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Tensor Train Low-rank Approximation (TT-LoRA): Democratizing AI with Accelerated LLMs

Afia Anjum, Maksim E. Eren, Ismael Boureima, Boian Alexandrov, Manish Bhattarai

arXiv:2408.01008v1cs.LGcs.AI

TL;DR

Fine-tuning large language models can demand substantial computational resources, while existing PEFT methods can retain high trainable-parameter counts at larger scales. TT-LoRA integrates tensor train decomposition while omitting adapter and LoRA-based structures. Across evaluated tasks and scales it reports greater performance with significant compression; on LLaMA3-8B SuperGLUE it uses approximately 170.5× fewer parameters than LoRA.

  • Problem

    Full fine-tuning of increasingly complex LLMs requires substantial computational resources, and LoRA and LoRETTA still require many trainable parameters when scaled to larger models.

    Source: §I · pp. 1–2

  • Method

    TT-LoRA uses tensor train decomposition for parameter-efficient fine-tuning, omitting the adapters and LoRA-based structure used in LoRETTA.

    Source: §I · p. 2

  • Results

    Across diverse model scales, TT-LoRA achieves greater performance with significant model compression; on LLaMA3-8B SuperGLUE it uses approximately 170.5× fewer parameters than LoRA.

    Source: §I · p. 2, B. SuperGLUE Experiments on LLaMA Family · p. 6

  • Takeaways & Limitations

    TT-LoRA provides a fine-tuning approach that reduces trainable parameters and is reported to reduce inference latency and computation overhead.

    Source: §I · p. 2

Abstract

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In recent years, Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing (NLP) tasks, such as question-answering, sentiment analysis, text summarization, and machine translation. However, the ever-growing complexity of LLMs demands immense computational resources, hindering the broader research and application of these models. To address this, various parameter-efficient fine-tuning strategies, such as Low-Rank Approximation (LoRA) and Adapters, have been developed. Despite their potential, these methods often face limitations in compressibility. Specifically, LoRA struggles to scale effectively with the increasing number of trainable parameters in modern large scale LLMs. Additionally, Low-Rank Economic Tensor-Train Adaptation (LoRETTA), which utilizes tensor train decomposition, has not yet achieved the level of compression necessary for fine-tuning very large scale models with limited resources. This paper introduces Tensor Train Low-Rank Approximation (TT-LoRA), a novel parameter-efficient fine-tuning (PEFT) approach that extends LoRETTA with optimized tensor train (TT) decomposition integration. By eliminating Adapters and traditional LoRA-based structures, TT-LoRA achieves greater model compression without compromising downstream task performance, along with reduced inference latency and computational overhead. We conduct an exhaustive parameter search to establish benchmarks that highlight the trade-off between model compression and performance. Our results demonstrate significant compression of LLMs while maintaining comparable performance to larger models, facilitating their deployment on resource-constraint platforms.

I. INTRODUCTION

TT-LoRA is presented as a parameter-efficient approach to fine-tuning large language models with fewer trainable parameters and reduced inference overhead. The paper benchmarks its compression–performance trade-off across tasks and model scales.

I. INTRODUCTION

  • Full fine-tuning of growing LLMs requires substantial computing resources, while LoRA and LoRETTA still need many trainable parameters at larger scales.The introduction links these resource demands to increased costs, restricted research access, and environmental concerns.Source: §I · pp. 1–2
  • TT-LoRA uses tensor train decomposition and omits the Adapter and LoRA-based structures used in LoRETTA.The authors state these changes reduce inference latency, model complexity, and computation overhead while improving compression.Source: §I · p. 2
  • The evaluation covers downstream tasks and models at different scales, including BERT-based models and LLaMA-2 and LLaMA-3.The authors also report an exhaustive parameter search to benchmark compression–performance trade-offs.Source: §I · p. 2
  • TT-LoRA achieves greater performance with significant model compression in benchmarks against other PEFT methods across diverse model scales.The paper points to Figure 1 for the DeBERTa GLUE comparison.Source: §I · p. 2

II. RELATED WORKS

The related-work section reviews adapter, prompt-based, low-rank, and tensor-based fine-tuning approaches. It positions TT-LoRA as a direct tensor decomposition approach intended to improve compression and avoid adapter-related inference latency.

