[论文阅读] Knowledge Fusion of Large Language Models

Knowledge Fusion of Large Language Models (FuseLLM)

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Methodology

整体Pipeline如下图所示

不同的动物代表不同的LLM。左边第一，第二分别是Ensemble以及Weight Merging方法。最右侧为本文提出的FuseLLM。

• Ensemble: 融合多个models的预测结果，比如求加权平均等。
• Weight Merging：在权重/参数层面融合，但通常仅限于相同架构的模型。
• FuseLLM 主要思想为：融合多个LLMs（可以是不同架构的）的probabilistic matrices，得到Fused Matrix后，喂给Target Model，起到知识蒸馏的作用。

这里面会涉及到一个关键：

• 不同LLM，使用的Tokenizer可能不同，设置也可能不一样（如 model_max_length ），分词结果可能不一样（比如对同一个句子分词，tokens总数不同），使用的Vocabulary也可能不一样，因此生成的probabilistic matrix在维度上可能有所不同，如何解决对齐问题？这个实际上就是 token alignment 问题，本文中着重描述了解决方案。

Definition of Problem

假设我们有一个语料库$\mathcal{C}$，$K$个source LLMs, 对于文本$t\in \mathcal{C}$，经过$K$个LLM处理，可以得到对应的概率分布矩阵 probabilistic distribution matrix： { P t θ j } j = 1 K \{\mathbf{P}^{\theta_j}_t\}^K_{j=1} {Ptθj​​}j=1K​，其中${\theta }_j$表示第$j$个LLM的参数。我们要做的就是将这$K$个概率分布矩阵融合，然后送入Target LLM中辅助训练：
$$\begin{array}{r}{\mathbf{P}}_t=\mathbb{F}\mathrm{usion}({\mathbf{P}}_t^{{\theta }_1},{\mathbf{P}}_t^{{\theta }_2},\dots ,{\mathbf{P}}_t^{{\theta }_K}),\end{array}$$
${\mathbf{P}}_t$即得到的融合概率分布矩阵（Fused Representation Matrix）。

为了将${\mathbf{P}}_t$迁移至target model中，我们假设${\mathbf{Q}}_t$为其输出的representation matrix，则Knowledge Fusion的训练目标为：
$$\begin{array}{r}{\mathcal{L}}_{\mathrm{Fusion}}=-{\mathbb{E}}_{t\sim \mathcal{C}}\left[\mathbb{D}({\mathbf{Q}}_t,{\mathbf{P}}_t)\right].\end{array}$$
其中$\mathbb{D}(\cdot ,\cdot )$表示差异性函数，具体实现可以是KL散度。
整体的模型损失如下：
$$\begin{array}{r}\mathcal{L}=\lambda {\mathcal{L}}_{\mathrm{CLM}}+(1-\lambda ){\mathcal{L}}_{\mathrm{Fusion}}.\end{array}$$
其中${\mathcal{L}}_{\mathrm{CLM}}$表示最原始的ground-truth之间的损失，$\lambda$为系数。

实现细节

Token Alignment

我们假设有两个LLM，使用不同的tokenizer。对同一段文本分词，得到的token序列不同，长度也不同：

如上图，用DeepSeek和TinyLlama各自的分词器分词，得到的结果完全不一样。最终预测的概率分布矩阵也不一样。

Token-Level Alignment

为了解决这个问题，FuseLLM采用基于最小编辑距离Minimal Edit Distance(MinED)的动态规划策略，在token-level实现对齐，以下图为例：

