Project summary

This project aims to develop and theoretically validate a "rank-adaptive, high-efficiency learning algorithm" that reduces GPU power consumption and computational resources during the training and inference of large language models (LLMs). It applies the theory of local empirical processes and the SVD prediction distortion bounds obtained in our manuscript submitted to IEEE Transactions on Information Theory (TIT), 'Rank-Adaptive Local Empirical Processes in Low-Rank Attention' (under review) (https://doi.org/10.5281/zenodo.23147548).

In modern Transformer training, the huge GPU power usage and excessive parameter computation have become serious environmental and economic challenges. In this study, we leverage the algebraic and physical properties of how parameters naturally contract to a low-rank submanifold M_{≦s} (rank collapse) in the dynamics of Self-Attention layers, establishing practical algorithms that can cut GPU computation and memory bandwidth by up to 90% without sacrificing accuracy, thereby reducing power consumption during training and inference.

What are this project's goals? How will you achieve them?

Over the course of a one-year research period, we aim to achieve the following three main technical goals:

1. Development of Rank-Adaptive Dynamic LoRA (Sub-Root Adaptive LoRA): Based on the fast contraction rate r^* = O(s(d_out + d_in) log s)/(λ_min n) derived from Sub-Root fixed-point solutions in the TIT paper, we will build a lightweight training algorithm that autonomously and dynamically assigns the optimal rank s^{(t)} for each layer during training, reducing GPU power consumption during fine-tuning.

2. Provable Zero-Shot GPU Lightening: Using the SVD prediction distortion upper bound

E_P [1/2 ||WX - ∏_s(W)X||_2^2] ≤ (λ_max(Σ_X)/2) (Σ_{j=s+1} σ_{j}(W)^2) as a direct indicator, we will implement a one-shot pruning technique that determines the minimum rank required to stay below the target error and compresses accordingly, all without retraining.

3. Rank-Collapsing Regularization: By applying a nuclear norm penalty or similar from the early stages of training to intentionally induce rank collapse, we propose a new objective function that automatically reduces GPU power load as training progresses.

【Specific Research Plan (1-Year Milestones)】

• Months 1-4 (Theoretical Formulation and Algorithm Design): We'll extend the formulation from our TIT paper (under review) to practical LLMs with multi-layer, multi-head attention in a PyTorch environment, and design algorithms for adaptive rank selection and one-shot compression to minimize GPU memory bandwidth and FLOPs usage.

• Months 5-8 (PyTorch Implementation and GPU Power Measurement Simulation): Using existing LLM models like LLaMA/Mistral and synthetic datasets, we'll run training and inference experiments with the proposed method. We'll measure accuracy retention and GPU power consumption (W/epoch, Joules/token) compared to standard AdamW/LoRA.

• Months 9-12 (Open-Source Release and Paper Publication): We'll open-source the PyTorch code library on GitHub and write an open-access paper, sharing the research results with the DevInterp community and top conferences.

How will this funding be used?

We are applying for a total of $60,000 USD for a one-year research period.

• Personnel Costs: $45,000 USD to support the living and research activities of the principal investigator (Hideki Ishiyama) so that he can dedicate himself fully to this project without taking on other contract work.

• Computational Resources / GPU Cloud Fees: $8,000 USD to run simulations measuring the matrix rank dynamics and power efficiency of LLM attention layers using cloud GPUs (H100/A100, etc.) from providers like Lambda Labs or RunPod.

• Workstation & AI Tooling: $3,000 USD to set up and maintain a high-efficiency pipeline for formula verification, code generation, and paper writing, including development environment setup and API usage fees.

• Outreach & Publication: $4,000 USD to cover open-access journal fees, documentation of open-source results, and costs for presenting results and gathering feedback within the research community.

Who is on your team? What's your track record on similar projects?

【Research Setup】

This project is led by independent researcher Hideki Ishiyama, who specializes in mathematical sciences, topology, and geometric machine learning, serving as the research lead. We also make use of advanced AI conversational tools (like Gemini Notebook) as interactive assistants.

【Track Record】

• IEEE Transactions on Information Theory (TIT) paper 'Rank-Adaptive Local Empirical Processes in Low-Rank Attention' (under review)

  Mathematical and numerical verification of a 99.22% reduction in parameter dimensions: In a 4096 × 4096 attention projection layer, contraction to rank s=16 reduced the effective statistical dimension p_{eff} from 16,770,000 dimensions to 13,816 dimensions (a 99.22% reduction in parameter space). We also proved and visualized the contraction of local Rademacher complexity.

What are the most likely causes and outcomes if this project fails?

In practical ultra-large language models (ranging from tens of billions to trillions of parameters), when extremely long contexts or multimodal inputs are involved, the smallest eigenvalue of the input covariance matrix λ_{min} may approach 0 (spectral degeneration). This could temporarily increase the local theoretical radius and reduce the accuracy of one-shot compression prediction errors.

[Alternative Outcomes in Case of Failure and Contributions to the Community]

Even if the target compression rates across all layers of a specific huge model are not achieved, we will release on GitHub an open-source PyTorch measurement toolkit for the attention singular value spectra of each layer and GPU power consumption correlation, along with a detailed dataset of SVD prediction distortion upper bounds. This will provide reproducible and valuable foundational data and insights for research communities studying AI Safety, DevInterp, and Green AI (energy-efficient AI).

How much money have you raised in the last 12 months, and from where?

$0 USD (Fully self-funded independent research) Until now, I have conducted foundational theoretical work and written papers entirely using my own funds and personal computing resources without receiving any external funding. This application will be my first attempt at securing external funding for this project.