TEMPER: 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
| 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 | |
| (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 |
| 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 | |
| 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 ✗ |
Appendix figures & tables23 assets
Supplementary material from the paper’s appendix.
Appendix
| 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… |
| 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 |
| 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 |
| 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 ✓ |
| 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) |
| 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 |
| 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 | |
| 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} |
| 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} |
| 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 |
| 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 |
| 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 | |
| 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 |
| 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 |
| 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 |
| # | 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? |
| 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% |
| 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% ∗ |
| 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 |
| 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 | |
| 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 |
| 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 ∗∗ |