ALETHEIA: Autonomous Loop for Experimental Theory and HEP Inference Across-data

ALETHEIA is an autonomous, self-completing framework that employs an active-learning loop to iteratively construct permutation-invariant physics foundation models (ManifoldInformer) for High Energy Physics, automatically identifying and incorporating new Standard Model Effective Field Theory operators based on residual analysis until the model achieves complete learning.

The Gist

Imagine you are trying to teach a robot to understand a complex, invisible landscape called "Physics." This landscape isn't made of mountains and rivers, but of invisible rules and forces that govern how particles behave. The paper introduces a tool called ALETHEIA (Greek for "Truth") that acts like a self-driving explorer for this landscape.

Here is how it works, broken down into simple concepts:

1. The Goal: Mapping an Invisible World

Scientists have a "map" of how the universe should work (the Standard Model), but they suspect there are hidden features they haven't found yet. These hidden features are like new ingredients in a recipe. The goal is to build a model that can learn exactly what these ingredients are and how they change the taste of the universe, using only data from particle collisions.

2. The Two Jobs: "Filling the Gaps" vs. "Adding New Rooms"

The paper argues that most previous methods tried to do two very different jobs at the same time, which confused the robot. ALETHEIA separates them into two distinct roles:

• Job A: The "Pin-Down" (Active Learning)
  Imagine you have a puzzle with a few missing pieces. You know where the missing pieces go, you just need to find the exact shape. This is what the "Active Learning" part does. It looks at the current model and asks, "If I test this specific scenario, will it help me pin down the numbers (coefficients) for the rules I already know?" It picks the most helpful test cases to make the model precise.
• Job B: The "Architect" (Physics Expansion)
  Now imagine you realize your puzzle is missing an entire section of the picture, not just a few pieces. You can't guess this by just looking at the gaps; you need to look at the shape of the error. This is the "Physics" part. ALETHEIA looks at what the model got wrong (the "residual"). If the error looks like a specific pattern, it knows a new "rule" (operator) needs to be added to the model. It doesn't guess; it reads the blueprint of the mistake.

3. The Engine: The "ManifoldInformer"

The brain of this system is a special neural network called the ManifoldInformer.

• Think of it as a translator that takes a chaotic pile of particle collision data (which has no order) and turns it into a clean, organized summary.
• It's "permutation-invariant," meaning it doesn't matter if the particles arrive in order A-B-C or C-B-A; the summary is the same.
• It learns to predict the "shape" of the physics rules so accurately that it can mathematically reconstruct the underlying theory with near-perfect precision (99.9% accuracy).

4. The Loop: How It Learns

ALETHEIA runs in a continuous cycle, like a self-correcting GPS:

1. Test: It picks a specific scenario to test (a "working point").
2. Check: It compares its prediction to the actual data.
3. Detect: It looks at the "fingerprint" of the mistake.
   • If the mistake is just a small wiggle in the numbers, the "Pin-Down" job kicks in to fix the numbers.
   • If the mistake reveals a whole new direction the model doesn't understand, the "Architect" job kicks in. It adds a new "room" to the model to handle that new direction.
4. Repeat: It keeps doing this until the model is so complete that adding more rules doesn't change anything.

5. The "Magic" Metric: The Singular Value

How does the system know when it's done? It uses a mathematical tool called Singular Value Decomposition (think of it as a "stress test" for the model).

• Imagine the model is a net catching fish. If there is a big hole in the net, a big fish (a large error) will slip through.
• The system measures the size of the biggest fish slipping through.
• When the system adds a new rule, that "big fish" suddenly shrinks to a tiny minnow.
• The paper shows that after four rounds of adding new rules, the "big fish" shrinks by a factor of 150. When the fish get so small they are smaller than the noise of the water, the system knows: "We have mapped the whole landscape. We are done."

6. The Result: A Self-Completing Map

The paper demonstrates this on a specific type of particle collision (Drell-Yan).

• The Hierarchy: It first learned the "big" rules (the four-fermion operators) which change the energy of the particles significantly.
• The Subtle Rules: Once those were mastered, it unlocked the "subtle" rules (vertex operators) which are like tiny tweaks to the angle of the particles.
• The Proof: The system knew it was finished not because a human told it to stop, but because adding the subtle rules didn't cause any new "big fish" to appear. The model was "span-complete"—it had captured the entire shape of the physics.

Summary

ALETHEIA is a self-driving scientist. It doesn't just guess what new physics might exist; it builds a model, checks where it fails, and automatically adds exactly the right new rules to fix those failures. It keeps doing this until the model is perfect, and it uses a digital "audit trail" (called Phoenix) to prove, in real-time, that it has learned the truth correctly and completely.

Key Takeaway: It separates the job of "fine-tuning numbers" from the job of "discovering new rules," allowing the AI to build a complete and accurate map of complex physics without human intervention.

