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arxiv: 2606.00241 · v1 · pith:NRAMEU7Anew · submitted 2026-05-29 · 💻 cs.LG · cs.AI· stat.ML

InfoAtlas: A Foundation Model for Zero-Shot Statistical Dependence Estimate

Zhengyang Hu , Yanzhi Chen , Hanxiang Ren , Qunsong Zeng , Youyi Zheng , Adrian Weller , Kaibin Huang , Yanchao Yang This is my paper

Pith reviewed 2026-06-28 22:55 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ML
keywords mutual information estimationstatistical dependencefoundation modelzero-shot learningneural estimatorshigh-dimensional data
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The pith

InfoAtlas estimates mutual information between high-dimensional variables in a single forward pass after pretraining on synthetic data.

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

The paper introduces InfoAtlas to solve the problem that neural mutual information estimators usually demand separate iterative optimization for each new dataset, which is too slow for many applications. Instead, the model is pretrained once on large volumes of synthetic data containing varied dependence structures, then reads out estimates directly from any input dataset. A sympathetic reader would care because this turns a per-instance training task into an inference task, allowing the same model to work across different dimensions, sample sizes, and real-world data without retraining. The central goal is to show that such a pretrained approach can reach accuracy levels comparable to specialized estimators while running far faster.

Core claim

InfoAtlas is a foundation model-like architecture that, after pretraining on large-scale synthetic data with rich dependence patterns, directly infers mutual information values from input datasets in a single forward pass and thereby eliminates the per-dataset optimization step required by prior neural estimators.

What carries the argument

InfoAtlas architecture that reformulates mutual information estimation as a zero-shot inference task performed after pretraining on synthetic dependence structures.

If this is right

  • InfoAtlas matches state-of-the-art neural estimators in accuracy on the tested tasks.
  • InfoAtlas runs approximately 100 times faster than methods that require iterative optimization per dataset.
  • A single InfoAtlas model handles inputs with varying dimensions and sample sizes without modification.
  • InfoAtlas produces usable estimates on complex real-world data after synthetic pretraining alone.

Where Pith is reading between the lines

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

  • The same pretraining strategy might allow zero-shot estimation of other dependence measures such as conditional mutual information or distance correlation.
  • If the model truly generalizes, it could support continuous monitoring of dependencies in streaming or high-velocity data settings where retraining is impossible.
  • The approach opens the possibility of treating statistical dependence estimation as a reusable capability rather than a repeated training exercise.

Load-bearing premise

Pretraining on large-scale synthetic data with rich dependence patterns is sufficient for the model to accurately infer mutual information on unseen real-world datasets without per-dataset optimization or fine-tuning.

What would settle it

Run InfoAtlas and a per-dataset optimized neural estimator on the same collection of real-world datasets with independently verifiable dependence values; if InfoAtlas estimates deviate consistently while the optimized estimator matches the verifiable values, the zero-shot claim fails.

Figures

Figures reproduced from arXiv: 2606.00241 by Adrian Weller, Hanxiang Ren, Kaibin Huang, Qunsong Zeng, Yanchao Yang, Yanzhi Chen, Youyi Zheng, Zhengyang Hu.

Figure 1
Figure 1. Figure 1: Conceptual comparison: prior methods vs our method. Existing neural MI estimators (left) requires iterative gradient-based optimization to train a neural network for each new dataset. In contrast, we uses a pre-trained architecture to directly generate MI estimates in a single forward pass (right), eliminating per-dataset training and achieving speedup while maintaining comparable accuracy. • We propose an… view at source ↗
Figure 2
Figure 2. Figure 2: The InfoAtlas estimation pipeline. Step 1: We pad input dimensions with noise to ensure all variables share the same dimensionality, while allowing flexible sample sizes. Step 2: A dual-path hypernetwork H—with joint and marginal branches—extracts features in alignment with the D-V formulation (Eq. 2). Cross-attention integrates these features, and a parameter-generation MLP is then used to produce the cri… view at source ↗
Figure 3
Figure 3. Figure 3: Independence testing under three types of data correlations. Each curve depicts the area under the curve (AUC) of the receiver operating characteristic (ROC) with respect to sequence length n. Seven MI estimators are compared: InfoAtlas, InfoNet, KSG, MINE, MINDE, InfoNCE and KNIFE. InfoAtlas uses 5-sliced MI with 32 slices, while InfoNet adopts 1-sliced MI with 128 slices. 5. Experiments 5.1. Setups Slici… view at source ↗
Figure 4
Figure 4. Figure 4: Comparing different methods on 512-dimensional CLIP-encoded image-text representations across five noise levels. The light-colored areas indicate error bounds from 20 repeated experiments. (Left to right) InfoAtlas with 5-sliced MI using S = 25 random projections; InfoNet with 1-sliced MI using more projections (up to S = 128); MINE and MINDE estimating original MI via gradient-based optimization. InfoAtla… view at source ↗
Figure 5
Figure 5. Figure 5: Point trajectory mutual information for video object segmentation on PointOdyssey (Zheng et al., 2023). We estimate mutual information I(trajectory(P ∗ ), trajectory(P)) between a reference point trajectory P ∗ (marked by ⋆) and every other point trajectory P across video frames, yielding ∼ 4 × 103 MI terms per video. (a,b) The estimated MI is consistently higher for points belonging to the same object as … view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of correlation matrices generated by various methods. Existing approaches often yield small off-diagonal elements, whereas the low rank factor method adjusts their magnitude by tuning the rank factor m. • Eigenvalue decomposition, where C = QDQT , with D ∈ R d×d being a diagonal matrix with positive entries sampled from Uniform[0.1, 10.1), and Q ∈ R d×d being an orthogonal matrix obtained via… view at source ↗
Figure 7
Figure 7. Figure 7: Independence testing across three correlation types and dimensions (16, 64, 128) across seven methods. Each curve plots the ROC-AUC as a function of sequence length n. The figure demonstrates that performance degrades with increasing dimensionality. A.3. Additional experimental details of independent testing experiments Test cases details. Below are three different relationships between X and Y in high dim… view at source ↗
Figure 8
Figure 8. Figure 8: Full visualization results of InfoAtlas estimated motion data [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Full visualization results of InfoAtlas estimated motion data. A.5. Details of model training and architecture We provide the details of model architecture and training protocol as below. Neural architecture details of InfoAtlas For the attention module in InfoAtlas, we configure the dimensionality of the key and value to 1536. The Weight-Decoding MLP comprises seven layers, each of which has 8196 hidden u… view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of slice dimension k and slice number S on CLIP-generated data (original dimension 1024). Increasing k recovers more ambient dependence per slice, while increasing S reduces Monte-Carlo variance but does not remove the bias introduced by low-dimensional projection. Now consider the one-dimensional projections of x and y along directions u and v. It is straightforward to verify that the projecte… view at source ↗
read the original abstract

