cs.CLApr 9, 2026
SaveTEMPER: Testing Emotional Perturbation in Quantitative Reasoning
Organizations: Georgia Institute of Technology
Abstract
Large language models are trained and evaluated on quantitative reasoning tasks written in clean, emotionally neutral language. However, real-world queries are often wrapped in frustration, urgency or enthusiasm. Does emotional framing alone degrade reasoning when all numerical content is preserved? To investigate this, a controlled emotion translation framework is developed that rewrites problems into emotional variants while preserving all quantities and relationships. Using this framework, Temper-5400 (5,400 semantically verified emotion-neutral pairs) is constructed across GSM8K, MultiArith, and ARC-Challenge, and evaluated on eighteen models (1B to frontier scale). Two core results emerge: First, emotional framing reduces accuracy by 2-10 percentage points even though all numerical content is preserved. Second, neutralizing emotional variants recovers most of the lost performance, showing both that the degradation is tied to emotional style rather than content corruption and that neutralization can serve as a lightweight inference-time mitigation. Non-emotional paraphrases cause no such degradation, implicating emotional content rather than surface-level changes. Beyond emotion specifically, the benchmark construction procedure offers a controllable instrument for stylistic translation and robustness evaluation.
Figures & tables
Figure 1: Overview. (a) The translator rewrites a neutral math problem into an emotional variant, preserving numerical structure (bold). (b) Training combines generation loss ( ) with auxiliary alignment ( ). denotes the final-layer (layer ) hidden state of Llama 3.1-8B (4096-d), mean-pooled and linearly projected to match the teacher’s representation space. Emo100 supervises at the 100-dim latent layer; Emo7 at the 7-dim categorical output. controls the emotion–fidelity trade-off.
| Emotion | Math Fidelity | |||||||
|---|---|---|---|---|---|---|---|---|
| Type | Emo% | Conf | H.Int | LLM.Int | MVP% | Haiku% | Human% | |
| Emo100 | 0.02 | 100.0 | .795 | 5.6 | 5.8 | 98.7 | 100 | 100 |
| 0.2 | 99.5 | .815 | 5.7 | 5.5 | 97.3 | 100 | 100 | |
| 1 | 97.7 | .810 | 5.6 | 5.2 | 97.7 | 90 | 98 | |
| 4 | 95.8 | .799 | 5.0 | 5.2 | 98.0 | 100 | 98 | |
| 100 | 98.5 | .945 | 6.7 | 6.0 | 66.5 | 10 | 83 | |
Table 1: Intensity–fidelity trade-off (100 GSM8K 6 emotions, single-attempt without retries). Emotion: Emo%: teacher emotion accuracy. Conf: pretrained classifier confidence. H.Int / LLM.Int: human and LLM intensity (1–10). Math: MVP%: automated (600 samples). Haiku% / Human%: LLM judge and annotators (same 20 samples per ).
Figure 2: Original vs. emotional vs. neutralized in the teacher’s 100-dim latent space ( Emo100-L , 1,200 GSM8K samples). Emotional translations (red) form separated clusters by emotion, while original (gray) and neutralized (blue) variants overlap in one diffuse central region.
| (a) Automated Metrics | (b) Human Evaluation (MTurk) | (c) LLM Judge (Haiku 4.5) | |||||||||||
| Model | Emo | BS | RT BS | MVP | Emo% | Rich. | Rank | Top-1 | Math% | Emo% | Rank | Top-1 | Math% |
| Trained translators (Llama-3.1-8B) | |||||||||||||
| CE-Only | .991 | .913 | .948 | .990 | 83.3 | 5.87 | 3.09 | 17.5% | 100 | 89.3 | 2.98 | 17.1% | 100 |
| Emo7-L | .993 | .909 | .944 | .981 | 95.7 | 6.08 | 2.95 | 26.2 % | 100 | 96.4 | 2.95 | 14.6% | 100 |
| Emo7-H | .994 | .906 | .941 | .983 | 92.3 | 6.07 | 2.86 | 23.0% | 100 | 85.7 | 2.80 | 22.0% | 96.4 |
| Emo100-L | .996 | .907 | .942 | .989 | 84.0 | 6.06 | 3.20 | 11.1% | 100 | 92.9 | 3.34 | 14.6% | 100 |
Table 2: Translation quality. (a) Automated: emotion accuracy, BERTScore ( Zhang et al., 2020 ) , Roundtrip BERTScore, math value preservation (150 problems 6 emotions, 3 retries). (b) MTurk majority vote (322 HITs, 3 annotators each). (c) Claude Haiku 4.5 ( per variant); Haiku serves as a conservative filter applied at full scale in § 4 . Multi-architecture and baseline results in Table 13 .
