SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Agreement calculation. We define the agreement between two types of judges as the probability of randomly selected individuals (but not identical) of each type agreeing on a randomly selected question. For example, if we are comparing GPT-4 and Claude, the agreement is the probability of GPT-4 and Claude agreeing on the vote for a randomly selected question. If we are comparing GPT-4 and humans, the agreement is the probability of GPT-4 and a randomly selected human agreeing on the vote for a randomly selected question. The agreement among humans themselves is the probability of two randomly selected but not identical humans agreeing on the vote for a randomly selected question.
Note that the agreement among humans could be a lower estimation compared to the agreement of GPT4 and humans. Consider three humans who voted "A", "A", and "B" for a question, respectively. The agreement among them is only  $\frac{1}{3}$ , as there are three pairs  $(\mathrm{A}, \mathrm{A})$ ,  $(\mathrm{A}, \mathrm{B})$ , and  $(\mathrm{A}, \mathrm{B})$ . But the agreement between GPT4 and those three is  $\frac{2}{3}$  if GPT4 voted "first" and  $\frac{1}{3}$  otherwise.
Therefore, to have a more comprehensive understanding of what happened, we introduce a new judge type called human-majority, which considers the majority of human votes for each question. The agreement between GPT4 and human-majority is then calculated as the probability of GPT4 agreeing with the majority of human votes on a randomly selected question. The upper bound of the agreement between GPT-4 and humans is the agreement between human-majority and human. When there is no majority vote for a question, the agreement is counted by an even split. For example, if there are an equal number of "A" and "B" human votes for a question, and GPT4 votes "A", the agreement is counted as  $\frac{1}{2}$  on this question.
More results. Table 13 shows more agreement results on MT-bench. In addition to expert labelers (denoted as "Human"), we also include author votes (denoted as "Author").
D.4 Category-wise scores with single-answer grading
We use single-answer grading to evaluate 6 models on MT-bench and plot the category-wise scores in Figure 20.
Table 13: Agreement between two types of judges on MT-bench. "G4-P" and "G4-S" denote GPT-4 with pairwise comparison and single-answer grading, respectively. "C" denotes Claude. "Human" denotes expert labelers (excluding authors). 'Human-M' denotes the majority vote of humans. The single-answer grading can be converted into pairwise comparison results for calculating the agreement. We report two setups: "S1" includes non-tie, tie, and inconsistent (due to position bias) votes and counts inconsistent as a tie; "S2" only includes non-tie votes. The agreement between two random judges under each setup is denoted as "R=". The top value in each cell is the agreement, and the bottom gray value is #votes.
Setup
Judge	S1 (R = 33%)	S2 (R = 50%)
G4-S	C	Author	Human	Human-M	G4-S	C	Author	Human	Human-M
G4-P	70%	63%	69%	66%	67%	97%	94%	92%	85%	85%
1138	1198	345	1343	821	662	582	201	859	546
G4-S	-	66%	67%	60%	60%	-	90%	94%	85%	85%
1136	324	1280	781	563	175	739	473
C	-	-	58%	54%	55%	-	-	89%	85%	86%
343	1341	820	141	648	414
Author	-	-	69%	65%	55%	-	-	87%	83%	76%
49	428	93	31	262	46
Human	-	-	-	63%	81%	-	-	-	81%	90%
721	892	479	631
(a) First Turn
Setup
Judge	S1 (R = 33%)	S2 (R = 50%)
G4-S	Author	Human	Human-M	G4-S	Author	Human	Human-M
G4-P	70%	66%	66%	68%	95%	88%	85%	85%
1161	341	1325	812	727	205	864	557
G4-S	-	65%	59%	61%	-	89%	84%	85%
331	1285	783	193	776	506
Author	-	67%	68%	63%	-	87%	86%	84%
49	413	87	31	273	54
Human	-	-	67%	83%	-	-	82%	91%
707	877	474	629
Figure 20: Category-wise scores of 6 models on MT-bench.
E Training Details of Vicuna Models
Vicuna is created by fine-tuning a LLaMA base model using user-shared conversations gathered from ShareGPT.com with its public APIs. ShareGPT is a website where users can share their ChatGPT conversations. To ensure data quality, we convert the HTML back to markdown and filter out some inappropriate or low-quality samples, which results in 125K conversations after data cleaning. We then divide lengthy conversations into smaller segments that fit the model's maximum context length.
We construct three training datasets with different scales from this cleaned ShareGPT dataset. Their statistics are in Table 8, where we also compare it with Alpaca [38] dataset. "All" is the full dataset. "Single" only includes the first turn of each conversation. "Selected" is a small high-quality dataset of 3K sequences. To construct the "Selected" dataset, we pick sequences that include at least 3 turns of conversations generated by GPT-4 and run a clustering algorithm to divide them into 3K clusters and pick the centroid of each cluster.
