Organizations: University of Nevada, Reno, Reno, NV, USA · Argonne National Laboratory, Lemont, IL, USA · University of Houston, Houston, TX, USA · University of California, Davis, Davis, CA, USA
Parameter-efficient fine-tuning (PEFT) methods, such as LoRA, enable scalable adaptation of foundation models by injecting low-rank adapters. However, their communication and storage costs remain a major bottleneck in resource-constrained settings. We propose SOLAR (Subspace-Oriented Latent Adapter Reparameterization), a post-training compression framework that substantially reduces the communication cost (i.e., the number of parameters to transmit or store) of PEFT adapters. SOLAR expresses each PEFT update as a linear combination of basis vectors formed from the foundation model's singular vectors with controlled random perturbations. By exploiting the subspace similarity (the alignment of principal directions) between the foundation model and task-specific fine-tuned updates, SOLAR decouples the adapter size from PEFT structure and ensures compact yet expressive representations. It is model-agnostic and compatible with existing PEFT methods, including LoRA, AdaLoRA, and other adapter modules. We theoretically establish a bound on the reconstruction error. Experiments on language and vision tasks using LLaMA, GPT, and ViT models demonstrate that SOLAR preserves task performance while significantly reducing model representation sizes, offering an effective and communication-efficient solution for deployment in distributed systems and edge devices.
Figures & tables
Figure 1: Overview of SOLAR. Given fine-tuned adapters (A,B) , SOLAR projects them onto structured subspaces derived from the pretrained model’s SVD. A seeded pseudo-random generator (seeded with a known value) deterministically creates the basis matrices. Top- k coefficients α and β are selected under a budget to reconstruct A~ and B~ , while the bases are never stored or transmitted. Only the coefficients α , β , and the seed need to be communicated or stored.
Model
Method
#
CIFAR-10
CIFAR-100
Food-101
T-ImageNet
Param
10
Full
10
Full
10
Full
10
Full
ViT-B
Full-FT
86M
91.1 ± .8
94.6 ± .5
78.2 ± .7
87.7 ± .3
65.8 ± .9
85.2 ± .4
78.1 ± 1.0
85.4 ± .6
LoRA ( r =4)
74K
92.3 ± .6
98.3 ± .2
81.8 ± .8
90.3 ± .4
72.4 ± .7
87.6 ± .3
77.9 ± .9
88.8 ± .4
NOLA
48K
92.2 ± .6
94.7 ± .5
81.3 ± .8
86.6 ± .4
72.6 ± .5
85.9 ± .2
78.4 ± .7
82.8 ± .5
SOLAR r=4(4→1.6)
41K
92.3 ± .7
98.3 ± .4
81.5 ± .7
89.8 ± .2
71.8 ± .6
87.0 ± .5
77.9 ± .8
87.9 ± .4
SOLAR NOLA(4→1.2)
32K
92.1 ± .7
94.5 ± .3
81.1 ± .6
85.4 ± .3
72.5 ± .6
85.4 ± .3
78.3 ± .8
82.3 ± .5
Table 1: Top-1 classification accuracy (%) of ViT-B and ViT-L on benchmark datasets under two settings: (1) few-shot (10 samples/class, 25 epochs) and (2) full-data (5 epochs). Results report mean ± std over 5 runs. SOLAR is applied with configuration method(N→k) , where N and k are in thousands.
Method
Byte Footprint
Oxford Pets
SUN397
CUB-200
ImageNet-1K
LoRA ( r =1)
74KB
93.0 ± .3
74.3 ± .2
84.7 ± .2
81.5 ± .4
NOLA
48KB
90.4 ± .5
61.7 ± .4
79.4 ± .4
77.4 ± .3
SOLAR r=1(2→0.2)
8KB (89% ↓ )
92.6 ± .4
73.9 ± .2
84.2 ± .3
81.3 ± .2
Table 2: Additional evaluation on vision datasets using ViT-B. The table shows bit-level representation footprint (32-bit baseline) and Top-1 accuracy. All models are trained for 10 epochs.
