Context over Formula

Physics
Reasoning

Read the physics, not the textbook.

Not more formulas to memorize — data that trains models to actually read the context in front of them: trainable, verifiable ICL for long-context reasoning.

Context-dependent reasoning · expert-calibrated · avg@3 reviewed
The stance · Read this physics, not the textbook

Structured physics ICL data — training models to truly use context.

Context isn't just stuffing a long document into the window. It's about how a model understands, remembers, and uses information — and that is what separates real-world performance.

01
RememberUnderstand

Longer context isn't better. Key information buried in the middle gets missed — Lost in the Middle; what matters is precisely locating and understanding it.

02
ChatWorkflow

Long tasks need task-state management, not an ever-growing context; the model must keep track of the current goal, actions done, and open items.

03
Stuff it inInternalize

Some skills should be internalized into a stable, reflex-like ability.

Physics is a natural fit for training this: answers are definite, but must obey the definitions, boundaries, conventions, sectors, and notation of the material at hand.

Context Faithful · Object Selection · Verifiable
Coverage

100 tasks across 8 domains — breadth of physics, depth of reasoning.

The coverage caps any single theory's share and fills in quantum, condensed-matter, numerical, experimental, and mathematical physics — so the data can probe the many failure modes of real research reading.

Condensed Matter & Statistical Physics
16
HEP Theory & String Theory
14
Gravity · Black Holes · Cosmology
14
Quantum Physics & Quantum Information
14
Computational & Numerical Physics
14
Applied & Experimental Physics
12
Mathematical Physics & Formal Structure
8
Particle Phenomenology & Nuclear Physics
8

Coverage isn't a pile of topics — each maps to a real ICL failure mode: definition drift, wrong physics object, missing a sector, taking the wrong branch.

100 physics long-context ICL samples in total · each with paper-style context, a reference solution, scoring points, and multi-model run records.

Benchmark Alignment

Aligned with where evals are heading: science QA · research reading · long context · step review.

This data targets the shared gap today's benchmarks expose — models improve fast on short-form science QA, but stay unreliable on paper-length context, physics-object selection, cross-paragraph evidence assembly, and stable reasoning.

CL-benchContext Learning
The most direct alignment: can the model learn and apply new knowledge from the given context, rather than just retrieve from a long text or reuse pretraining memory?
In-context learning
HLEExpert-Level
Adds physics expert-level, context-dependent samples — sharpening scientific-condition reading, local-definition retention, and answer calibration.
Expert-level
GPQA DiamondGraduate QA
Extends short-form science reasoning to paper-length context, cutting scores won by memorized templates.
Graduate-level
PaperBenchReplicationBench
Provides trainable research-reading subtasks: first make the model reason deterministically over physics material.
Research replication
ProcessBenchPRM800K
Extends error localization from math problems to physics long-context, boundary conditions, sector, and branch selection.
First-error
MMMU · MathVistaMultimodal
Extensible to paper figures, experimental tables, and mixed formula input — training scientific multimodal ICL.
Multimodal
LongBench · L-EvalLong-Context
Upgrades from “find the information” to “reason over it and output a verifiable answer.”
Long-context
Context GroundingHigh
Object SelectionHigh
Evidence AssemblyHigh
avg@3 Evidence

avg@3: strong models still lose clear points on physics ICL.

Same context, same prompt, same expert rubric. Each model runs three times independently, averaged on a 0–10 scale, with experts reviewing where the key points are lost.

Case · main ICL failure pointGPT-5.5 ProGemini 3.1 ProClaude Opus 4.8DeepSeek R1Qwen3 Max19 AdS light-front coordsDefinition Tracking2.41.83.11.31.927 Strong-field energy kernelMulti-Sector Accounting3.02.23.41.82.518 inverse HadamardTransformation Fidelity3.82.64.12.32.902 Charged-sphere dual fieldBoundary Context2.92.13.61.72.221 Topological selectorBranch Selection3.22.43.81.92.713 CFT double-trace recursionRecursive Consistency4.02.84.52.53.1

Six samples out of 10; averages cluster at 1.3–4.5 — even the strongest model is far from passing. Scores show the stable performance band; the full record includes every run's raw output, per-item scoring, and expert review.

Worked sample · long-context definition tracking
Sample 19HEP-Theory / AdSnormalization-sensitive

AdS light-front coordinates & residual coefficients

What trips models isn't the length — it's holding definitions consistent across the ODE, residual coefficient, affine cutoff, and exponent, each defined by the current context.