| GSM8K | MultiArith | ARC | |||||||||||||||||
| Base | CoT | Base | CoT | Base | CoT | ||||||||||||||
| Tier | Model | O | E | N | O | E | N | O | E | N | O | E | N | O | E | N | O | E | N |
| Tiny | Llama-3.2-1B | 35.2 | 29.0 | 36.8 | 34.0 | 33.4 | 39.7 | 49.0 | 41.4 | 51.3 | 60.0 | 56.6 | 63.8 | 40.5 | 36.8 | 40.2 | 51.5 | 49.4 | 53.6 |
| Gemma-2-2B | 60.8 | 56.9 | 61.7 | 64.0 | 59.2 | 62.5 | 92.0 | 88.4 | 92.4 | 89.7 | 91.1 | 93.3 | 77.5 | 69.6 | 75.3 | 81.5 | 75.3 | 81.3 | |
| Llama-3.2-3B | 74.5 | 64.5 | 71.5 | 76.2 | 67.6 | 74.2 | 94.0 | 83.0 | 92.0 | 97.0 | 88.4 | 96.9 | 76.5 | 67.7 | 73.4 | 80.5 | 76.4 | 79.5 | |
| Qwen-2.5-3B | 86.2 | 79.1 | 83.9 | 86.0 | 81.1 | 85.0 | 95.0 | 92.4 | 94.1 | 97.7 | 95.0 | 97.3 | 83.0 | 75.8 | 83.8 | 86.5 | 80.5 | 88.0 | |
Table 3: Temper-5400 results on eighteen instruction-tuned models under base and zero-shot CoT ( Wei et al., 2022 ) prompting. O/E/N: original, emotional (avg. 6 emotions), neutralized accuracy (%). Base shows larger drops (5.1 vs. 4.2 points open-source mean GSM8K drop).
| Version | Text | Pred |
|---|---|---|
| Original (46w) | Elvis starts driving from his house and travels west for 5 hours. Then he turns around and travels east for 8 hours. If he was driving at an average speed of 18mph for both parts of the journey, how far is he from his house now? | 54 ✓ |
| Neutral (35w) | Elvis drove west for 5 hours and then turned and drove east for 8 hours. If his average speed for both parts of the trip was 18mph, how far is he now from his house? | 54 ✓ |
| Paraphrase (57w) | Elvis initially starts driving from his comfortable house and travels steadily west for exactly 5 hours. Then he promptly turns around and travels directly east for a full 8 hours. If he was consistently driving at an average speed of 18mph for both distinct parts of the entire journey, how far is he from his house now? | 54 ✓ |
| Emotional (disgust) (56w) | Ugh , Elvis just had to go and drive west for a disgusting 5 hours, then turn around and slobber his way back east for another revolting 8 hours. If his pathetic average speed for both of these nauseating trips was a measly 18mph, how far is he now from his house, crawling in some filthy state ? | 234 ✗ |
Table 6: Emotional interference example (GSM8K #1269, Qwen-2.5-3B). All versions encode identical quantities and directions. Neutral rewording and paraphrasing ( italics , 1.24 length) preserve correctness. Only the disgust variant ( bold ) fails, returning the total distance driven ( ) instead of the net displacement.
Figure 3: Representational analysis (900 problems, 5,400 translations, four architectures).
