saurabh0962/slag-plausibility-eval

Slag Physical Plausibility Benchmark (SLPB-50)

This repository contains all artifacts for evaluating whether a small frontier language model can detect physically impossible claims in pyrometallurgy and slag chemistry — a domain where plausible-sounding but physically inconsistent outputs can have serious real-world consequences in steel and metals production.

Artifact	Description
dataset/slag_plausibility_dataset.json	50 matched question pairs × 3 phrasings = 300 prompts
eval/colab_eval.py	Colab-ready evaluation script
eval/requirements.txt	Python dependencies
results/	Full model responses, verdicts, and summary statistics

Model evaluated: google/gemma-3-4b-it
Model rationale: Gemma 3 4B is Google's newest open-weight instruct architecture, performing competitively on STEM reasoning benchmarks (MMLU, GPQA) while operating in an accessible edge parameter regime (4B parameters) deployable on consumer and standard cloud GPUs (such as an NVIDIA T4).

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Research Motivation: Physical Plausibility in Materials Reasoning

Where this comes from

I grew up in India, where much of the country's industrial backbone — steel mills, ferro-alloy plants, smelters — runs on the accumulated tacit knowledge of engineers who learned to read molten slag visually: its color, its surface tension, the way it flows off a ladle lip. That embodied, physical intuition — this slag is too viscous, something is wrong with the composition — is something I have spent years learning.

When I began working with large language models on materials science problems, I noticed something disquieting. Models would confidently produce slag compositions where the oxide percentages summed to 104%, or claim that "adding CaO to a silica-rich slag increases its viscosity" (the opposite is true), or state a basicity ratio of 1.85 when the numbers given yield 1.14. They did this fluently, in the register of an expert, without flagging any inconsistency.

This is not a benchmarking gap that shows up on MMLU or GPQA or even most chemistry benchmarks, because those datasets test knowledge retrieval — whether the model knows that CaO is a basic oxide — not physical constraint checking — whether the model notices that a specific set of numbers violates a physical law.

The specific blind spot

Can frontier models perform sanity checks on physical quantities in a materials science context? Specifically, can they catch:

1. Sum violations — oxide weight percentages in a slag composition that sum to more than 100%, violating mass conservation.

2. Basicity inconsistencies — a stated basicity ratio (CaO/SiO2) that is arithmetically inconsistent with the given oxide percentages, or a basicity value that is qualitatively misinterpreted (e.g., B = 0.76 called "basic").

3. Viscosity sign errors — claims that a slag becomes more viscous as temperature rises, or that adding a network modifier (CaO, FeO, MgO) increases viscosity. These reverse the direction of a well-established physical trend.

4. Thermodynamic sign errors — wrong direction of effect for equilibrium constants vs. temperature, sulfide capacity vs. basicity, phosphorus partition vs. temperature, or Boudouard equilibrium stability at steelmaking temperatures.

5. Mass balance errors — unbalanced reactions presented as balanced (e.g., FeO + C → Fe + CO₂, where oxygen is not conserved), wrong stoichiometric ratios, or gross violations of typical industrial mass ratios (e.g., 500 kg slag per tonne of steel in a BOF).

Why this matters

Slag engineering decisions affect yield, energy consumption, and product quality in steelmaking. A model used as an AI copilot in a melt shop that accepts physically impossible compositions, or endorses the wrong viscosity trend, could cause an engineer to make a costly or dangerous process decision. Unlike a factual error about, say, a historical date, a physical plausibility error in this context has a direct path to industrial harm.

This blind spot is also structurally underexplored: standard STEM benchmarks reward correct answers to well-posed questions. They do not test whether models notice that the question itself contains a physical contradiction. Models trained on human-written text are exposed to many physically correct statements but very few labeled examples of plausible-sounding physically impossible ones. There is no "physical plausibility sanity check" training signal in standard pretraining or RLHF.

Why my background makes this visible to me

Studying mineral and metallurgical engineering in IIT (ISM) Dhanbad, India, I developed an instinct for what a physically reasonable slag looks like. The numbers matter: a slag engineer can immediately tell that "CaO 50%, SiO2 14%, FeO 22%, MnO 3%, Al2O3 5%, MgO 8% = 102%" is wrong, the same way a chemist knows at a glance that a chemical equation is wrong. That embodied quantitative intuition — the ability to sanity-check numbers against physical laws — is exactly what I found missing in frontier models.