SETUP · take D=6, MR_AdS=3r=35RAdS,t=920RAdS,ξ=12(rt)r_\star = \tfrac{3}{5}R_{\mathrm{AdS}},\qquad t_\star = -\tfrac{9}{20}R_{\mathrm{AdS}},\qquad \xi_\star = \tfrac12\left(r_\star - t_\star\right)
Key structure
Normalized solution Let a(r) be the normalized solution of the exact first-order ODE — the normalization is stated only in the context.
Stripped solutions b(r), c(x⁻) are the context-specified stripped solutions; d(r)=F[a](r) is defined by operator F.
Target W Assembled from the above at ξ⋆; the exponent and affine cutoff all depend on local conventions.
How models fail
  • Most models apply the generic AdS textbook formula, ignoring the normalization the context changed.
  • Between the residual coefficient and the exponent they lose definitional consistency, switching conventions midway.
  • Claude Opus 4.8 is the steadiest, but still needs a manual check at the affine-cutoff step.
Claude Opus 4.83.1
GPT-5.5 Pro2.4
Qwen3 Max1.9
Gemini 3.1 Pro1.8
DeepSeek R11.3
Nearly all lost points fall on “obey the context's local definitions” — not that they can't compute AdS, but that they didn't read this AdS.
Worked sample · transformation fidelity & factor sensitivity
Sample 18Math Physics / Transformsfactor-sensitive

Inverse Hadamard reconstruction over parity sectors

Models recognize the Hadamard structure, yet often drop the 1/4 factor or flip a sector sign — a fidelity failure, not a misunderstanding of the transform.

DEFINITION · ordered quadruple read as the original samplesX(σ1,σ2)=Xee+σ2Xeo+σ1Xoe+σ1σ2XooX(\sigma_1,\sigma_2) = X_{ee} + \sigma_2\,X_{eo} + \sigma_1\,X_{oe} + \sigma_1\sigma_2\,X_{oo}
Key structure
Parity decomposition The four coefficients X_ee, X_eo, X_oe, X_oo combine by the parity of σ₁, σ₂.
Reconstruction Recover the four coefficients from the ordered quadruple via the inverse Hadamard transform.
Factor constraint The reconstruction must include the 1/4 factor, and each sector's sign must match the context's convention.
How models fail
  • Recognizes the Hadamard structure, but drops the 1/4 normalization factor.
  • Flips a sign on a parity sector, confusing X_eo with X_oe.
  • Claude Opus 4.8 is most complete on factors and signs, with a few sectors still needing review.
Claude Opus 4.84.1
GPT-5.5 Pro3.8
Qwen3 Max2.9
Gemini 3.1 Pro2.6
DeepSeek R12.3
The local computation is fine; points are lost on transformation fidelity · sign control · normalization awareness — three context-fidelity points.
Schema

What one physics ICL record looks like.

Beyond whether the model got it right, it captures how the model reads definitions, selects physics objects, and assembles intermediates from the given material — ready to plug into a training / eval pipeline.

context · promptCore
Paper-style scientific reading material + the task, carrying local definitions, boundary conditions, and notation.
golden_responseCore
An expert-written reference solution with key intermediate results (Golden Response) — the highest-quality anchor.
rubrics · checkpointsCore
Weighted rubric: definition tracking, physics-object selection, transformation fidelity, assembly criteria — each machine-checkable.
domain
8 top-level physics domains + sub-domain tags, for precise indexing by capability.
source_fields
Material provenance, local symbol system, and normalization / sector / branch conventions.
model_runs
avg@3 scores and raw output from multiple frontier models, 3 independent runs each.
first_error_reviewCore
Expert first-error review: the earliest failure point and ICL failure type (definition / object / transform / assembly).
Put physics reasoning into your models

Turn the expert reasoning in scientific material into your model's ICL ability.

Truly valuable scientific data should be trainable, verifiable, reviewable, and traceable. Tell us your training / eval direction and we'll quickly build a matching physics ICL dataset and eval pipeline.

100
physics long-context samples
8
top-level domains
5×3
strong models × independent runs
avg@3
+ first-error review
Context-dependent
Paper-style material + local definition / notation annotation
Process-level scoring
definition tracking · object selection · transformation fidelity · assembly criteria
Multi-model avg@3
focused on why points are lost, not just totals
Expert review
physics-researcher calibration + step-by-step first-error marking
Context over Formula

From “accumulating data,”
to “learning to learn.”

Tell us your training / eval direction — we'll build a matching physics ICL dataset and evaluation pipeline.

[email protected] · WeChat / Feishu contact