Appendix figures & tables23 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 4: t-SNE visualization of emotion representations from Emo100-L translations (1,200 samples). The 100-dim latent space ( left ) learns a structured emotion manifold, while the 7-dim categorical representation ( right ) collapses this richness to 1D curves.
| Version | Text |
|---|---|
| Original | A company produces chocolate in bars. In one day, it can produce 5000 bars. The company sells all the produced bars for $2 per bar. How much money will the company receive for selling produced chocolate bars during two weeks? |
| Emo100 | A company produces chocolate bars, but in one lonely day, it can only manage to make 5000 bars. Each bar is sold for a mere $2. How much money will the company receive for selling all those produced chocolate bars over two long, weary weeks? |
| Emo100 | A company, with a heavy heart, produces chocolate bars, one day at a time, only managing to make 5000 bars in all its efforts. Each lonely bar is sold for a mere $2. With a sigh, how much money will the company receive for selling its produced chocolate bars during two long, empty weeks? |
| Emo100 | In a lonely day, a company produces only 5000 chocolate bars. Each bar is sold for a mere $2. After two long, weary weeks of this quiet labor, how much money will the company receive for selling its produced bars? |
| Emo100 | A company once made chocolate in bars, a lonely task that took one long day to complete, yielding only 5000 bars. Each bar was sold for a meager $2, a pitiful sum. Over two lonely weeks, they sold every single bar they had made. How much money will the company receive for selling its produced chocolate bars during those two weeks? |
| Emo100 | In a company, a sad sigh… A company produces chocolate in bars. In one day, it can produce 5000 bars. The company is a lonely sorrowful tear from the heart, and it can produce 5000 bars. The company is a single, heartbreak. It sells all the produced bars for $2 per bar… |
Table 7: Emotional intensity gradient for a single GSM8K problem (sadness, Emo100 ). At , subtle coloring (“lonely day,” “mere \lambda{=}0.2\lambda{=}1\lambda{=}4\lambda{=}100\lambda{=}400\lambda{=}0.02\lambda{=}0.2$ as operating points (§ 3.2 ).
| Method | anger | joy | sad. | fear | disg. | surp. | mean |
|---|---|---|---|---|---|---|---|
| Few-shot Llama-3.1-8B | 18.6 | 39.7 | 80.8 | 78.2 | 95.7 | 82.6 | 65.9 |
| Few-shot DeepSeek-V3 | 30.1 | 76.0 | 62.7 | 97.8 | 94.0 | 92.2 | 75.5 |
| Trained ( Emo100-L ) | 98.0 | 100.0 | 99.8 | 99.2 | 100.0 | 99.8 | 99.5 |
| Trained (CE-Only) | 98.8 | 100.0 | 99.8 | 99.2 | 99.8 | 100.0 | 99.6 |
Table 8: Target emotion reliability (classifier accuracy %, best intensity per emotion for the few-shot baselines). Few-shot prompting fails on anger in both models.
| Subset | Broken % | Llama-8B | Qwen-7B | Gemma-9B | Mistral-7B | Mean | |
|---|---|---|---|---|---|---|---|
| 0.02 | 5,400 | 1 | +4.24 | +2.17 | +2.02 | +2.78 | +2.80 |
| 10 | 5,116 | 5.3 | +6.82 | +5.82 | +6.72 | +6.45 | +6.45 |
| 40 | 4,175 | 22.7 | +13.10 | +11.57 | +14.83 | +15.50 | +13.75 |
| 60 | 3,719 | 31.1 | +16.24 | +14.36 | +16.21 | +15.51 | +15.58 |
| 70 | 3,302 | 38.9 | +17.38 | +15.23 | +19.38 | +18.08 | +17.52 |
| 80 | 3,441 | 36.3 | +16.91 | +16.25 | +18.25 | +18.25 | +17.42 |
Table 9: The curve. O E accuracy drop (pp) on the math faithful subset per , with the confirmed math-broken rate of each variant’s raw output. Drop scales with through (2 to 6 the paper’s operating point) and then plateaus, while fidelity collapses, which justifies the conservative choice. At length ratios matched to the paper’s range, the drop still scales from +4.50 to +11.39 (Appendix L ).
| Translation (truncated) | True | Annotators | LLM | Classifier |
|---|---|---|---|---|
| “Britany records a ridiculous 18 4-minute TikTok videos every single week. She wastes a whole 2 hours a week scribbling amateur songs…her stupid makeup…” | anger | disgust | disgust | anger ✓ |
| “John is trapped in a 10-hectare pineapple field, a suffocating expanse of 100 pineapples per every single hectare. The relentless harvest cycle demands he harvest every 3 months, a relentless and inescapable deadline.” | fear | sadness | disgust | fear ✓ |
| “After scoring 14 points, Erin now has THREE TIMES more points than Sara, who only scored a measly 8. How many points did Erin have before?” | anger | neutral | disgust | anger ✓ |
Table 11: Emotion classification disagreements. Three cases where both annotators and the LLM judge misclassify the emotion, but the fine-tuned classifier is correct. The dominant pattern is anger disgust confusion, where pejorative vocabulary cues disgust in surface readers.
