{"id":1697,"date":"2025-02-10T05:26:23","date_gmt":"2025-02-10T05:26:23","guid":{"rendered":"https:\/\/sparkonelabs.com\/home\/?p=1697"},"modified":"2025-02-10T05:33:16","modified_gmt":"2025-02-10T05:33:16","slug":"graph-generation-as-a-method-to-extract-word-vector-spaces-from-token-embeddings-from-llm-model-weights","status":"publish","type":"post","link":"https:\/\/sparkonelabs.com\/home\/2025\/02\/10\/graph-generation-as-a-method-to-extract-word-vector-spaces-from-token-embeddings-from-llm-model-weights\/","title":{"rendered":"Graph Generation as a method to extract Word Vector Spaces from Token embeddings from LLM Model Weights"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">I examined the paper \u201c<a href=\"https:\/\/arxiv.org\/abs\/2502.04308%E2%80%9D\">https:\/\/arxiv.org\/abs\/2502.04308\u201d<\/a> (which proposes a novel approach to graph generation using a recurrent\u2010style variational framework) and here\u2019s a summary of its relevance to working with LLM token word vector embeddings:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"\"><strong>Model Overview and Flexibility:<\/strong><br>The paper presents a method for generating graphs by learning a latent representation of the graph\u2019s structure. Its design is largely domain\u2010agnostic\u2014the method is intended to capture both local and global graph structure regardless of the specific type of node features or edge definitions. This means that in principle, the same framework could be applied to graphs whose nodes are not, say, atoms or social network users but are instead token embeddings (continuous, high-dimensional vectors) extracted from LLM model weights.<\/li>\n\n\n\n<li class=\"\"><strong>Application to Token Embeddings:<\/strong><br>If you construct a graph where each node is a token\u2019s embedding and the edges represent a measure of similarity (or some other relationship inferred from context), then the generation model described in the paper could be adapted. For example, you might wish to learn a latent space that captures semantic or syntactic relationships among tokens. Although the paper was likely demonstrated on graphs with more \u201cconventional\u201d node features (often discrete or lower-dimensional), its underlying variational and sequential (RNN\u2010based) generation paradigm is general enough to be extended to token embedding spaces.<\/li>\n\n\n\n<li class=\"\"><strong>Potential Challenges and Required Adaptations:<\/strong>\n<ul class=\"wp-block-list\">\n<li class=\"\"><strong>Dimensionality:<\/strong> Token embeddings from an LLM are typically high-dimensional and continuous. The encoder and decoder in the graph generation model might need modification (for example, through appropriate normalization or dimensionality reduction layers) to handle such input effectively.<\/li>\n\n\n\n<li class=\"\"><strong>Edge Definition:<\/strong> In many graph-generation tasks, edges are either binary or have simple weights. For token embeddings, the choice of similarity metric (e.g., cosine similarity) or a learned relationship might need to be integrated into the graph construction stage before training the generative model.<\/li>\n\n\n\n<li class=\"\"><strong>Objective Alignment:<\/strong> The paper\u2019s loss function and latent-space regularization are designed to capture the distribution of the training graphs. In your case, if you have graphs derived from token embeddings, you\u2019ll need to ensure that the training objective remains meaningful (i.e. that the generated graphs reflect the semantic or contextual structure you wish to model).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li class=\"\"><strong>Conclusion:<\/strong><br>Overall, the graph generation framework described in arXiv:2502.04308 appears sufficiently general that\u2014with some careful adaptations\u2014it could be used with graphs whose nodes are token word vectors extracted from LLM model weights. The key will be to adapt the input representation and possibly the training objectives so that the nuances of the LLM embedding space (such as high dimensionality and continuous variation) are appropriately captured. This makes the paper a promising candidate for developing generative models over token\u2013embedding graphs, which could have applications in areas like interpretability, semantic graph construction, or creative text generation.