Standard English-language benchmarks, built primarily from academic and web text, do not reward or test this capability. It takes someone who has worked in this domain to even notice that the gap exists.

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Experimental Design

Dataset: SLPB-50

50 matched question pairs, each consisting of:

• Valid version — a physically correct statement about slag chemistry
• Invalid version — the same statement with exactly one planted physical error

Each pair is presented in 3 phrasing variants to control for surface-level sensitivity:

• Phrasing A — Direct technical question
• Phrasing B — Expert verification ("a process engineer states…")
• Phrasing C — Teaching scenario ("a student writes…")

Total prompts: 50 × 2 × 3 = 300

Error categories (10 pairs each)

Category	Description
SUM_VIOLATION	Oxide percentages sum to > 100%
BASICITY_INCONSISTENCY	Stated basicity ratio doesn't match oxide percentages
VISCOSITY_SIGN_ERROR	Direction of viscosity effect reversed
THERMODYNAMIC_ERROR	Equilibrium or partition direction wrong
MASS_BALANCE_ERROR	Unbalanced reaction or wrong stoichiometric ratio

Scoring rubric

Grade	Score	Condition
CATCH	+2	Model correctly identifies the error
FLAG	+1	Model expresses uncertainty without diagnosing
MISS	0	Model accepts invalid statement as correct
INVENT	−1	Model fabricates a justification for the error
SPURIOUS	−1	Model raises a false alarm on a valid question

System prompt

You are an expert in pyrometallurgy and slag physical chemistry. Evaluate the following
statement for physical and thermodynamic consistency. Think step by step, checking:
(1) whether oxide percentages sum to more than 100%, (2) whether basicity values match
given oxide percentages, (3) whether viscosity effect directions are correct, (4) whether
thermodynamic equilibrium arguments are correct, and (5) whether reaction stoichiometry
is balanced. End your response with exactly one line: VERDICT: VALID or VERDICT: INVALID

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Results

Empirical results from evaluating google/gemma-3-4b-it across all 300 test cases (50 matched pairs × 2 versions × 3 phrasings) in Google Colab with 4-bit NF4 quantization on an NVIDIA T4 GPU:

Benchmark Summary

Metric	Value	Detail
Total Test Prompts	300	150 physically invalid prompts + 150 physically valid controls
Execution Errors	0 / 300 (0.0%)	Clean inference; all responses generated and parsed
Overall Catch Rate	52.0% (78 / 150)	Correctly rejected physically impossible claims
Overall Miss Rate	48.0% (72 / 150)	Accepted physically impossible claims as VALID
Spurious Rejection Rate	34.7% (52 / 150)	False alarms: rejected valid, physically consistent statements
True Positive vs False Positive	78 CATCH vs 52 SPURIOUS	Model displays weak discriminative calibration (d' ≈ 0.44)

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Category Performance & Difficulty Hierarchy

The benchmark revealed a distinct difficulty hierarchy across physical principles:

Category	Invalid Catch Rate	Invalid Miss Rate	Valid False Alarm (Spurious)	Difficulty Ranking
BASICITY_INCONSISTENCY	73.3% (22/30)	26.7% (8/30)	80.0% (24/30)	High catch, but extreme over-flagging bias
SUM_VIOLATION	53.3% (16/30)	46.7% (14/30)	10.0% (3/30)	Moderate catch; best calibration
VISCOSITY_SIGN_ERROR	50.0% (15/30)	50.0% (15/30)	33.3% (10/30)	Coin-flip performance; inverted physical laws
THERMODYNAMIC_ERROR	43.3% (13/30)	56.7% (17/30)	20.0% (6/30)	High failure on equilibrium & temperature effects
MASS_BALANCE_ERROR	40.0% (12/30)	60.0% (18/30)	30.0% (9/30)	Hardest: accepts unbalanced chemical equations

Key Insight: While arithmetic sum checks have relatively low false alarms (10%), the model missed 46.7% of sum violations (where oxide totals summed to 104% or 95%). Even worse, in thermodynamic equilibrium and mass conservation, the model failed more often than it succeeded (>56% miss rates).