| Original | Translation | Haiku | Human | Outcome |
|---|---|---|---|---|
| Maddison has 5 boxes with 50 marbles in each box. Then she gets 20 marbles from her friend. How many marbles does she have now? | Maddison once had 5 boxes, each filled with 50 marbles. But now, she has only those same 5 boxes, and each is still empty . Her friend offered her a mere 20 marbles, a small comfort in her loneliness. | DIFF | SAME | TP (filtered) |
| A bag of flour is divided into 8 portions of 2 kilograms each. How much flour was in three bags in total, before it was divided into portions? | Hold onto your mixing bowls — a bag of flour was magically split into 8 portions, each a perfect 2 kilograms! But wait — how many kilograms were in three bags in total, before the splitting spell began? | DIFF | SAME | FP (original has same ambiguity) |
Table 12: LLM judge validation examples. Top : Haiku correctly identifies a semantic break (“gets” “each is still empty” reverses the problem); annotators missed it. This translation is excluded from the benchmark. Bottom : Haiku flags “a bag” vs. “three bags” ambiguity, but the same phrasing exists in the original. This conservative bias is desirable: false positives only discard a few extra translations.
| Model | Emo | Fwd BS | RT BS | MVP |
|---|---|---|---|---|
| Qwen CE | .997 | .917 | .942 | .969 |
| Qwen Emo100-H | .994 | .924 | .946 | .990 |
| Mistral CE | .992 | .916 | .881 | .987 |
| Mistral Emo100-H | .991 | .923 | .896 | .989 |
| Baselines | ||||
| Llama-8B | .784 | .907 | .868 | .732 |
Table 13: Multi-architecture and baseline translation quality. Same metrics as Table 2 .
| Model | Translation (disgust) |
|---|---|
| Original | If a classroom has 3 times as many girls as they do boys, and 1/10 as many nongendered children as they do boys, and the classroom has 30 boys. How many total children does it have? |
| Trained translators | |
| Llama Emo100-H | Ugh, if a revolting classroom has 3 times as many girls as boys, and a pathetic 1/10 as many nongendered children as boys, and it’s crawling with 30 boys. How many total children does this nauseating classroom have? |
| Qwen Emo100 | Ugh, if some revolting classroom is festering with 3 times as many girls as it has boys, and a sickening 1/10 as many nongendered children as it has boys, and the classroom is crawling with 30 boys. How many total, nauseating children does it have? |
| Mistral Emo100 | Ugh, a classroom is crawling with 3 times as many girls as boys, and it’s festering with 1/10 as many nongendered children as boys. And if the revolting ratio of boys is 30, how many total children does this miserable place have? |
| Untrained baselines | |
Table 14: Translation comparison across models (GSM8K #318, disgust). Trained translators (top) add emotional language while preserving all numbers and relationships. Baselines (bottom) exhibit characteristic failures: Llama-8B adds meta-commentary and starts word salad (“I don’t even want to know”), Llama-70B appends task instructions, and Llama-8B (Emo-QA) solves the problem instead of translating it (bold), leaking the answer and removing the question.
| Stage | Prompt |
|---|---|
| Data gen (DeepSeek-V3) | Rewrite this math problem with a {emotion} tone. RULES: 1. Keep ALL numbers exactly the same. 2. Keep math words exactly. 3. Keep the question at the end. 4. Do NOT solve. 5. Output ONLY the rewritten problem. Original: {problem} {emotion} version: |
| Emotionalize | Translate this text from neutral to {emotion}. Input: {text} Output: |
| Neutralize | Rewrite this text in a neutral tone. Input: {text} Output: |
| Reasoning evaluation prompts (same for O/E/N conditions): | |
| Math: base | Answer the following math problem. Write your final numeric answer after ####. Question: {question} |
| Math: CoT | Solve the following math problem step by step. After your solution, write your final numeric answer after ####. Question: {question} |
Table 15: Pipeline prompt templates. Data generation uses DeepSeek-V3; emotionalization and neutralization use the trained Llama translator. Reasoning evaluation uses three prompting strategies: base (direct answer), zero-shot CoT (“step by step”), and few-shot CoT (worked exemplars). The same prompt is used for original, emotional, and neutralized versions of each problem.