II. RELATED WORKS

  • Adapter methods train bottleneck modules while keeping pretrained weights fixed, but add sequential computation that increases inference latency, especially at small batch sizes.Figure 2a illustrates the adapter structure.Source: §II · p. 2, Figure 2 · p. 3
  • Prefix, prompt, and p-tuning add trainable vectors or embeddings to model inputs or internal points, using part of the fixed sequence length and potentially reducing space for task input.These approaches are illustrated in Figure 2b.Source: §II · p. 2, Figure 2 · p. 3
  • LoRA freezes the pretrained weight matrix and learns a low-rank update as the product BA, but can still require many trainable parameters.The paper gives over 16 million updated parameters for LoRA fine-tuning of LLaMA-2-70B.Source: §II · p. 2
  • LoRETTA uses tensor factors in adapter-based or matrix-factorization variants, yet can still require many trainable parameters for larger models such as LLaMA2-70B or MoE.The two variants are LoRETTAadp and LoRETTArep.Source: §II · pp. 2–3
  • TT-LoRA directly decomposes weight updates into small tensors, avoiding the LoRA-based structure and adapters used in LoRETTA.The paper reports that TT-LoRA surpasses LoRETTA in accuracy and compression across BERT and LLaMA classification tasks.Source: §II · p. 3

III. TENSOR TRAIN BASED LOW-RANK ADAPTATION (TT-LORA)

This section introduces TT-LoRA after formulating the fine-tuning objective and outlining challenges with conventional full fine-tuning.

III. TENSOR TRAIN BASED LOW-RANK ADAPTATION (TT-LORA)

  • The section first formulates the LLM fine-tuning objective, then presents TT-LoRA’s design and how it addresses the stated challenges.Source: §III · p. 3

A. Problem Statement

The paper frames fine-tuning as adapting a pretrained language model to downstream tasks using input-output examples, with full fine-tuning optimizing output-token predictions.

A. Problem Statement

  • Downstream tasks are represented by input-output pairs, with outputs taking forms such as token sequences, labels, or continuous values.Examples include a social media post paired with a sentiment label and a question paired with its answer.Source: A. Problem Statement · p. 3
  • The objective maximizes cumulative log probability for each target token given the input and preceding output tokens.The model starts from pretrained weights and updates them for the downstream task.Source: A. Problem Statement · p. 4
  • Full fine-tuning updates all pretrained parameters, making |∆θ| equal to |θ0| and costly as model size grows.The paper contrasts this with a PEFT strategy that reduces trainable parameters to ϕ, where |∆ϕ| ≪ |∆θ|.Source: A. Problem Statement · p. 4

B. Proposed Method

TT-LoRA represents weight updates with low-rank tensor-train cores while keeping pretrained weights frozen, aiming to reduce trainable parameters during downstream adaptation.

B. Proposed Method

  • TT-LoRA constrains the update to a pretrained weight matrix with a low-rank representation, motivated by low intrinsic dimension and hypothesized low intrinsic rank of weight updates [25] [19].The update is represented as a d-dimensional tensor before decomposition.Source: B. Proposed Method · p. 4
  • Tensor-train decomposition represents the update tensor as a sequence of small, low-rank three-dimensional cores whose neighboring cores interact locally.The tensor is split into d cores with shapes defined by the TT ranks and tensor dimensions.Source: B. Proposed Method · p. 4
  • During fine-tuning, pretrained weights W0 remain frozen while the tensor-train update is trainable and scaled by α before addition.The adapted layer applies a linear transformation to input x.Source: B. Proposed Method · p. 5
  • 1,135 trainable parameters versus 1,769,472 in full fine-tuning yields 1560x compression for a 768 × 2304 weight matrix at TT-rank 5.The passage says lower TT-rank or higher tensor dimension can increase compression further.Source: B. Proposed Method · p. 5

IV. RESULTS AND DISCUSSION

The experiments evaluate TT-LoRA across language-understanding and generation tasks, compare it with several fine-tuning baselines, and search configurations for compression-performance trade-offs.

IV. RESULTS AND DISCUSSION

  • The evaluation covers DeBERTa and RoBERTa on GLUE and LLaMA-2-7B and LLaMA-3-8B on SuperGLUE.The models span different scales and tasks from language understanding to generation.Source: §IV · p. 5
  • TT-LoRA is compared with full fine-tuning, Adapters, Prompt Tuning, Prefix Tuning, P-tuning, BitFit, LoRA, and LoRETTA.Source: §IV · p. 5
  • The study searches for tensor shapes and TT ranks to establish benchmarks illustrating the trade-off between model compression and performance.Source: §IV · p. 5
  • Experiments ran on four NVIDIA Hopper H100 GPUs, each paired with an NVIDIA Grace CPU via NVLink-C2C.The GPUs have 96GB of HBM2 memory.Source: §IV · p. 5

A. GLUE Experiments on BERT Family

On GLUE, TT-LoRA achieves superior or comparable performance to other PEFT methods on DeBERTa with no more than 0.2M trainable parameters, and performs strongly on average across RoBERTa task sets. The experiments target the Wq and Wv self-attention matrices.