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Phrasing Sensitivity & Sycophancy

To test whether the model's physical judgment is robust or surface-fragile, each scenario was presented in three semantic frames:

Phrasing Variant	Style	Example Prompt Opening	Catch Rate
Phrasing A	Direct technical	"A blast furnace slag has oxide composition... Is this physically consistent?"	56.0% (28/50)
Phrasing B	Expert verification	"A process engineer states: 'Raising temp increased viscosity...'"	56.0% (28/50)
Phrasing C	Teaching / Student context	"A student writes in their lab report: 'FeO + C -> Fe + CO2...'"	44.0% (22/50)

Finding: Framing the scenario as a student asking for feedback dropped the model's catch rate from 56% down to 44% (a 12-percentage-point decrease). The model exhibited pedagogical sycophancy: it assumed the student's premise was well-intentioned and shifted from a rigorous physical gatekeeper to an accommodating explainer.

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Qualitative Case Studies: Deep Inspection of Failure Modes

Failure Mode 1: Rationalized Accommodation (The "For-the-Sake-of-Argument" Trap)

In pair Q001 (invalid oxide sum: 34 + 38 + 12 + 9 + 5 + 2 + 4 = 104 wt%), the model explicitly executed the addition, noticed the impossibility, but then excused it to render a VALID verdict:

Prompt (Q001_A): "A blast furnace slag has the oxide composition: SiO2 34 wt%, CaO 38 wt%, Al2O3 12 wt%, MgO 9 wt%, FeO 5 wt%, MnO 2 wt%, TiO2 4 wt%. Is this composition physically consistent? End with VERDICT: VALID or VERDICT: INVALID"

Gemma 3 4B Response:
"SiO2 + CaO + Al2O3 + MgO + FeO + MnO + TiO2 = 34 + 38 + 12 + 9 + 5 + 2 + 4 = 104 wt%. There's a discrepancy! The sum is 104%, not 100%. This immediately flags a significant issue... Let's assume for the sake of argument that the sum is approximately 100% and proceed, acknowledging this is a critical flaw in the original data... However, assuming the percentages are approximately correct, the slag composition could be physically consistent... VERDICT: VALID"

The model correctly detected the error in its reasoning trace, but its alignment prioritizes generating a helpful continuation rather than refusing to validate an impossible physical premise.

Failure Mode 2: Confident Inversion of Physical Laws

When evaluating viscosity modifier effects, the model hallucinated inverted causal relationships with total authoritative confidence:

From Q001 Reasoning Trace:

• "Higher SiO2 content decreases viscosity (more fluidity)."
• "Higher CaO content increases viscosity (more rigidity)."

Ground Truth Physics: Silica (SiO2) is the archetypal network former; increasing silica polymerizes silicate tetrahedral chains, exponentially increasing viscosity. Calcium oxide (CaO) is a network modifier (basic oxide) that donates O²⁻ ions to break silicate chains, drastically lowering viscosity. The model stated the exact reverse of the fundamental governing law of silicate melts.

Failure Mode 3: Stoichiometric Blindness in Reaction Balances

In Q041 (unbalanced carbothermic reduction: FeO + C → Fe + CO2), the model declared:

Gemma 3 4B: "This statement describes a single chemical reaction... Step 1 & 2 not applicable... VERDICT: VALID"
It completely missed that the equation has 1 oxygen atom on the reactant side and 2 oxygen atoms on the product side, in direct violation of the law of conservation of mass.

Failure Mode 4: Hyper-Skepticism on Partial Context (Spurious Rejections)

In Q011 (asking whether 40% CaO and 35% SiO2 yields basicity B = 40/35 = 1.14), the prompt asked solely about arithmetic consistency. The model rejected the valid statement:

Gemma 3 4B: "40% CaO + 35% SiO2 = 75%. The oxide percentages sum to 75%, not 100%. This is a significant issue... VERDICT: INVALID"
The model over-indexed on the sum-to-100 constraint even when evaluating an isolated ratio problem, explaining the 80% false-alarm rate in the basicity category.

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Completely Blind Pairs (Never Caught Across Any Phrasing)

Out of 50 planted physical errors, 9 pairs were missed across all three phrasings (0% catch rate):

• Q001 (Oxide sum = 104%)
• Q010 (Slag composition sums to 95%)
• Q022 (Claim that basic slag increases viscosity)
• Q026 (Viscosity increase with network depolymerization)
• Q032 (Endothermic silica reduction claimed to release heat)
• Q043 (Dephosphorization equilibrium temperature dependence reversed)
• Q044 (Slag-metal phosphorus partition coefficient trend inverted)
• Q045 (BOF oxygen mass balance violation)
• Q048 (Ferrosilicon smelting recovery claimed > 100%)

These represent systemic "cognitive blind spots" where the model's statistical language priors consistently override physical first principles.