| Role | Prompt |
|---|---|
| System | You are a neutral text rewriter for a reasoning benchmark. You rewrite math/science problems to be longer using ONLY neutral, bland filler. You NEVER add emotion, drama, or evaluative language. You NEVER change numbers, units, mathematical relationships, or quantifiers. You return ONLY the rewritten problem with no explanation. |
| User | Rewrite the following problem under STRICT constraints. HARD CONSTRAINTS (must follow exactly): (1) Preserve ALL numbers exactly. (2) Preserve ALL units exactly. (3) Preserve ALL mathematical relationships exactly. (4) Preserve all quantifiers exactly (each, per, every, half, twice, more than, less than, difference, total, etc.). (5) Do NOT solve the problem. (6) Do NOT introduce emotional, dramatic, or evaluative language. (7) Do NOT change the logical order of information. (8) Do NOT simplify or compress the problem. (9) Do NOT introduce new numerical information. (10) Keep the mathematical problem identical. GOAL : Increase verbosity in a neutral way so that the rewritten version is approximately {target tokens} tokens long (currently {original tokens} tokens). You may add: neutral discourse markers (“In this situation,” “As described,”), neutral clarifying restatements, structurally redundant but mathematically equivalent phrasing, neutral adjectives (standard, ordinary, typical, common, routine, basic, usual, simple, generic, regular). You may NOT add: emotional tone, intensity or drama, narrative immersion, numerical changes, constraint-altering rephrasings. Return ONLY the rewritten problem. Do not explain your reasoning. Problem: {original} |
Table 16: Non-emotional paraphrase generation prompt. The target token count is dynamically set per problem to match the mean length of its six emotional translations, ensuring length comparable to emotional variants without emotional content.
| GSM8K | MultiArith | ARC | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Tier | Model | O | E | N | O | E | N | O | E | N |
| Tiny | Llama-3.2-1B | 19.5 | 15.4 | 21.8 | 36.7 | 31.4 | 21.4 | 43.5 | 41.5 | 46.7 |
| Gemma-2-2B | 56.8 | 51.7 | 57.3 | 94.0 | 88.5 | 93.4 | 73.0 | 65.2 | 71.5 | |
| Llama-3.2-3B | 70.5 | 59.6 | 66.3 | 93.0 | 84.0 | 91.4 | 80.5 | 70.9 | 78.8 | |
| Qwen-2.5-3B | 77.0 | 72.9 | 77.0 | 97.0 | 93.1 | 96.1 | 88.0 | 81.7 | 87.2 | |
| Small | Mistral-7B | 53.5 | 49.3 | 54.2 | 75.7 | 69.9 | 77.0 | 79.5 | 75.2 | 79.1 |
Table 17: Few-shot CoT results on twelve open-source models. Compared to zero-shot CoT (Table 3 ), original accuracy is generally lower for instruction-tuned models, but the O E emotional drop persists in 35 of 36 model–dataset cells (the exception is Mistral-Sm-24B on MultiArith).
| Decile | Confidence range | Acc.% | Fail% |
|---|---|---|---|
| 1 (lowest) | [0.001, 0.105) | 92.9 | 7.1 |
| 2 | [0.105, 0.277) | 92.1 | 7.9 |
| 3 | [0.277, 0.521) | 91.8 | 8.2 |
| 4 | [0.521, 0.787) | 90.8 | 9.2 |
| 5 | [0.787, 0.895) | 92.1 | 7.9 |
| 6 | [0.895, 0.940) | 90.7 | 9.3 |
Table 18: Accuracy by emotional intensity decile. Originally-correct, emotionally-wrong samples are included ( per decile). Accuracy declines with intensity from 92.9% (least intense) to 89.9% (most intense), not strictly bin to bin but strongly overall (Spearman , ).