Measuring statistical dependency between high-dimensional random variables is a fundamental task in data science and machine learning. Neural mutual information (MI) estimators offer a promising avenue, but they typically require costly iterative optimization for each new dataset, making them impractical for real-time applications. We present InfoAtlas, a foundation model-like architecture that eliminates this bottleneck by directly inferring MI in a single forward pass. Pretrained on large-scale synthetic data with rich dependence patterns, InfoAtlas learns to identify diverse dependence structures and predict MI directly from the dataset. Comprehensive experiments demonstrate that InfoAtlas matches state-of-the-art neural estimators in accuracy while achieving $100\times$ speedup, can flexibly handle varying dimensions and sample sizes through a single unified model, and generalizes effectively to complex, real-world scenarios. By reformulating MI estimation as an inference task, InfoAtlas establishes a foundation for real-time dependency analysis.

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 / 0 minor

Summary. The paper introduces InfoAtlas, a foundation model pretrained on large-scale synthetic data with rich dependence patterns to perform zero-shot mutual information (MI) estimation via a single forward pass. It claims to match state-of-the-art neural MI estimators in accuracy, deliver 100× speedup, flexibly handle varying dimensions and sample sizes with one unified model, and generalize effectively to complex real-world scenarios, thereby reformulating MI estimation as an inference task.

Significance. If the central claims hold, the work would enable real-time dependency analysis without per-dataset optimization, which is a meaningful practical advance for applications requiring fast statistical dependence estimates. The unified model handling variable input sizes would be a notable strength if rigorously demonstrated.

major comments (2)
  1. [Abstract] The zero-shot generalization claim (abstract) is load-bearing for the core contribution yet rests on the unverified assumption that the synthetic pretraining distribution is sufficiently dense in the space of real joint distributions; no coverage metrics, domain-shift bounds, or ablations across synthetic generator families are provided to substantiate this.
  2. [Abstract] The reported matching of SOTA neural estimators on unseen real data (abstract) cannot be assessed for robustness without details on the evaluation protocol, including whether test real-world datasets were held out from any influence on model selection or synthetic data design.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on the zero-shot claims and evaluation details. We address each major comment below and will revise the manuscript to provide the requested substantiation and clarifications.

read point-by-point responses

  1. Referee: [Abstract] The zero-shot generalization claim (abstract) is load-bearing for the core contribution yet rests on the unverified assumption that the synthetic pretraining distribution is sufficiently dense in the space of real joint distributions; no coverage metrics, domain-shift bounds, or ablations across synthetic generator families are provided to substantiate this.

    Authors: We agree that explicit coverage metrics, domain-shift bounds, and ablations would strengthen the zero-shot generalization argument. While the manuscript's real-world experiments provide empirical evidence of effective generalization, we will add in revision: quantitative coverage analysis of dependence structures in the synthetic pretraining distribution, discussion of domain-shift considerations, and ablations using multiple synthetic generator families. These will appear in a new subsection on pretraining data characterization. revision: yes

  2. Referee: [Abstract] The reported matching of SOTA neural estimators on unseen real data (abstract) cannot be assessed for robustness without details on the evaluation protocol, including whether test real-world datasets were held out from any influence on model selection or synthetic data design.

    Authors: We will revise the manuscript to include a detailed evaluation protocol section. This will explicitly state that all real-world test datasets were held completely out of the synthetic data design process and model selection (which used only synthetic validation splits). The protocol description will cover data handling, splits, and selection criteria to enable full assessment of robustness. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is empirical pretraining plus forward-pass inference.

full rationale

The paper describes pretraining a transformer-style model on large-scale synthetic joint distributions to enable single-pass MI inference on new inputs. This is a standard supervised learning setup with no equations or claims that reduce the target MI estimate to a fitted parameter by construction, no load-bearing self-citations of uniqueness theorems, and no renaming of known results as novel derivations. Generalization claims rest on held-out real-world datasets rather than tautological reuse of training statistics. The central performance assertions are therefore falsifiable against external benchmarks and do not collapse into the pretraining procedure itself.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Populated from abstract claims only. Full paper would likely contain additional free parameters from the neural architecture and training losses.

free parameters (1)
  • neural network weights
    The model is pretrained on synthetic data, so its parameters are fitted to that distribution.
axioms (1)
  • domain assumption Synthetic datasets with rich dependence patterns are representative of real-world statistical dependencies
    The zero-shot generalization claim rests on this premise.

pith-pipeline@v0.9.1-grok · 5705 in / 1178 out tokens · 24322 ms · 2026-06-28T22:55:24.250414+00:00 · methodology

discussion (0)

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Reference graph

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