A. GLUE Experiments on BERT Family

  • The experiments apply TT-LoRA to the Wq and Wv self-attention matrices, with early stopping after five epochs without validation-loss improvement.The best model is selected using the lowest observed validation loss.Source: A. GLUE Experiments on BERT Family · p. 5
  • TT-LoRA achieves superior or comparable DeBERTa performance on GLUE with no more than 0.2M trainable parameters.Table I presents the comparative analysis of PEFT methods on BERT-family models.Source: A. GLUE Experiments on BERT Family · p. 5, Table I · p. 6
  • For RoBERTa, TT-LoRA reduces trainable parameters by approximately 6,200× versus full fine-tuning, 31.5× versus LoRA, and 5× versus BitFit and LoRETTAadp.Despite these reductions, it outperforms other PEFT methods except full fine-tuning in average model accuracy across various GLUE task sets.Source: A. GLUE Experiments on BERT Family · p. 6

B. SuperGLUE Experiments on LLaMA Family

On SuperGLUE, TT-LoRA performs strongly on LLaMA2-7B and matches or exceeds LoRA across tasks on LLaMA3-8B, with substantially fewer trainable parameters. The experiments use the Wq and Wv self-attention matrices.

B. SuperGLUE Experiments on LLaMA Family

  • The LLaMA experiments fine-tune Wq and Wv and report F1 for CB and WSC and accuracy for BoolQ and COPA.Training stops when validation loss fails to improve for five consecutive epochs.Source: B. SuperGLUE Experiments on LLaMA Family · p. 6
  • On LLaMA2-7B, TT-LoRA outperforms all other PEFT methods on CB and WSC, all but LoRETTArep on BoolQ, and is comparable on COPA.It surpasses competing PEFT methods on average while reducing trainable parameters versus baselines by approximately 67,384× to 5.1×.Source: B. SuperGLUE Experiments on LLaMA Family · p. 6
  • On LLaMA3-8B, TT-LoRA matches or exceeds LoRA across SuperGLUE tasks with approximately 170.5× fewer trainable parameters.Table II presents the comparative analysis of PEFT methods on LLaMA-family models.Source: B. SuperGLUE Experiments on LLaMA Family · p. 6, Figure 4 · p. 7

C. Memory Performance

With weights stored at 16-bit precision, TT-LoRA reduces trainable-parameter storage for both DeBERTa and LLaMA2-7B relative to the reported baselines.

C. Memory Performance

  • 39 KB of trainable-parameter storage is required for TT-LoRA on DeBERTa.This is approximately 2.5×, 5×, 15×, and 7000× less storage than LoRETTArep, LoRETTAadp, LoRA, and full fine-tuning, respectively.Source: C. Memory Performance · p. 7
  • 195 KB of trainable-parameter storage is required for TT-LoRA on LLaMA2-7B.This is approximately 5×, 8.8×, 42×, and 65,925× less storage than LoRETTArep, LoRETTAadp, LoRA, and full fine-tuning, respectively.Source: C. Memory Performance · p. 7
  • The storage comparison assumes model weights are stored with 16-bit precision.The authors identify the reduced storage requirement as relevant to fine-tuning on resource-constrained hardware.Source: C. Memory Performance · p. 7

D. Hyperparameters

The authors tune TT-LoRA hyperparameters through Ray Tune and HyperBand, selecting configurations by validation loss. Their reported BoolQ analysis links trainable-parameter counts and α to accuracy.

D. Hyperparameters

  • Around 200 Ray Tune searches use HyperBand to explore learning rates and model parameters, including tensor shapes, ranks, and α.The search aims to minimize validation loss with fewer simulations.Source: D. Hyperparameters · p. 7, Table III · p. 7
  • On LLaMA2-7B BoolQ, accuracy tends to decrease as trainable parameters are reduced, and α also influences accuracy.The figure compares compression and accuracy across TT-LoRA tensor formats and other PEFT approaches.Source: Figure 5 · p. 7, D. Hyperparameters · p. 8
  • The best model configurations are selected by lowest validation loss, and the optimal TT-LoRA settings are summarized in Table IV.The authors identify tensor shape, tensor rank, α, and learning rate as optimal hyperparameters.Source: D. Hyperparameters · p. 7, Table IV · p. 8
  • Despite reductions in trainable parameters, TT-LoRA maintains superior or comparable performance to other PEFT methods on the LLaMA2-7B BoolQ comparison.The authors state that this can minimize trainable parameters within strict hardware limits.Source: D. Hyperparameters · p. 8

V. CONCLUSION

TT-LoRA uses tensor train decomposition to reduce trainable parameters and achieves higher or comparable average accuracy with a smaller model size across BERT- and LLaMA-based tasks.

V. CONCLUSION

  • TT-LoRA achieved higher or comparable average accuracy with a significantly smaller model size than other state-of-the-art PEFT methods.The comparison covers fine-tuning BERT- and LLaMA-based models across various tasks.Source: §V · p. 8
  • TT-LoRA leverages tensor train decomposition to significantly reduce the number of trainable parameters.Source: §V · p. 8
  • The authors plan to extend TT-LoRA to larger models, including LLaMA3.1-405B, Grok 2.0, and Mistral Large.Source: §V · p. 8
  • Future work will explore compressing additional layers within LLMs to pursue greater compression.Source: §V · p. 8

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