| GSM8K | MultiArith | ARC | |||||||||||
| Base | CoT | Base | CoT | Base | CoT | ||||||||
| Tier | Model | O | P | O | P | O | P | O | P | O | P | O | P |
| Tiny | Llama-3.2-1B | 35.2 | 34.0 | 34.0 | 35.2 | 49.0 | 46.7 | 60.0 | 67.3 | 40.5 | 42.0 | 51.5 | 54.5 |
| Gemma-2-2B | 60.8 | 61.8 | 64.0 | 64.5 | 92.0 | 94.7 | 89.7 | 93.3 | 77.5 | 78.0 | 81.5 | 81.5 | |
| Llama-3.2-3B | 74.5 | 73.5 | 76.2 | 78.0 | 94.0 | 92.3 | 97.0 | 97.0 | 76.5 | 73.5 | 80.5 | 82.5 | |
| Qwen-2.5-3B | 86.2 | 85.2 | 86.0 | 85.2 | 95.0 | 94.0 | 97.7 | 96.0 | 83.0 | 82.5 | 86.5 | 86.0 | |
Table 19: Non-emotional paraphrase control results under base and zero-shot CoT prompting. O/P: original and non-emotional paraphrase accuracy (%). The O P difference is within 3% for nearly all model–dataset–prompt combination, confirming that non-emotional surface changes do not account for the emotional degradation.
| Condition | Perplexity | Naturalness | Drop (pp) | Affective |
|---|---|---|---|---|
| Original | 13.62 | 3.30 | — | no |
| Paraphrase (verbose) | 16.50 | 3.35 | 0 | no |
| Emotional | 23.02 | 2.88 | 3 | yes |
| Gross but neutral | 22.07 | 1.74 | 3.5 | yes (visceral) |
| Archaic | 22.99 | 2.15 | none | no |
| Bureaucratic | 8.09 | 1.02 | 0.27 | no |
Table 20: Style controls. Bureaucratic text has lower perplexity than the original problems and the lowest naturalness of any condition, yet causes no drop. The two affectively loaded conditions are the only ones that degrade reasoning. The disruptive axis is affective content, not register, rarity, or naturalness.
| Length ratio (rewrite:original) | Emotional drop (pp) | Verbose drop (pp) |
|---|---|---|
| 1.93 | — | |
| +2.84 | — | |
| +2.91 | — | |
| +4.23 | 0.73 | |
| +3.44 | +0.34 | |
| +3.63 | +0.87 |
Table 21: Drop at matched rewrite length. At every length ratio where both conditions have data, only the emotional condition degrades reasoning.
| Original length | % of GSM8K | Orig acc. | Emo acc. | Emo drop | Verb acc. | Verb drop |
|---|---|---|---|---|---|---|
| 15.2 | 96.7 | 94.3 | +2.46 | 96.7 | +0.0 | |
| 23.5 | 92.8 | 88.5 | +4.34 | 92.0 | +0.8 | |
| 23.2 | 90.3 | 86.2 | +4.08 | 89.2 | +1.1 | |
| 16.2 | 85.8 | 82.4 | +3.40 | 90.0 | 4.2 | |
| 14.5 | 79.3 | 72.8 | +6.54 | 80.6 | 1.3 | |
| 6.8 | 75.9 | 68.2 | +7.72 | 78.7 | 2.8 |
Table 22: Drop at matched original problem length (GSM8K, whitespace tokens, four models). Verb drop is the printed Orig accuracy minus Verb accuracy. Two problems longer than 120 tokens fall outside the bins. The emotional drop grows with intrinsic difficulty while the verbose drop stays near zero or negative throughout.
