage guarantees that respect graph structure while avoiding per-task model training.

Core claim

STOIC integrates an STGNN point forecaster with a tabular foundation model by reshaping spatial-temporal residuals into tabular data, enabling in-context calibration of conformal prediction intervals that capture both sequential and relational dependencies and outperform standard conformal baselines on five energy benchmarks.

What carries the argument

The STOIC pipeline, which converts spatial-temporal residuals from STGNN forecasts into a tabular representation for zero-shot in-context learning by a tabular foundation model.

If this is right

  • Prediction intervals maintain valid coverage while adapting to both temporal sequences and spatial relations across energy nodes.
  • No additional training of the foundation model is required after the initial STGNN point forecasts are obtained.
  • The same residual-to-tabular step applies to both synthetic simulations and real electricity or district-heating networks.
  • Operators obtain tighter, more reliable uncertainty bands than those from existing conformal prediction methods.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The tabular reformulation step could be tested on other graph time-series tasks such as traffic flow or sensor networks to check whether the same coverage gains appear.
  • If the foundation model truly extracts relational signals from the reshaped residuals, specialized graph-aware conformal wrappers might become unnecessary in many settings.
  • Scaling the tabular representation to very large graphs would require checking whether context-window limits begin to degrade calibration quality.

Load-bearing premise

Converting spatial-temporal residuals into a flat tabular layout lets a general-purpose foundation model recover the original sequential and relational structure without any task-specific fine-tuning.

What would settle it

Running STOIC on a held-out energy network where the resulting intervals show coverage below the nominal level while a standard conformal method maintains it.

Figures

Figures reproduced from arXiv: 2606.31804 by Alice Cicirello, Keivan Faghih Niresi, Olga Fink.

Figure 1
Figure 1. Figure 1: Overview of the proposed STOIC framework. The pipeline consists of four stages: (1) train [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Visual comparison of 90% PIs across conformal methods for the CKW Smart Meter dataset. The [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Visual comparison of 90% PIs for the EWZ District Heating dataset. The plots illustrate the [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Sensitivity of STOIC to calibration set size on the SCS dataset. [PITH_FULL_IMAGE:figures/full_fig_p021_4.png] view at source ↗
read the original abstract

Accurate energy demand forecasting is essential for the reliable operation and planning of modern sustainable energy systems. Spatial-temporal graph neural networks (STGNNs) have recently achieved strong performance in point forecasting by jointly modeling temporal dynamics and relational dependencies across interconnected energy nodes. However, in real-world energy systems, accurate point forecasts alone are insufficient, as operators also require reliable uncertainty estimates to support risk-aware decision-making, grid stability, and operational planning under uncertainty. Conformal prediction provides a principled and model-agnostic framework for uncertainty quantification with statistical coverage guarantees, making it particularly attractive for safety-critical energy applications. However, existing conformal prediction approaches often fail to fully capture the complex spatial-temporal structure of energy systems. To address these limitations, we propose STOIC (Spatial-Temporal Graph Conformal Prediction with In-Context Learning), a novel framework that integrates graph-based forecasting with the zero-shot calibration capabilities of tabular foundation models. STOIC first generates point forecasts using an STGNN and subsequently reformulates spatial-temporal residuals into a tabular representation suitable for in-context learning. Leveraging a tabular foundation model, STOIC calibrates prediction intervals without task-specific retraining, effectively capturing both sequential and relational dependencies. We evaluate STOIC on five diverse benchmarks, including synthetic simulations as well as real-world electricity and district heating networks. Across all datasets, STOIC consistently outperforms existing conformal prediction baselines, delivering more reliable and robust uncertainty estimates for complex graph-structured energy time series.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces STOIC, a framework that generates point forecasts via spatial-temporal graph neural networks (STGNNs) on energy networks, reformulates the resulting spatial-temporal residuals into a tabular format, and applies zero-shot conformal calibration using a tabular foundation model via in-context learning. It claims this captures both sequential and relational dependencies without task-specific retraining and yields superior uncertainty estimates compared to existing conformal baselines across five benchmarks (synthetic plus real electricity and district heating networks).