All models (Vicuna-7B/13B) are trained with the same hyperparameters: global batch size=128, learning=2e-5, epochs=3, seq length=2048. Except for "Selected", which we train for 5 epochs. The training code is built on top of the Alpaca code but additionally handles multi-turn conversations. The training is done with 8x A100 GPUs. The longest single training run takes around 2 days. We utilize SkyPilot [49] managed spot instances for saving training costs and FlashAttention [11] for memory optimizations. The training code is available at https://github.com/lm-sys/FastChat.
Table 14: Dataset statistics
Dataset Name	Alpaca	Selected	Single	All
#Token	4.4M	4.8M	184M	370M
#Sequence	52K	3K	257K	257K
Avg. turns of conversation	1.0	4.0	1.0	2.9
Avg. response length (token)	65	343	473	373
In this study, we use more data (125K) than the version in our earlier blog post (70K).
F Exploring Vicuna as a judge
In this paper, we mostly evaluate the ability of close-sourced models such as GPT-4 as a proxy for human evaluations. However, model services such as GPT-4 can also become expensive with a growing number of evaluations. On the other hand, popular open-sourced LLMs, e.g. Vicuna-13B shows strong language understanding capability, and are much cheaper than close-sourced LLMs. In this section, we further explore the potential of using Vicuna-13B as a more cost-friendly proxy.
F.1 Zero-Shot Vicuna
When using as-it-is (zero-shot), Vicuna-13B noticeably suffers from limitations we discuss, e.g. position bias. As shown in Table 15, Vicuna-13B has a consistency rate from  $11.2\%$  to  $16.2\%$  across different prompt templates, much lower than all the closed-sourced models. In addition, it has a high error rate (from  $22.5\%$  to  $78.8\%$ ) because of its weaker instruction-following capability. In many scenarios, Vicuna-13B provides responses such as "Answer A is better than answer B", without following the pre-defined template. These responses are rendered as natural languages and are difficult to be parsed automatically, making the model less useful in a scalable and automatic evaluation pipeline.
F.2 Arena Fine-tuned Vicuna
Training Due to the incapability of the zero-shot Vicuna-13B model, we further finetune the model with human votes from Chatbot Arena. Specifically, we randomly sample 22K single-turn votes from the arena, covering all models supported by the time of this paper submission (GPT-4, GPT-3.5, Claude-v1, Vicuna-13b, Vicuna-7b, Koala-13B, Alpaca-13B, LLaMA-13B, Dolly-12B, FastChat-T5, RWKV-4-Raven, MPT-Chat, OpenAssistant, ChatGLM, and StableLM), to expose the model with a wider range of chatbot outputs and human preferences. We use 20K votes for training, and 2K for validation. To address the aforementioned weak instruction following problem, we formulate the problem as a 3-way sequence classification problem. Thus, the model simply needs to predict which one of the chat-bot outputs is better (or tie), without needing to exactly following the provided answer template. In particular, we construct an input by using the default prompt and the two model answers. The labels are A, B, and tie (including both-bad-vote and tie-vote). We train for 3 epochs with a cosine learning rate scheduler and a 2e-5 maximum learning rate. We use the 2K validation dataset to choose hyper-parameters, and test on the same 3K dataset in the main body of the paper.
Position bias results The results for position bias are provided in Table 15. The consistency improves significantly from  $16.2\%$  to  $65.0\%$ . Due to the classification formulation, every output is recognizable (error rate  $0\%$ ). In addition, we measure the classification accuracy over the test dataset.
Agreement results It achieves  $56.8\%$  when including all three labels, and  $85.5\%$  when excluding tie predictions and labels, significantly outperforming random guesses of  $33\%$  and  $50\%$  respectively, and show positive signals to match GPT-4 (66% and 87% respectively). In conclusion, a further fine-tuned Vicuna-13B model shows strong potential to be used as a cheap open-sourced replacement for expensive closed-sourced LLMs. A similar conclusion is also found by a concurrent paper[42].
Table 15: Position bias of the Vicuna-13B model without and with further fine-tuning. We denote them as Vicuna-13B-Zero-Shot and Vicuna-13B-Fine-Tune respectively. Consistency is the percentage of cases where a judge gives consistent results when swapping the order of two assistants. "Biased toward first" is the percentage of cases when a judge favors the first answer. "Error" indicates wrong output formats. The largest number in each column is in bold.
Judge	Prompt	Consistency	Biased toward first	Biased toward second	Error
Vicuna-13B-Zero-Shot	default	15.0%	53.8%	8.8%	22.5%
Rename	16.2%	12.5%	40.0%	31.2%
score	11.2%	10.0%	0.0%	78.8%
Vicuna-13B-Fine-Tune	default	65.0%	27.5%	7.5%	0.0%