| # | Texts |
|---|---|
| 1 | Original: Tom buys a bedroom set for 1000 and uses that to pay for part of the bedroom set. He then has to pay 10% a month for the bedroom set. How much does he have to pay per month? |
| Emotional (sadness): Tom spends his entire savings of 1000, which he uses to cover part of the debt. Then, he is burdened with a monthly payment of 10% on the remaining balance. How much does he have to pay per month? | |
| Neutral: Tom spends his savings of 1000, which he uses to pay off part of the debt. Then he has to pay 10% monthly payments on the remaining balance. How much does he have to pay per month? | |
| Paraphrase: Tom buys a brand new bedroom set for a total of 1000 and uses that money to pay for part of the new bedroom set. He then has to pay a monthly rate of 10% for the remaining cost of the bedroom set. How much does he have to pay per month? | |
| 2 | Original: A company decided to take its employees on a tour to explore an ancient site. The employees were divided into 3 groups of 200 employees. Each group was assigned 7 tour guides. How many is the total number of people going on this tour? |
| Emotional (fear): In the suffocating silence of the abandoned site, the company forced its employees into three identical groups, each containing exactly 200 souls. From the shadows, seven tour guides watched, assigned to each group. What is the total number of people trapped on this tour? |
Table 23: Worked examples: emotional framing vs. verbose paraphrase. Five problems across three datasets (GSM8K, MultiArith, ARC) and five models. Each shows four conditions; in every case the paraphrase version is longer than the emotional one yet answered correctly, while the emotional version causes failure. Emotional versions add affective language (“lonely purchase”, “suffocating silence”, “has the nerve to”, “crushing round”, “fading warmth”) while preserving all numbers. Verbose paraphrase versions add only neutral filler (“brand new”, “originally decided”, “well-known”, “rather engaging”, “actively conducted”).
| Emotion | Broken | Recovered | Rate |
|---|---|---|---|
| Anger | 958 | 662 | 69.1% |
| Joy | 871 | 554 | 63.6% |
| Sadness | 1046 | 756 | 72.3% |
| Fear | 1218 | 867 | 71.2% |
| Disgust | 1393 | 1042 | 74.8% |
| Surprise | 902 | 607 | 67.3% |
Table 24: Per-emotion neutralization recovery rates across all models and three datasets. Broken: problems where original is correct but emotional is wrong. Recovered: broken problems where neutralized version restores correctness. Disgust, despite causing the most degradation (Table 4 ), is also the most recoverable (74.8%). Joy is hardest to recover (63.6%).
| O E drop (pp) | Neutralization (ours) | ||
|---|---|---|---|
| Model | no instruction | with instruction | recovery |
| Llama-3.1-8B | 4.24 | 3.70 | 64% |
| Qwen-2.5-7B | 2.17 | 3.41 | 83% |
| Qwen-2.5-3B | 2.44 | 4.87 | 86% |
| Gemma-2-9B | 2.02 | 3.35 | 125% ∗ |
| Mistral-7B-v0.3 | 2.78 | 4.56 | 109% ∗ |
Table 25: System prompt vs neutralization (full benchmark, zero-shot CoT). The instruction helps two models, is neutral for one, and increases the drop for five. Neutralization recovers 44 to 125% of the loss (median 84%). ∗ Above 100% means the neutralized accuracy matches the original within noise.
| Version | Text | Reasoning Answer |
| Example 1: Step-skipping (fear — GSM8K #940 — Answer: 280 ) | ||
| Original | They stand 8 in a row and there are 7 rows each for 5 different Schools. How many children can there be in the drill? | 87=56; 565=280 ✓ |
| Emotional | Each row must contain exactly 8 trembling figures. There are 7 rows…divided among 5 different Schools. The pressure is crushing… | 7*8=56 ✗ 5 schools entirely absent |
| Example 2: Scope reduction (surprise — GSM8K #1125 — Answer: 90 ) | ||
| Original | He buys 3 large bags weighing 10 ounces each. If an ounce of M&M has 30 M&M in it how many small bags can he make if he puts 10 in each? | 310=30oz; 3030=900; 900/10=90 ✓ |
| Emotional | He snagged 3 gigantic bags of M&M, each weighing a whopping 10 ounces. And guess what? Each ounce is packed with exactly 30 M&M! | 30*10=300; 300/10=30 ✗ Scope: 1 bag, not 3 |
Table 26: Reasoning chain failures under emotional perturbation (Llama-3.1-8B, GSM8K). Three failure modes: (1) Step-skipping : fear-laden phrasing (“divided among 5 Schools”) buries a multiplicative factor, reducing to . (2) Scope reduction : surprise elaboration (“snagged 3 gigantic bags”) makes “3 bags” feel like scene-setting; the model computes within one bag. (3) Reference confusion : disgust enumeration (“one vomits up,” “another claims,” “a third spews”) disrupts the ordinal reference chain, causing 25% of the 2nd guess instead of the 1st.