Significance. If the empirical claims and the tabular encoding step hold, the work would demonstrate a practical way to obtain distribution-free coverage guarantees for graph-structured time series by repurposing tabular foundation models, which could reduce the need for domain-specific conformal methods in energy applications.

major comments (2)
  1. [Abstract / Method] The abstract and method description provide no specification of the tabular encoding (e.g., whether adjacency information, node indices, edge features, or temporal window flattening appear as columns or rows). Without this, it is impossible to verify that relational graph structure is preserved rather than discarded, which directly undercuts the central claim that the foundation model captures both sequential and relational dependencies.
  2. [Abstract / Experiments] The abstract asserts consistent outperformance on all five datasets but supplies no quantitative metrics, baseline definitions, statistical significance tests, or coverage plots. This absence prevents evaluation of whether the reported gains are load-bearing or merely marginal.
minor comments (2)
  1. The title refers to 'Relational and Sequential Conformal Inference' while the abstract uses 'Spatial-Temporal Graph Conformal Prediction'; align terminology for clarity.
  2. [Method] Clarify whether the tabular foundation model receives any graph-derived features at all or operates purely on flattened residuals.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight opportunities to improve clarity in the abstract and method sections. We address each point below and will revise the manuscript to incorporate the suggested enhancements where feasible.

read point-by-point responses

  1. Referee: [Abstract / Method] The abstract and method description provide no specification of the tabular encoding (e.g., whether adjacency information, node indices, edge features, or temporal window flattening appear as columns or rows). Without this, it is impossible to verify that relational graph structure is preserved rather than discarded, which directly undercuts the central claim that the foundation model captures both sequential and relational dependencies.

    Authors: We agree that the current abstract and high-level method overview lack sufficient detail on the tabular encoding, which is necessary to substantiate how relational structure is retained. The full method section describes reformulating residuals into a tabular format with rows as node-time instances and columns incorporating node features, lagged residuals, and relational encodings derived from the graph adjacency (e.g., aggregated neighbor residuals as additional columns). However, this was not explicitly stated in the abstract or summarized at the start of the method. In the revision, we will expand both the abstract (within length constraints) and the method section to explicitly detail the encoding scheme, including how adjacency information is flattened into tabular columns to preserve relational dependencies for the foundation model's in-context learning. revision: yes

  2. Referee: [Abstract / Experiments] The abstract asserts consistent outperformance on all five datasets but supplies no quantitative metrics, baseline definitions, statistical significance tests, or coverage plots. This absence prevents evaluation of whether the reported gains are load-bearing or merely marginal.

    Authors: Abstracts are conventionally concise and qualitative, with quantitative details reserved for the experiments section (which includes tables of coverage rates, interval widths, and comparisons to baselines such as standard conformal prediction and graph-specific variants, along with coverage plots). That said, the referee's point is valid for strengthening the abstract's claims. In the revised version, we will add a sentence to the abstract summarizing key quantitative improvements (e.g., average coverage improvement and reduced interval width across datasets) and note that all gains are statistically significant per paired tests reported in the experiments. Full metrics, baseline definitions, and plots remain in Sections 4 and 5. revision: partial

Circularity Check

0 steps flagged

No circularity: empirical framework with no load-bearing derivation

full rationale

The paper presents STOIC as a methodological combination of STGNN point forecasts followed by tabular reformulation of residuals for zero-shot foundation-model calibration in conformal prediction. No equations, uniqueness theorems, fitted parameters renamed as predictions, or self-citation chains appear in the abstract or described approach. The central claim rests on empirical outperformance across five benchmarks rather than any algebraic reduction or self-referential definition. The tabular encoding step is presented as an engineering choice whose validity is tested experimentally, not derived from prior results by the same authors. This is a standard non-circular empirical proposal.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

No information is available from the abstract to populate free parameters, axioms, or invented entities.

pith-pipeline@v0.9.1-grok · 5797 in / 1068 out tokens · 40289 ms · 2026-07-01T06:46:11.675079+00:00 · methodology

discussion (0)

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Reference graph

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