{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/pldr-llms-learn-a-generalizable-tensor","title":"PLDR-LLMs Learn A Generalizable Tensor Operator That Can Replace Its Own Deep Neural Net At Inference","arxiv_id":"2502.13502","date":"2025-02-19","proceeding":null,"authors":["Burc Gokden"],"abstract":"We show that Large Language Model from Power Law Decoder Representations (PLDR-LLM) is a foundational model whose deductive outputs are invariant tensors up to a small perturbation. PLDR-LLM learns a singularity condition for the deductive outputs that enable the once-inferred energy-curvature tensor $\\mathbf{G}_{LM}$ to replace the deep neural network of power law graph attention (PLGA) generating the deductive outputs at inference. We demonstrate that a cache for $\\mathbf{G}_{LM}$ (G-cache) and KV-cache can be implemented in a straightforward manner to improve the inference time. The invariance and generalizable nature of deductive outputs is at a very high fidelity where deductive outputs have same RMSE and determinant values up to 15 decimal places after caching, and zero-shot benchmark scores remain unchanged. Ablation studies show that learned deductive outputs have distinct loss and accuracy characteristics from models pretrained with transferred, randomly initialized or identity tensors as a constant tensor operator and an LLM with scaled-dot product attention (SDPA) is a special case of PLDR-LLM where $\\mathbf{G}_{LM}$ is predefined as identity. The observed invariance characteristic introduces a novel asymmetry between training and inference phases with caching. We outline observed common characteristics of the deductive outputs for the learned singularity condition. We provide an implementation of a training and inference framework for PLDR-LLM with KV-cache and G-cache.","url_abs":"https://arxiv.org/abs/2502.13502v1","url_pdf":"https://arxiv.org/pdf/2502.13502v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"pldr-llms-learn-a-generalizable-tensor","repo_url":"https://github.com/burcgokden/PLDR-LLM-with-KVG-cache","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"graph-attention","task_name":"Graph Attention"},{"task_slug":"large-language-model","task_name":"Large Language Model"}],"methods":[{"method_slug":"attention","method_name":"Attention"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}