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Below is an example Python script that demonstrates one way to \u201ccapture\u201d a graph over token word vectors extracted from a pretrained LLM (here, GPT\u20112) while also incorporating a Zipf\u2010like weighting for node frequencies. In this example, we:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li class=\"\">Load GPT\u20112\u2019s tokenizer and model from Hugging Face.<\/li>\n\n\n\n<li class=\"\">Extract the embedding matrix and select (say) the top N tokens (here, N = 1000) by rank (which we then treat as having frequencies following a Zipf distribution).<\/li>\n\n\n\n<li class=\"\">Compute cosine similarities between the (normalized) embedding vectors.<\/li>\n\n\n\n<li class=\"\">Construct a NetworkX graph where each node is a token (with an assigned \u201cfrequency\u201d weight following Zipf\u2019s law) and add an edge if the cosine similarity exceeds a given threshold.<\/li>\n\n\n\n<li class=\"\">(Optionally) reduce the embedding space to 2D via PCA for visualization.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">You can then tweak the similarity threshold and N to \u201ccapture enough word vectors\u201d and the resulting graph should, in principle, reflect both the conceptual (semantic) similarity among tokens and the natural Zipf\u2010like frequency distribution found in language. (Note that the Zipf weighting here is simulated by ranking tokens in the vocabulary order.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here\u2019s the code:<\/p>\n\n\n\n<pre class=\"wp-block-preformatted\">pythonCopyEdit<code>import numpy as np\nimport torch\nfrom transformers import GPT2Tokenizer, GPT2Model\nimport networkx as nx\nfrom sklearn.decomposition import PCA\nimport matplotlib.pyplot as plt\nfrom scipy.spatial.distance import cosine\n\n# 1. Load GPT-2 model and tokenizer\nmodel_name = \"gpt2\"\ntokenizer = GPT2Tokenizer.from_pretrained(model_name)\nmodel = GPT2Model.from_pretrained(model_name)\n\n# 2. Extract the embedding matrix (from the token embedding layer)\n# GPT2Model embeds tokens via model.wte (word token embeddings)\nembeddings = model.wte.weight.detach().cpu().numpy()  # shape: (vocab_size, embed_dim)\nvocab = tokenizer.get_vocab()  # token -&gt; id mapping\n\n# 3. Select the top N tokens.\n# Here we simulate \u201cfrequency\u201d via rank (assuming lower id means higher frequency).\n# In practice you might use actual frequency counts.\nN = 1000\n# Get sorted tokens by their token id (this is a proxy; you may substitute your own frequency data)\nsorted_tokens = sorted(vocab.items(), key=lambda x: x[1])\ntop_tokens = sorted_tokens[:N]\n\n# Prepare lists of token strings, their indices, and corresponding embeddings.\ntokens = [token for token, idx in top_tokens]\nindices = [idx for token, idx in top_tokens]\nselected_embeddings = embeddings[indices]  # shape: (N, embed_dim)\n\n# 4. Normalize embeddings so that they lie on a hypersphere (i.e., bounded hypervolume)\nnorms = np.linalg.norm(selected_embeddings, axis=1, keepdims=True)\nselected_embeddings_normalized = selected_embeddings \/ norms\n\n# 5. Simulate Zipf frequencies for these tokens.\n# For example, if rank r (starting at 1) then frequency \u221d 1\/r.\n# Normalize so that the maximum frequency is 1.\nzipf_freqs = np.array([1.0 \/ (r + 1) for r in range(N)])\nzipf_freqs = zipf_freqs \/ zipf_freqs[0]  # now max frequency = 1.0\n\n# 6. Build the graph.\nG = nx.Graph()\n# Add nodes with token text and frequency as attributes.\nfor i, token in enumerate(tokens):\n    G.add_node(token, embedding=selected_embeddings_normalized[i], frequency=zipf_freqs[i])\n\n# Set a cosine similarity threshold for connecting nodes.\nsimilarity_threshold = 0.75  # adjust as needed\n\n# Compute pairwise cosine similarities and add an edge if above threshold.