Technical Summary

Technical Summary: ALETHEIA – Autonomous Loop for Experimental Theory and HEP Inference Across-data

Problem Statement
The paper addresses the challenge of automating the scientific cycle of model proposal, data generation, and model adjustment in High Energy Physics (HEP). Specifically, it targets the inference of physics foundation models from data representing unknown physics manifolds, such as those described by the Standard Model Effective Field Theory (SMEFT). A key difficulty in this domain is distinguishing between two conflated tasks in existing literature: completing a representation (pinning coefficients for a fixed set of operators) and expanding a representation (determining which new operators or degrees of freedom are missing). The paper argues that active learning is well-suited for the former but ill-suited for the latter when missing directions are weakly identified, necessitating a separation of these roles.

Methodology
The authors propose ALETHEIA, a self-completing tool that automates the learning of physics manifolds through an active-learning loop. The system is built around three core components:

1. The ManifoldInformer (Foundation Model):

   • A novel neural architecture designed for permutation-invariant, per-event representations.
   • It utilizes a shared per-event encoder ($\psi_\theta$) that processes kinematic vectors (e.g., $\log m_{\ell\ell}, \cos \theta^*$) using Deep Sets or Energy-Flow pooling.
   • A closed-form ridge head solves for the manifold coordinate $w_\theta(c)$ for a given working point $c$ (Wilson coefficients) using a linear system $(K^\top K + \alpha I)^{-1}K^\top V$.
   • The latent space is trained to recover the analytic morphing geometry of SMEFT, specifically the linear interference terms (tangents) and quadratic squared-amplitude terms (curvatures), validated via linear probes.

2. The Complete-Then-Expand Loop:
   The loop separates the tasks of acquisition and expansion:

   • Acquisition (AL Completes): Given a fixed operator content, an acquisition rule (specifically a residual-energy rule or EPIG) selects working points that maximize the "out-of-span" energy. This pins the model's coefficients using fewer samples than random sampling.
   • Expansion (Physics Expands): The system monitors a residual-SVD fingerprint. It computes the residual operator $R$ (the part of the log-likelihood ratio not captured by the current encoder). If the leading singular value $\sigma_1$ of $R$ exceeds a completion floor $\tau$, the system performs a $\psi$-extension: it appends the dominant residual direction $u_1$ to the encoder's feature space.
   • Operator Unlocking: The expansion of operator content is not driven by the acquisition rule but by SMEFT power counting. The loop completes the leading-order manifold (e.g., four-fermion operators) before unlocking subleading tiers (e.g., vertex operators).

3. Monitoring and Control:
   The entire process is instrumented using Arize-Phoenix spans. The loop monitors the trace of $\sigma_1$ and the ratio $\sigma_1/\sigma_2$.

   • "Learning Correctly": Verified when a $\psi$-extension causes an immediate, significant collapse in $\sigma_1$ (e.g., a factor of 31 reduction).
   • "Learned Completely": Verified when $\sigma_1$ falls below the noise floor and remains there even after unlocking new operator tiers, indicating the manifold is span-complete.

Key Results
The method was demonstrated on a neutral-current Drell-Yan process with dimension-six SMEFT operators (four four-fermion and four vertex operators) using an analytic oracle.

• Latent Recovery: The ManifoldInformer's latent space recovered the analytic morphing tangents with $R^2 = 0.99999$ and curvatures with $R^2 = 0.954$, confirming the encoder captures the exact analytic geometry.
• Residual Collapse: Starting with a mass-only encoder ($D_\psi=5$), the loop performed four extensions ($D_\psi: 5 \to 9$). The first extension collapsed the peak residual singular value from 5.36 to 0.173 (a factor of 31). Across all four extensions, $\sigma_1$ fell from 4.03 to 0.026 (a factor of $\sim 150$).
• Span-Completeness: After the four extensions, $\sigma_1$ remained below the completion floor ($\tau=0.30$). When the subleading vertex operators were unlocked, no further extensions were triggered, demonstrating that the basis constructed for the leading tier already spanned the angular structure of the subleading tier.
• Efficiency: The residual-energy acquisition arm reached the completion state no later than a random acquisition arm (median 5 cycles vs. 6), though the primary metric was correctness and completeness rather than raw sampling speed.

Significance and Claims
The paper claims that ALETHEIA provides a rigorous framework for self-completing physics foundation models. Its primary contributions are:

1. Separation of Roles: It decouples the task of "pinning coefficients" (handled by active learning) from "selecting new operators" (handled by residual structure and power counting). This prevents the acquisition rule from guessing the wrong physics directions.
2. Operational Signatures of Completeness: It introduces a method to read "learning correctly" and "learned completely" directly from the monitored trace ($\sigma_1$ collapse and stability), rather than relying on post-hoc analysis or assertions.
3. Generalizability: The architecture is presented as generalizable to any setting with an exact generative structure (like the SMEFT morphing polynomial) that allows for ordering model complexity.

The authors explicitly state modesty regarding sampling speedup on this specific analytic oracle, noting that the advantage of active learning over random sampling is expected to manifest primarily in scenarios with expensive simulators and higher operator dimensions. The core contribution is the completeness diagnostic and the separation of acquisition and expansion logic.