Large Reasoning Models (LRMs) impose substantial energy costs during deployment, yet current compression methods apply uniform quantization across all components, risking damage to critical reasoning circuits. We present a reasoning-aware compression framework that benchmarks quantization conditions across five reasoning benchmarks, GSM8K, FOLIO, MATH-500, ProofWriter, and MuSiQue, with hardware-level GPU energy measurement; profiles per-module INT4 vulnerability across all 196-224 (layer, projection) pairs via a perturbation sweep on a held-out calibration split, then selectively restores the most sensitive circuits to FP16. Three findings emerge. First, INT4 quantization can increase energy by extending reasoning chains; a 25% power reduction becomes a net energy increase on GSM8K. Second, vulnerability is task-dependent: attention projections are more critical for mathematical reasoning, and sensitivity patterns differ by architecture in logical inference. Third, selective compression achieves Pareto-optimal points inaccessible to uniform methods: R1-Qwen-7B Top-10% on ProofWriter gains +12 pp over FP16 at -9.7% energy, validated on held-out data across five reasoning benchmarks.
Figures & tables
Dataset
Task Type
Split
Samples/Experiment
Experiments
Maximum Tokens.
GSM8K
Arithmetic
test
30 (non-overlap)
8
2,048
FOLIO
Logic/NLI
validation
30 (offset)
8
1,024
MATH-500
Competition math
test
30 (offset)
8
2,048
ProofWriter
Formal deduction
train
30 (offset)
8
1,024
MuSiQue
Multi-hop QA
validation
30 (offset)
8
1,024
Table 1: Dataset Configuration Summary
Condition
Description
FP16 Baseline
Full float16 precision — accuracy upper bound and energy lower bound.
Full INT4
Uniform 4-bit NormalFloat (NF4) quantization via BitsAndBytes across all linear projections.
INT4+Attention
Attention projections ( q, k, v, o ) restored to FP16; MLP projections remain INT4.
INT4+MLP
MLP projections ( gate, up, down ) restored to FP16; attention projections remain INT4.
Selective Comp.
INT4 with top 10%, 20%, 30%, 40% most vulnerable layers restored to FP16 via perturbation sweep rankings.
Table 2: Compression Conditions
DeepSeek-R1-Distill-Llama-8B
DeepSeek-R1-Distill-Qwen-7B
Condition
Acc (%)
Energy (J)
Tokens
Power (W)
Acc (%)
Energy (J)
Tokens
Power (W)
FOLIO
FP16
32.50
2,759
500
182.7
45.83
2,196
454
171.3
Full INT4
36.25
2,824 ∗
504
135.4
44.17
2,043
423
134.3
INT4+Attention
35.42
2,649
488
152.0
45.00
2,079
439
144.6
INT4+MLP
34.58
3,000 ∗
502
162.1
42.92
2,206 ∗
430
150.7
Table 3: Grouped protection results (held-out evaluation split, 50/50 partition). Bold = best INT4 condition per model-dataset pair. ∗ = energy increase relative to FP16. Mean across 8 experiments of 30 samples each.
DeepSeek-R1-Distill-Qwen-7B
DeepSeek-R1-Distill-Llama-8B
Condition
Prot.
FOLIO Acc
GSM8K Acc
FOLIO E (J)
GSM8K E (J)
FOLIO Tok
GSM8K Tok
FOLIO Acc
GSM8K Acc
FOLIO E (J)
GSM8K E (J)
FOLIO Tok
GSM8K Tok
FP16 Reference
all
44.00
94.00
2,301
3,308
460
679
33.33
79.33
2,590
4,314
499
771
Full INT4
0
43.33
93.33
2,125
3,208
425
669
36.67
70.00
2,595
6,197
504
1,092
Top 10%
19/22
38.67
92.00
2,195
3,471
442
691
35.33
70.67
2,562
6,358
504
1,148
Top 20%
39/44
36.67
92.00
2,261
3,513
450
703
34.00
78.00
2,597
6,082
491
1,089
Top 30%
58/67
36.67
92.67
2,221
3,431
435
689
36.67
75.33
2,633
5,794
500
1,038
Table 4: Selective compression: accuracy (%), energy (J/query), output tokens, and power (W) — FOLIO and GSM8K (held-out evaluation split). Bold = best accuracy per model-dataset pair. Shaded row = FP16 reference.
