The strategies for Reliable Long-form Transcription in whisper.cpp differs from OpenAI's Whisper

[bobqianic]

I suddenly wanted to take a closer look at the OpenAI Whisper paper, and one section that caught my attention is the one I highlighted in yellow. Then I checked the whisper.cpp code and found that there are mainly two issues: the size of the temperature increment, and the method of calculating the compression ratio. The temperature in whisper.cpp increases by 0.4 each time instead of the 0.2 mentioned in the paper. Additionally, whisper.cpp uses entropy as a substitute for the gzip compression ratio, while OpenAI Whisper actually compresses the text and calculates the real gzip compression ratio. @ggerganov

Temprature:

whisper/transcribe.py

whisper.cpp/whisper.cpp

Line 3833 in 0de8582

/*.temperature_inc =*/ 0.4f,

whisper.cpp/whisper.cpp

Lines 4545 to 4554 in 0de8582

	// a set of temperatures to use
	// [ t0, t0 + delta, t0 + 2*delta, ..., < 1.0f + 1e-6f ]
	std::vector<float> temperatures;
	if (params.temperature_inc > 0.0f) {
	for (float t = params.temperature; t < 1.0f + 1e-6f; t += params.temperature_inc) {
	temperatures.push_back(t);
	}
	} else {
	temperatures.push_back(params.temperature);
	}

Gzip Compression Ratio:

whisper/utils.py

whisper.cpp/whisper.cpp

Lines 4326 to 4372 in 0de8582

	static void whisper_sequence_score(
	const struct whisper_full_params & params,
	whisper_sequence & sequence) {
	if (sequence.result_len == 0) {
	return;
	}
	double result = 0.0f;
	for (int i = 0; i < sequence.result_len; ++i) {
	result += sequence.tokens[i].plog;
	}
	sequence.sum_logprobs = result;
	sequence.avg_logprobs = result/sequence.result_len;
	double penalty = sequence.result_len;
	if (params.length_penalty > 0.0f) {
	penalty = pow((5.0 + penalty)/6.0, params.length_penalty);
	}
	sequence.score = result/penalty;
	// compute the entropy of the sequence of the last 32 tokens
	{
	const int n = 32;
	int cnt = 0;
	double entropy = 0.0f;
	std::map<whisper_token, int> token_counts;
	for (int i = std::max(0, sequence.result_len - n); i < sequence.result_len; ++i) {
	token_counts[sequence.tokens[i].id]++;
	cnt++;
	}
	for (const auto & kv : token_counts) {
	const auto p = kv.second/(double)cnt;
	entropy -= p*log(p);
	//WHISPER_PRINT_DEBUG("entropy: %d %f %f, count %d\n", kv.first, p, log(p), kv.second);
	}
	sequence.entropy = entropy;
	}
	}

[ggerganov]

The reason for the temp increase to be 0.4 is that it is faster processing when the fallback triggers. After we add efficient batched decoding, we will reduce it to 0.2.

We don't use gzip because it is not trivial to implement the compression. Entropy estimation works in a similar way and it's much easier to implement

[bobqianic]

We don't use gzip because it is not trivial to implement the compression. Entropy estimation works in a similar way and it's much easier to implement

In some scenarios, this assertion doesn't hold. Consider the following case. While the entropy of this segment is OK, the compression ratio does not meet expectations.

[best_decoder.sequence.entropy: 3.149363]
[00:33:03.860 --> 00:33:05.860]   I don't know who they are, but I'm sure they're going to tell us something.
[00:33:05.860 --> 00:33:07.860]   I don't know who they are, but I'm sure they're going to tell us something.
[00:33:07.860 --> 00:33:09.860]   I don't know who they are, but I'm sure they're going to tell us something.
[00:33:09.860 --> 00:33:11.860]   I don't know who they are, but I'm sure they're going to tell us something.
[00:33:11.860 --> 00:33:13.860]   I don't know who they are, but I'm sure they're going to tell us something.
[00:33:13.860 --> 00:33:15.860]   I don't know who they are, but I'm sure they're going to tell us something.
[00:33:15.860 --> 00:33:17.860]   I don't know who they are, but I'm sure they're going to tell us something.
[00:33:17.860 --> 00:33:19.860]   I don't know who they are, but I'm sure they're going to tell us something.
[00:33:19.860 --> 00:33:21.860]   I don't know who they are, but I'm sure they're going to tell us something.

gzip compression ratio is 8.0357 >> 2.4

[_286_][_500_][_380_][_458_][_261_][_1289_][_436_][_366_][_11_][_457_][_286_][_478_][_988_][_436_][_434_][_516_][_281_][_980_][_505_][_746_][_13_]

I don't know who they are, but I'm sure they're going to tell us something.

[_286_][_500_][_380_][_458_][_567_][_436_][_366_][_11_][_457_][_286_][_478_][_988_][_436_][_434_][_516_][_281_][_980_][_505_][_746_][_13_]

I don't know who they are, but I'm sure they're going to tell us something.

Possible reasons:

1. Various combinations of tokens can yield identical text.
2. Tokens are created during the training of BPE, and since they are already in a highly compressed form, entropy of tokens doesn't serve as a reliable measure.
3. The approach adopted for calculating entropy in whisper.cpp is not sufficient. As highlighted by C.E. Shannon in A Mathematical Theory of Communication, the formula $$H(S) = -\sum_{i=1}^{n} p_i \log_2(p_i)$$ is applicable solely to sequences where successive symbols are independent.