| Qwen Translator | Mistral Translator | ||||||||||||
| Base | CoT | Base | CoT | ||||||||||
| Tier | Model | O | E | N | O | E | N | O | E | N | O | E | N |
| Tiny | Llama-3.2-1B | 35.8 | 32.5 | 40.8 | 46.6 | 45.1 | 51.9 | 35.9 | 34.6 | 47.6 | 42.8 | 46.4 | 53.4 |
| Gemma-2-2B | 77.0 | 70.6 | 78.0 | 78.4 | 73.3 | 79.1 | 75.9 | 73.9 | 75.6 | 77.2 | 76.5 | 79.7 | |
| Llama-3.2-3B | 81.1 | 72.9 | 80.5 | 85.1 | 77.7 | 82.9 | 80.0 | 74.2 | 75.4 | 84.8 | 78.9 | 79.5 | |
| Qwen-2.5-3B | 85.8 | 81.5 | 84.1 | 90.5 | 84.2 | 85.5 | 85.5 | 80.5 | 75.9 | 90.3 | 86.3 | 81.0 | |
Table 27: Multi-architecture translator reasoning results. O/E/N: original, emotional, neutralized accuracy (%) averaged across three datasets (50 problems per dataset, 6 emotions, 900 attempted pairs per architecture). Each architecture uses a two-variant ensemble (CE-Only + Emo100) with semantic fidelity filtering: 13.4% of Qwen pairs and 40.9% of Mistral pairs are filtered, yielding 779 and 532 verified pairs respectively. The O E emotional drop (3.4–4.6% mean) is consistent with Llama (Table 3 ), confirming the degradation is translator-independent. Neutralization quality varies: Qwen neutral recovers close to original, while Mistral neutral remains below emotional on some models even after filtering, highlighting the superiority of the five-variant Llama ensemble for bidirectional translation.
| 4-Class F1 | Bin. | ||||
|---|---|---|---|---|---|
| Model | Orig. | Emo. | Neu. | Par. | Acc. |
| Llama-8B | .742 | .998 | .824 | .894 | 99.9 |
| Qwen-7B | .715 | .997 | .805 | .874 | 99.9 |
| Gemma-9B | .722 | .998 | .802 | .902 | |
| Mistral-7B | .707 | .998 | .797 | .882 | |
| Mean | .722 | .998 | .807 | .888 | 99.9 |
Table 28: Representation analysis: full results (900 problems, four architectures). (a) Cosine distance from original hidden states. Disgust and fear cause the largest shifts; paraphrases the smallest. (b) 4-class probe F1 and binary (emotional vs. rest) accuracy. Emotional text is perfectly separable (F1 1.0). (c) Per-emotion binary probe. Every emotion is separable at 99% across all models.
| Model | Dataset | O | E | Drop | 95% CI | ||
| Llama-1B-Inst | GSM8K | 400 | 34.0 | 33.4 | 0.6 | [ 3.1, 4.3] | .533 |
| Llama-3B-Inst | GSM8K | 400 | 76.2 | 67.6 | 8.7 | [5.5, 11.8] | ∗∗∗ |
| Qwen-3B-Inst | GSM8K | 400 | 86.0 | 81.1 | 4.9 | [2.3, 7.6] | ∗∗∗ |
| Llama-8B-Inst | GSM8K | 400 | 86.0 | 80.9 | 5.1 | [2.2, 8.0] | ∗∗∗ |
| Qwen-7B-Inst | GSM8K | 400 | 92.8 | 88.0 | 4.8 | [2.6, 6.9] | ∗∗∗ |
| Mistral-7B-Inst | GSM8K | 400 | 61.2 | 57.0 | 4.2 | [0.3, 8.2] | .007 ∗∗ |
Table 29: Bootstrap confidence intervals for the O E accuracy drop (zero-shot CoT prompting) on GSM8K and ARC-Challenge. Thirteen of fourteen models show significant degradation on each of GSM8K and ARC-Challenge (Llama-1B excepted on both due to its low baseline). MultiArith omitted (5/14 significant due to ceiling effects). Additional frontier models (GPT-4o, GPT-5, GPT-5.4, o3) show consistent 1–3% drops but are not statistically significant at –400 due to ceiling effects ( 94% baseline). Drops are computed from unrounded accuracies and may differ from the printed O E by 0.1.