DeepSeek-R1-Distill-Qwen-7B
DeepSeek-R1-Distill-Llama-8B
Condition
Prot.
MATH Acc
ProofW Acc
MATH E (J)
ProofW E (J)
MATH Tok
ProofW Tok
MATH Acc
ProofW Acc
MATH E (J)
ProofW E (J)
MATH Tok
ProofW Tok
FP16 Reference
all
66.25
72.00
7,934
1,931
1,467
391
57.50
34.00
8,092
2,596
1,396
494
Full INT4
0
66.25
82.00
7,519
1,796
1,443
368
56.67
36.00
8,469
2,612
1,508
501
Top 10%
19/22
57.08
84.00
8,095
1,743
1432
354
46.25
32.00
8,519
2,658
1491
509
Top 20%
39/44
57.50
79.33
8,033
1,869
1439
371
49.17
32.67
8,392
2,667
1412
506
Top 30%
58/67
59.17
79.33
7,996
1,868
1298
364
46.67
32.00
7,863
2,744
1440
507
Table 5: Selective compression: accuracy (%), energy (J/query), output tokens, and power (W) — MATH-500 and ProofWriter (held-out evaluation split for ProofWriter; full-dataset results for MATH-500). Bold = best accuracy per model-dataset pair. Shaded row = FP16 reference.
DeepSeek-R1-Distill-Qwen-7B
DeepSeek-R1-Distill-Llama-8B
Condition
Prot.
Acc (%)
Energy (J)
Tokens
Power (W)
Acc (%)
Energy (J)
Tokens
Power (W)
FP16 Reference
all
7.87
2,552
462
181.2
14.31
2,658
475
165.4
Full INT4
0
8.00
2,465
448
147.9
14.51
2,543
471
138.7
Top 10%
19/22
6.53
2,492
462
147.7
11.92
2,736
475
141.3
Top 20%
39/44
5.27
2,430
454
148.3
13.42
2,603
478
139.4
Top 30%
58/67
8.71
2,450
464
154.6
12.88
2,592
481
140.1
Table 6: Selective compression: accuracy (%), energy (J/query), output tokens, and power (W) — MuSiQue (held-out evaluation split). Bold = best accuracy per model. Shaded row = FP16 reference.
Appendix figures & tables5 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 1: Vulnerability heatmap for R1-Qwen-7B all benchmark. Rows = projection types; columns = layer indices (0–27).
Figure 2: Vulnerability heatmap for R1-Llama-8B for all benchmarks. Rows = projection types; columns = layer indices (0-31). The sparser pattern relative to R1-Qwen-7B is consistent with Full INT4 frequently matching FP16 accuracy on Llama-8B.
Model
Dataset
Baseline
Max Drop
Safe Pairs
R1-Llama-8B
FOLIO
40.0%
+ 0.0 pp
224/224
GSM8K
53.3%
+ 13.3 pp
214/224
MATH-500
26.7%
+ 3.3 pp
221/224
ProofWriter
56.7%
+ 36.7 pp
104/224
MuSiQue
0.0%
+ 0.0 pp
224/224
R1-Qwen-7B
FOLIO
43.3%
+ 10.0 pp
175/196
Appendix
Table 7: Per-module vulnerability summary from calibration-split perturbation sweep. Max drop = accuracy drop of most vulnerable (layer, projection) pair. Safe = pairs with zero or negative drop.
Dataset
K %
Top- K
Random- K
Bottom- K
R1-Llama-8B Full INT4 = 37.92%
FOLIO
10
38.33
37.64
40.00
FOLIO
20
38.33
38.61
40.83
FOLIO
30
38.33
14.72
13.33
FOLIO
40
17.50
15.42
9.17
R1-Llama-8B Full INT4 = 73.33%
Appendix
Table 8: Top- K % vs. Random- K % vs. Bottom- K % accuracy (%). Random- K % is mean of 3 seeds. Full INT4 baseline shown for reference.
Model
Dataset
Condition
Δ Acc (pp)
Sig.
Δ E (J)
Sig.
R1-Qwen-7B
FOLIO
Full INT4
− 1.67
n.s.
− 153
†
R1-Qwen-7B
FOLIO
INT4+Attn
− 0.83
n.s.
− 117
n.s.
R1-Qwen-7B
FOLIO
INT4+MLP
− 2.92
n.s.
+ 10
n.s.