Table 4
Model
LLaMA-3.2 1B
LLaMA-2 13B (4-bit)
Method
LoRA
NOLA
SOLAR
LoRA
NOLA
SOLAR
r =8
1000
r=8(4→1.2)
r =1
1000
r=1(1→0.3)
# Params
852K
64K
81K (90% ↓ )
819K
140K
51K (94% ↓ )
Val Loss
1.51
1.87
1.52
1.05
1.29
1.05
MMLU Acc
30.1
25.9
28.3
54.5
51.8
54.5
Table 5: Model representation efficiency for LLaMA models. SOLAR compresses LoRA adapter updates across various model sizes.
Method
GPT-2 Small
GPT-2 Medium
MET
# Params
MET
# Params
Full-FT
28.4
124M
46.2
355M
LoRA ( r =4)
29.7
147K
47.2
393K
NOLA
29.1
48K
46.8
350K
SOLAR ( r =4, 1→0.3 )
29.7
15K (90% ↓ )
46.4
30K (92% ↓ )
SOLAR ( r =1, 0.1→0.1 )
26.1
4K (97% ↓ )
44.8
9K (98% ↓ )
Table 6: Performance and parameter efficiency on E2E NLG using GPT-2 Small and Medium. All methods use rank-4 adapters applied to the Query and Value projections.
Figure 2: Subspace similarity between the W and ΔW matrices (Q, K, V) from the first layer of the ViT-B model using LoRA with rank r=4 .
Figure 8
Dataset
LoRA
SOLAR
Overhead (%)
CIFAR-10
1176
14
1.19
CIFAR-100
1165
14
1.20
Food-101
3480
67
1.92
Tiny-ImageNet
2081
15
0.72
ImageNet-1K
56634
155
0.27
Table 8: Runtime Overhead: LoRA (10 epochs) vs. SOLAR post-training on ViT-B across vision datasets. Times in seconds.
Appendix figures & tables16 assets
Supplementary material from the paper’s appendix.
Appendix
Dataset
Training Samples
Number of Classes
CIFAR-10
50,000
10
CIFAR-100
50,000
100
Food-101
75,750
101
Tiny-ImageNet
100,000
200
ImageNet-1K
1,281,167
1,000
Appendix
Table 9: Dataset statistics used in experiments. Each dataset includes the number of training samples and classes.
Dataset
Samples
Avg. Seq. Length
Context
Stanford Alpaca
52,000
∼ 256 tokens
LLaMA-3 instruction tuning
MMLU
15,858
∼ 200 tokens
LLaMA-3 Generalization evaluation
E2E NLG
42,000
∼ 35 tokens
GPT-2 generation fine-tuning
Appendix
Table 10: Dataset statistics in LLM experiments.
Method
Dataset
Query (Q)
Classifier Head
SOLAR
CIFAR-10
12×((1600+1600)+324000+4000)+1=41,401$$
10×768+10=7,690$$
CIFAR-100
41,401
100×768+100=76,900$$
Food-101
41,401
101×768+101=77,669$$
Tiny-ImageNet
41,401
200×768+200=154,000$$
LoRA
CIFAR-10
12×[(768×4)+(4×768)]=73,728$$
10×768+10=7,690$$
CIFAR-100
73,728
100×768+100=76,900$$
Appendix
Table 11: Number of representation parameters for ViT-B (Rank = 4). Each row reports the parameter count for query projections and the classifier head using SOLAR and LoRA across different datasets. The classifier head parameter count is shared across methods and is computed as (num_classes × 768 + num_classes) . For SOLAR, the query projection count corresponds to: number of layers × (top k coefficients for A + top k coefficients for B + encoded basis for A + encoded basis for B ) +1 (seed value). All SOLAR rows follow the form N→topk where N is the original subspace size. For LoRA, the query projection count corresponds to: number of layers × (input dimension × rank for A + rank × output dimension for B ), where rank is 4.
