ECoM Reasoning — Efficient Chain-of-Modality Reasoning for SLMs

§ 1

Overview

Spoken language models (SLMs) enable natural human-computer interaction, but their reasoning ability still lags behind text-based LLMs, especially on spoken mathematical question answering. A key reason is that SLMs reason over purely verbalized mathematical expressions, which are harder to interpret than symbolic text.

We propose Efficient Chain-of-Modality Reasoning (ECoM Reasoning) — the first framework to introduce compressed reasoning into SLMs. By compressing the textual component so it jointly serves as speech guidance and reasoning representation, ECoM Reasoning improves accuracy while using a dramatically smaller token budget than standard CoM.

Training employs Progressive Compression, a curriculum-based strategy that gradually transitions the model from full-form reasoning to compressed reasoning traces.

+21% vs CoM
no reasoning

+3% vs CoM
full traces

40% text tokens
budget used

ECoM Reasoning Framework overview diagram

Figure 1. The ECoM Reasoning Framework. The text reasoning component is progressively compressed during training, ultimately serving dual roles as both speech guidance and compact reasoning representation.

Progressive Compression training pipeline across three stages

Figure 2. The Progressive Compression training pipeline. Stage 1 trains on direct answers; Stage 2 introduces full reasoning text tokens R′; Stage 3 replaces them with compressed reasoning tokens R̂′, which are then used at inference to guide speech generation.

§2 Token-Level Compression §3 Framework Response Comparison §4 Compression Ratio Ablation

§ 2

Token-Level Compression Examples

Progressive Compression reduces the reasoning trace token-by-token. Each row shows the retained text at a given compression ratio. Highlighted spans are answer-critical tokens preserved across all levels.

Work Rate Problem Example 1

Question

a and b can do a piece of work in 4 days. With the help of c they finish the work in 3 days. c alone can do that piece of work in?

Ground Truth: 12 days

100%

c = 1 / 3 – 1 / 4 = 1 / 12 => 12 days answer : d

80%

c = 1 / 3 – 1 / 4 = 1 12 12 days answer d

60%

= 1 / 3 – 1 4 12 12 days answer d

40%

1 3 1 4 12 12 days answer

20%

3 4 12 days

Multi-Step Arithmetic Example 2

Question

Bobby can deadlift 300 pounds at 13. When he is 18 he can deadlift 100 pounds more than 250% of his previous deadlift. How many pounds did he add per year?

Ground Truth: 110

100%

His new deadlift is 300*2.5+100=850 pounds. So he added 850-300=550 pounds. This took 18-13=5 years. So he added 550/5=110 pounds per year.

80%

new deadlift 300*2.5+100=850 pounds added 850-300=550 took 18-13=5 years added 550/5=110 pounds per year

60%

deadlift 300*2.5+100=850 added 850-300=550 18-13=5 years 550/5=110 pounds

40%

deadlift 300*2.5+100=850 added 18-13=5 years 550/5=110 pounds

20%

300+100 550/5=110 pounds

Olympiad Reasoning Example 3

Question

Problem 3. Vasya solved problems for 15 days — at least one each day. Each day (except the first), if cloudy he solved one more; if sunny, one less. In the first 9 days, Vasya solved 13 problems.

a) What was the weather on the 10th day? How many problems? b) What is the maximum Vasya could solve on the 15th day?

Ground Truth: 7

100%

Answer. a) 10th day cloudy, Vasya solved 2; b) 7. Since 10th day = 2, each subsequent day max +1, in 5 days max 2+5=7 if cloudy 11th–15th.

80%

10th day cloudy Vasya 2 problems b) 7. 10th day 2 each subsequent 1 more 5 days max 2+5=7 cloudy 11th–15th.

60%

10th cloudy Vasya 2 7. Vasya 2 each 1 5 days 2+5=7 cloudy 11th–15th.