R1-Qwen-7B
GSM8K
Full INT4
− 0.42
n.s.
− 19
n.s.
R1-Qwen-7B
GSM8K
INT4+Attn
− 1.25
n.s.
− 187
n.s.
R1-Qwen-7B
GSM8K
INT4+MLP
− 0.42
n.s.
+ 255
n.s.
Appendix
Table 9: Two-sample t -test p -values for accuracy and energy differences between each INT4 condition and FP16 baseline ( n=5 experiments, held-out split). ∗∗∗p<0.001 , ∗∗p<0.01 , ∗p<0.05 , †p<0.10 , n.s. not significant.
Recursive reasoning models solve hard structured tasks with a few million parameters by iterating a latent state, but deploying them on edge hardware means compressing them -- and quantization noise compounds across recursive cycles rather than accumulating over output tokens, so single-pass intuitions fail. Here, we ask what survives. Across a full precision sweep and three tasks, aggressive compression preserves local prediction but destroys global reasoning: pruning, distillation, and linear attention drive puzzle-exact accuracy to zero while cell accuracy holds. Naive INT4 is different: its damage is architectural, striking MLP-mixing recursion but not attention on the same task, and per-channel calibration reverses it without retraining, where quantization-aware training does not. We also introduce carry-trajectory fidelity, the cosine similarity to the full-precision reasoning path, as a label-free signal that predicts both the damage and the recovery before any task evaluation, with a threshold that transfers across tasks. The result is a deployment recipe: flash-streamed embeddings remove a 99.4 MB bottleneck, one recursive cycle matches full-depth accuracy at 6x fewer FLOPs, and calibrated INT4 brings the backbone to 3.3 MB, inside a 4 MB budget.
Pearse Jim, Steven Kolawole, Opegbemi Matthias Busoye +2
Quantization is widely used to reduce the inference cost of large language models, but its effect on reasoning models is not fully captured by final-answer accuracy or per-token latency. We show that low-bit post-training quantization can introduce a hidden test-time compute cost: quantized reasoning models often generate longer chains of thought even when they still answer correctly. Across mathematical reasoning, code generation, scientific question answering, and agentic tool-use benchmarks, we find that INT4/INT3 quantization can preserve accuracy but increase reasoning-token usage, offsetting the expected per-token speedup. To measure this effect, we introduce the CoT Token Inflation Ratio, which compares reasoning length between quantized and full-precision models averaged across all evaluation benchmarks. We further show that token inflation is accompanied by behavioral changes in the reasoning trace, including more intermediate steps and greater semantic repetition. These changes translate into measurable end-to-end real-world serving penalties. Finally, we evaluate mitigation strategies and find that prompting and decoding-time sampling offer inconsistent accuracy-length trade-offs, while quantization-aware training shows more promise in reducing both accuracy degradation and token inflation. Our results suggest that reasoning-token usage should be reported alongside accuracy when evaluating quantized reasoning models.
Xinyu Lian, Walid Krichene, Beichen Huang +4
University of Illinois Urbana-Champaign · Microsoft · Anyscale +1
Large Reasoning Models (LRMs) achieve strong performance on complex tasks by leveraging long Chain-of-Thought (CoT), but often suffer from overthinking, leading to excessive reasoning steps and high inference latency. Existing CoT compression methods struggle to balance accuracy and efficiency, and lack fine-grained, step-level adaptation to redundancy and reasoning bias. Therefore, we propose State-Aware Reasoning Compression with Knowledge Guidance (STACK), a framework that performs step-wise CoT compression by explicitly modeling stage-specific redundancy sources and integrating with a retrieval-augmented guidance. STACK constructs online long-short contrastive samples and dynamically switches between knowledge-guided compression for uncertain or biased reasoning state and self-prompted compression for overly long but confident state, complemented by an answer-convergence-based early stopping mechanism to suppress redundant verification. We further propose a reward-difference-driven training strategy by combining Proximal Policy Optimization (PPO) and Direct Preference Optimization (DPO), enabling models to learn state-conditioned compression strategies. Experiments on three mathematical reasoning benchmarks show that STACK achieves a superior accuracy-efficiency balance, reducing average response length by 59.9% while improving accuracy by 4.8 points over existing methods.
Yi Sui, Chaozhuo Li, Dawei Song
Beijing Institute of Technology, China · Beijing University of Posts and Telecommunications, China · The Open University, UK