具体实现的源代码other.py如下：

def dtw(series_1, series_2, norm_func=np.linalg.norm):"""Use dynamic time wrapping to align to tokenizers, modified from:https://github.com/talcs/simpledtw/blob/master/simpledtw.py""""""Parameters----------series_1: List[str]blending_input_tokensseries_2: List[str]base_input_tokensnorm_func: functionedit distance evaluation between 2 tokensReturn Values----------matches: List[Tuple]matched pairs between a base token and a blending tokenmatrix[-1, -1]: int the total cost for mapping the two series of tokensmappings_series_1: List[List]mapping from blending tokens to base tokenseg: [0], [1, 2], [3, 4, 5], [6], ...mappings_series_2: List[List]mapping from base tokens to blending tokensmatrix: List[int]the dtw matrix"""matrix = np.zeros((len(series_1) + 1, len(series_2) + 1))matrix[0, :] = np.infmatrix[:, 0] = np.infmatrix[0, 0] = 0for i, vec1 in enumerate(series_1):for j, vec2 in enumerate(series_2):cost = norm_func(vec1, vec2)matrix[i + 1, j + 1] = cost + min(matrix[i, j + 1], matrix[i + 1, j], matrix[i, j])matrix = matrix[1:, 1:]i = matrix.shape[0] - 1j = matrix.shape[1] - 1matches = []mappings_series_1 = [list() for v in range(matrix.shape[0])]mappings_series_2 = [list() for v in range(matrix.shape[1])]while i > 0 or j > 0:matches.append((i, j))mappings_series_1[i].append(j)mappings_series_2[j].append(i)option_diag = matrix[i - 1, j - 1] if i > 0 and j > 0 else np.infoption_up = matrix[i - 1, j] if i > 0 else np.infoption_left = matrix[i, j - 1] if j > 0 else np.infmove = np.argmin([option_diag, option_up, option_left])if move == 0:i -= 1j -= 1elif move == 1:i -= 1else:j -= 1matches.append((0, 0))mappings_series_1[0].append(0)mappings_series_2[0].append(0)matches.reverse()for mp in mappings_series_1:mp.reverse()for mp in mappings_series_2:mp.reverse()return matches, matrix[-1, -1], mappings_series_1, mappings_series_2, matrix