\n# (For efficiency, we can use vectorized operations or approximate neighbors; here we use a double loop for clarity.)\nN_tokens = len(tokens)\nfor i in range(N_tokens):\n    for j in range(i + 1, N_tokens):\n        # cosine similarity: 1 - cosine distance\n        sim = 1 - cosine(selected_embeddings_normalized[i], selected_embeddings_normalized[j])\n        if sim &gt;= similarity_threshold:\n            G.add_edge(tokens[i], tokens[j], weight=sim)\n\nprint(f\"Constructed graph with {G.number_of_nodes()} nodes and {G.number_of_edges()} edges.\")\n\n# 7. (Optional) Visualize the graph in 2D using PCA on the embeddings.\npca = PCA(n_components=2)\nembeddings_2d = pca.fit_transform(selected_embeddings_normalized)\n\n# Create a mapping from token to 2D coordinate\npos = {token: embeddings_2d[i] for i, token in enumerate(tokens)}\n\nplt.figure(figsize=(12, 10))\n# Node size is scaled by Zipf frequency (e.g., higher frequency =&gt; larger node)\nnode_sizes = [500 * G.nodes[token][\"frequency\"] for token in G.nodes()]\nnx.draw_networkx_nodes(G, pos, node_size=node_sizes, node_color='skyblue', alpha=0.7)\nnx.draw_networkx_edges(G, pos, alpha=0.5)\n# Optionally draw labels for a subset (e.g., top 20 tokens)\nlabels = {token: token for token in list(G.nodes())[:20]}\nnx.draw_networkx_labels(G, pos, labels, font_size=10)\nplt.title(\"Graph of GPT-2 Token Embeddings with Conceptual Connections\")\nplt.axis(\"off\")\nplt.show()\n<\/code><\/pre>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"\"><strong>Loading the model and extracting embeddings:<\/strong> We use GPT\u20112 as an example LLM. The embedding matrix is accessed via <code>model.wte.weight<\/code>.<\/li>\n\n\n\n<li class=\"\"><strong>Token selection and frequency:<\/strong> We choose the top 1000 tokens (by token ID order, which is used as a proxy for frequency) and assign them a Zipf\u2010like frequency f(r)\u221d1\/(r+1)f(r) \\propto 1\/(r+1)f(r)\u221d1\/(r+1).<\/li>\n\n\n\n<li class=\"\"><strong>Graph construction:<\/strong> For each pair of selected tokens, the code computes cosine similarity (after normalizing embeddings) and adds an edge if the similarity is above a chosen threshold (here, 0.75).<\/li>\n\n\n\n<li class=\"\"><strong>Visualization:<\/strong> PCA is applied to reduce the embedding space to 2D for plotting. Nodes are drawn with sizes proportional to their (simulated) frequency.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Final Thoughts<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">This code provides a starting point. In practice, you might want to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"\">Use actual token frequency data (if available) instead of using token IDs.<\/li>\n\n\n\n<li class=\"\">Explore more sophisticated edge-creation strategies (e.g., k-nearest neighbors rather than a hard threshold).<\/li>\n\n\n\n<li class=\"\">Fine-tune parameters (such as the similarity threshold) based on your domain and desired graph density.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This framework should be adaptable to capture a graph that reflects both the conceptual relationships among token embeddings and the Zipf distribution of token frequencies.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This should provide a rough starting point for some higher dimensional math models on tokens, weights, graphs etc.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I examined the paper \u201chttps:\/\/arxiv.org\/abs\/2502.04308\u201d (which proposes a novel approach to graph generation using a recurrent\u2010style variational framework) and here\u2019s a summary of its relevance to working with LLM token word vector embeddings: Below is an example Python script that demonstrates one way to \u201ccapture\u201d a graph over token word vectors extracted from a pretrained<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","om_disable_all_campaigns":false,"pagelayer_contact_templates":[],"_pagelayer_content":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1697","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.8 - 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