40%

10th cloudy Vasya 2 7. 2 1 5 2+5=7 cloudy 11th 15th

20%

10th cloudy Vasya 2 7 5 2+5=7 cloudy 11th 15th

§ 3

Framework Response Comparison

Three frameworks on four question types. Audio outputs are generated speech from each model. CoM Reasoning uses the full chain-of-thought trace; ECoM Reasoning uses a compressed trace at ~40% tokens.

Legend: CoM (no reasoning) CoM Reasoning (full trace) ECoM Reasoning (compressed, ours) ✓ Correct ✗ Wrong

Addition Problem Case 1 · SingleEQ

Question

Jessica spent $10.22 on a cat toy, and a cage cost her $11.73. What was the total cost of Jessica's purchases?

Ground Truth: $21.95

CoM ✗ Wrong

Jessica spent $10.22 on a cat toy and a cage cost her $11.73 what was the total cost of Jessica's purchases? To find the total cost, add cost of cat toy and cage. Cost of cat toy: $10.22. Cost of cage: $11.73. Total cost = $10.22 + $11.73 = $22.00. So, the total cost is $22.00.

CoM Reasoning ✓ Correct

1. Cost of cat toy: $10.22. 2. Cost of cage: $11.73. Starting from hundredths: 2+3=5, tenths: 2+7=9, dollars: 10+11=21. Total = 21.95. The answer is 21.95.

ECoM Reasoning ✓ Correct

cat toy $10.22 cage $11.73 $21.95. The answer is 21.95.

Distance Problem Case 2 · SVAMP

Question

If the cave is 919 feet deep and they need to travel 1307 feet. How far is the end of the cave?

Ground Truth: 2226

CoM ✗ Wrong

If the cave is 919 feet deep and they need to travel 1307 feet how far is the end of the cave? To find the distance from end to starting point: 1307 − 919 = 388 feet.

CoM Reasoning ✗ Wrong

Path = 1307 feet, depth = 919 feet. Horizontal distance x = 1307 − 919 = 388. The answer is 388.

ECoM Reasoning ✓ Correct

cave 919 feet deep 1307 feet end 919 + 1307 = 2226 feet. The answer is 2226.

Code Execution Case 3 · ProgramSynth

Question

Here's a piece of code: sum starts at 0; i goes from 4 to 9; each time, i is added to sum; finally, print sum. What will be printed?

Ground Truth: 39

CoM ✗ Wrong

sum = 0; i = 4; while (i > 0) { sum += i; i-- } print sum. Initialize sum = 0, i = 4. Loop while i > 0: iterations produce sum = 4+3+2+1 = 10.

CoM Reasoning ✗ Wrong

sum = 0; i goes from 4 to 9 each time i added to sum… option a. The answer is 14.

ECoM Reasoning ✓ Correct

sum 4 5 6 7 8 9 = 39. The answer is 39.

Knowledge Question Case 4 · LLaMA-QA

Question

Who wrote the famous book "Pride and Prejudice"?

Ground Truth: Jane Austen

CoM ✓ Correct

Who wrote the famous book "Pride and Prejudice"? The famous book was written by Jane Austen, an English novelist. The novel was first published in 1813 and is considered one of the greatest works of English literature.

CoM Reasoning ✓ Correct

Jane Austen (1775–1817), English novelist. Pride and Prejudice published 1813. Celebrated for social commentary, character development, themes of class and gender. The answer is Jane Austen.

ECoM Reasoning ✓ Correct

Jane Austen. The answer is Jane Austen.

§ 4

Compression Ratio Ablation

Sweeping the compression ratio from 100% (full trace) to 0% (no trace) on ECoM Reasoning. The 40% ratio achieves the best efficiency–accuracy trade-off and is marked as the recommended operating point.

MultiArith Ratio Sweep

Question

A book store had 41 books in the bargain bin. If they sold 33 books, but then put 2 more in the bin, how many books would be in the bin?