Logit-Level Alignment

利用该对齐结果，将不同LLMs得到的representation matrix对齐。关键代码other.py如下：

def transform_step_logits(base_model_tokenizer: transformers.tokenization_utils_base.PreTrainedTokenizerBase,blending_model_tokenizer: transformers.tokenization_utils_base.PreTrainedTokenizerBase,base_model_vocab: Dict[str, int],base_model_input_ids: List[int],blending_model_input_ids: List[int],blending_model_per_step_logits: List[List[float]],blending_model_per_step_indices: List[List[int]],vocab_align_type: str = "hard",blending_to_base_mapping: Dict[str, str] = None,
):"""Align blending model per step logits & indices with base model.""""""Parameters----------base_model_tokenizer: transformers.tokenization_utils_base.PreTrainedTokenizerBaseblending_model_tokenizer: transformers.tokenization_utils_base.PreTrainedTokenizerBasebase_model_vocab: Dict[str, int]mapping token to id using vocabulary of base modelbase_model_input_ids: List[int]ids of base_model_input_tokensblending_model_input_ids: List[int]ids of blending_model_input_tokensblending_model_per_step_logits: List[List[float]]logits for each token in blending_model_input_tokens blending_model_per_step_indices: List[List[int]]indices corresponding to logits for each token in blending_model_input_tokens vocab_align_type: str = "hard"blending_to_base_mapping: Dict[str, str] = Nonemapping each blending token to its corresponding base token Return Values----------aligned_blending_model_per_step_logits: List[List[float]]aligned logits for each token in base_model_input_tokens for the FuseLLM trainingaligned_blending_model_per_step_indices: List[List[int]]aligned indices corresponding aligned logits for each token in base_model_input_tokens for the FuseLLM training. Use the base model vocabulary to look up the token."""base_model_tokens = base_model_tokenizer.convert_ids_to_tokens(base_model_input_ids)blending_model_tokens = blending_model_tokenizer.convert_ids_to_tokens(blending_model_input_ids)base_model_special_token = TOKENIZER_TO_SPECIAL_TOKEN[base_model_tokenizer.__class__]blending_model_special_token = TOKENIZER_TO_SPECIAL_TOKEN[blending_model_tokenizer.__class__]def dist_fn(a, b):"""Calculate editdistance between two tokens, a is from blending model, b is from base model."""aa = a.replace(blending_model_special_token, "")bb = b.replace(base_model_special_token, "")dist = editdistance.eval(aa, bb)return dist_, _, _, base_to_blending, _ = dtw(blending_model_tokens, base_model_tokens, norm_func=dist_fn)aligned_blending_model_per_step_logits, aligned_blending_model_per_step_indices = ([],[],)for i, blending_idx in enumerate(base_to_blending):aligned_blending_model_per_step_logit = []aligned_blending_model_per_step_index = []if len(blending_idx) == 1:  # one base token map to one blending tokenj = blending_idx[0]base_token = base_model_tokens[i]blending_token = blending_model_tokens[j].replace(blending_model_special_token, base_model_special_token)if ((blending_model_tokenizer.__class__== transformers.GPTNeoXTokenizerFastor blending_model_tokenizer.__class__== transformers.GPT2TokenizerFast)and i == 0and base_token.startswith(base_model_special_token)and not blending_token.startswith(base_model_special_token)):blending_token = (base_model_special_token + blending_token)  # special case for mptif vocab_align_type == "hard":if (base_token == blending_token):  # find the aligned mapping, use the corresponding logits# the logits and indices at this stepfor blending_logit, blending_index in zip(blending_model_per_step_logits[j],blending_model_per_step_indices[j],):# the token corresponds to the logit and indicesblending_t = blending_model_tokenizer.convert_ids_to_tokens([blending_index])[0].replace(blending_model_special_token, base_model_special_token)if blending_t in base_model_vocab:aligned_index = base_model_vocab[blending_t]  # the index of the token in base model vocabif (aligned_indexnot in aligned_blending_model_per_step_index):aligned_blending_model_per_step_index.append(aligned_index)aligned_blending_model_per_step_logit.append(blending_logit)else:  # find error aligned mapping, use the one-hot logitsaligned_blending_model_per_step_index.append(base_model_vocab[base_token])aligned_blending_model_per_step_logit.append(1.0)elif vocab_align_type == "soft":if (base_token == blending_token) or (blending_token in blending_to_base_mappingand base_token == blending_to_base_mapping[blending_token]):  # find the aligned mapping, use the corresponding logits# the logits and indices at this stepfor blending_logit, blending_index in zip(blending_model_per_step_logits[j],blending_model_per_step_indices[j],):# the token corresponds to the logit and indicesblending_t = blending_model_tokenizer.convert_ids_to_tokens([blending_index])[0].replace(blending_model_special_token, base_model_special_token)blending_t = blending_to_base_mapping[blending_t]if blending_t in base_model_vocab:aligned_index = base_model_vocab[blending_t]  # the index of the token in base model vocabif (aligned_indexnot in aligned_blending_model_per_step_index):aligned_blending_model_per_step_index.append(aligned_index)aligned_blending_model_per_step_logit.append(blending_logit)else:logger.warning(f"blending_t: {blending_t} not in base_model_vocab!")else:  # find error aligned mapping, use the one-hot logitsaligned_blending_model_per_step_index.append(base_model_vocab[base_token])aligned_blending_model_per_step_logit.append(1.0)else:logger.warning(f"The vocab_align_type: '{vocab_align_type}' is not support!")raise NotImplementedErrorelse:  # one base token map to multiple blending token, in this case only fit base token. use the one-hot logitsbase_token = base_model_tokens[i]aligned_blending_model_per_step_index.append(base_model_vocab[base_token])aligned_blending_model_per_step_logit.append(1.0)aligned_blending_model_per_step_indices.append(aligned_blending_model_per_step_index)aligned_blending_model_per_step_logits.append(aligned_blending_model_per_step_logit)return (aligned_blending_model_per_step_logits,aligned_blending_model_per_step_indices,)

Fusion Strategies:

得到对其的representation matrix以后，由于不同的LLM具有不同的性能，可以使用概率分布矩阵与ground-truth之间的交叉熵损失(CE loss)评估LLM的优劣，再根据此判断选择哪些LLM参与知识融合。CE loss越低，证明模型效果更好。具体而言，作者提出了两种Fusion Strategy:

1. MinCE: 仅选择CE loss最小的representation matrix用于知识融合。
2. AvgCE: 基于各个模型的CE loss，采用多个representation matrices的加权平均，用于知识融合。

整体的算法流程如下：

• 注：这里Eq.5实际是本文中上述的Eq.3

一些思考

本文的思路是将多个LLMs输出的概率分布矩阵视为知识，将知识融合后，送入target LLM进行训练，以达到融合多种模型知识，提升目标模型性能的目的。但在实际的实现当中我们会发现，logit-level的alignment，要么是直接采用blending_model_per_step_logits/indices，要么直接用ground-truth one-hot作为融合后的知识，而没有充分评估logit-level中，blending/base_model_per_step_logits之间的差异性。为此，Probabilistic Token Alignment for Large Language Model Fusion提出采用Probabilistic Token Alignment方法，在logit-level实现alignment。