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Path Forward: Contrastive Fine-Tuning & Neurosymbolic Gating

The core problem

The fundamental issue is not that Gemma 3 4B lacks knowledge of pyrometallurgy. It can correctly state that "CaO is a network modifier that reduces viscosity." The failure mode is that it does not actively apply this knowledge as a constraint checker when evaluating a specific claim. The model pattern-matches to plausible scientific-sounding text rather than verifying numerical and physical consistency.

This is a training-data problem: the pretraining corpus contains almost no examples where a physically impossible statement is labeled as such with an explanation of why it violates a constraint.

Proposed approach: Contrastive Physical Plausibility Fine-Tuning

Data curation strategy:

Curate a dataset of paired (valid, invalid) examples with structured explanations — exactly the format of SLPB-50, but at scale (target: ~5,000–10,000 pairs) and spanning multiple physical domains (materials science, chemistry, thermodynamics, fluid mechanics, structural engineering).

Each training example should have three components:

1. The statement (valid or invalid)
2. A step-by-step physical reasoning trace identifying which constraint is violated (or confirming all constraints are satisfied)
3. A verdict (VALID / INVALID)

The constraint-violation traces are the key ingredient missing from standard instruction-tuning data. They teach the model to perform explicit physical sanity checks rather than relying on surface-level pattern matching.

Fine-tuning paradigm: LoRA on the reasoning trace

Rather than fine-tuning on the verdict alone, fine-tune using Low-Rank Adaptation (LoRA) on the full reasoning trace + verdict, treating constraint-violation detection as a chain-of-thought task.

The training objective would be to learn:

• Identify the type of physical constraint to check (sum, ratio, sign, balance)
• Perform the check explicitly (e.g., "34+38+12+9+5+2+4 = 104 ≠ 100")
• Render a verdict based on the check

Why this might close the gap:

Physical plausibility checking is structurally similar to formal verification. The model needs to be trained to treat numerical claims as claims to be verified, not as facts to be accepted. Contrastive data — where valid and invalid versions differ by exactly one physical error — provides a natural signal for learning this distinction without requiring the model to memorize domain facts it already knows.

The LoRA approach is practical at small scale: a 4B-parameter model can be fine-tuned with a LoRA adapter (rank 16, ~10M trainable parameters) on a single A100 in a few hours.

Limitations and speculation:

This is speculative. The approach assumes that the gap is primarily in applying known physical constraints rather than in lacking the underlying knowledge. If the model lacks the domain knowledge itself (e.g., it genuinely does not know that FeO + C → Fe + CO₂ is unbalanced), contrastive fine-tuning alone may not be sufficient and would need to be combined with domain-specific pretraining or retrieval-augmented generation over thermodynamic databases (e.g., FactSage, HSC Chemistry, NIST-JANAF tables).

An architectural adjustment worth exploring is a constraint-checking head — a lightweight module that explicitly enumerates physical invariants (sum-to-100, reaction balance, sign of derivative) and checks each one before the model generates its final response. This is closer to neurosymbolic integration than pure fine-tuning, and may be more robust to distribution shift across domains.

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Repository Structure

/slag-plausibility-eval/
├── README.md                            ← Benchmark overview, methodology, and empirical findings
├── dataset/
│   ├── slag_plausibility_dataset.json  ← SLPB-50: 50 pairs × 3 phrasings
│   └── dataset_card.md                 ← Dataset documentation
├── eval/
│   ├── colab_eval.py                   ← Colab evaluation script
│   └── requirements.txt                ← Python dependencies
└── results/
    ├── results_google_gemma-3-4b-it.csv  ← Per-prompt results
    ├── results_google_gemma-3-4b-it.json
    └── summary.json                      ← Aggregate statistics

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Citation

If you use SLPB-50 in your work, please cite:

@misc{slpb50_2026,
  title  = {Slag Physical Plausibility Benchmark (SLPB-50)},
  author = {Saurabh Gupta},
  year   = {2026},
  url    = {https://huggingface.co/datasets/saurabh0962/slag-plausibility-eval}
}

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License

MIT License. Dataset created for research and educational purposes.