Method
Dataset
Query (Q)
Classifier Head
SOLAR
CIFAR-10
24×((500+500)+321000+1000)+1=25,501$$
10×1024+10=10,250$$
CIFAR-100
25,501
100×1024+100=102,500$$
Food-101
25,501
101×1024+101=103,625$$
Tiny-ImageNet
25,501
200×1024+200=204,800$$
LoRA
CIFAR-10
24×[(1024×4)+(4×1024)]=196,608$$
10×1024+10=10,250$$
CIFAR-100
196,608
100×1024+100=102,500$$
Appendix
Table 12: Number of representation parameters for ViT-L (Rank = 4). Each row shows the parameter counts for Query projections and the classifier head using SOLAR and LoRA across different datasets. The classifier head parameter count is shared across methods and is calculated as (num_classes × 1024 + num_classes) .
Method
Dataset
MLP
Classifier Head
NOLA
CIFAR-10
12×2×2×1000+1=48,001$$
10×768+10=7,690$$
CIFAR-100
48,001
100×768+100=76,900$$
Food-101
48,001
101×768+101=77,669$$
Tiny-ImageNet
48,001
200×768+200=154,000$$
Appendix
Table 13: Number of representation parameters for ViT-B (Rank = 4). Each row shows the parameter counts for MLP projections (for NOLA) and classifier head across datasets. The classifier head parameter count is shared across methods and is calculated as (num_classes × 768 + num_classes) .
Method
Representation Footprint (Bytes)
LoRA ( r=1 )
12×[(768×1)+(1×768)]×4=73,728$$
SOLAR for ViT-B 8Bit ( r=1 , 500→50 )
12×[(50+50)+8500]×1+1=1,951$$
SOLAR for ViT-B 8Bit ( r=1 , 100→10 )
12×[(10+10)+8100]×1+1=391$$
LoRA ( r=4 )
24×[(1024×4)+(4×1024)]×4=786,432$$
SOLAR for ViT-L 32Bit ( r=4 , 4000→1600 )
24×[(1600+1600)+324000]×4+1=319,201$$
SOLAR for ViT-L 16Bit ( r=4 , 4000→1600 )
24×[(1600+1600)+164000]×2+1=165,601$$
Appendix
Table 14: Byte-level footprint of representation parameters for ViT-B and ViT-L using LoRA and SOLAR. Each value reflects the total number of bytes required to store adapter updates (excluding classifier heads). For LoRA, storage is computed as: number of layers × ( rank × output dimension for B + input dimension × rank for A ) × precision in bytes (e.g., 4 bytes for 32-bit float). For SOLAR, storage is computed as: number of layers × ( top k coefficients for A + top k coefficients for B + encoded basis vectors for A + encoded basis for B ) × precision in bytes, plus 1 byte to store a random seed. For example, the row " 500→50 " denotes that 500 -dimensional subspaces are sparsified to top- k=50 coefficients, with encoded bases represented at 1 bit per element (8 elements per byte).
Model (Rank)
Configuration
Total Parameters
LLaMA-3.2 1B ( r =8)
16 layers (Q, V)
16×[(2048×8+8×2048)+(2048×8+8×512)]=851,968$$
NOLA
16 layers (Q, V)
16×2×(1000+1000)=64,000$$
SOLAR ( r =8, 4K→1.2K )
16 layers (Q, V)
16×2×(1200+1200+324000)+1=80,801$$
LLaMA-3.2 3B ( r =1)
28 layers (Q, V)
28×[(3072×1+1×3072)+(3072×1+1×1024)]=286,720$$
NOLA
28 layers (Q, V)
28×2×(1000+1000)=112,000$$
SOLAR ( r =1, 1000→150 )
28 layers (Q, V)
28×2×(150+150+321000)+1=18,551$$
Appendix
Table 15: Number of representation parameters for LLaMA-3 models using LoRA, NOLA, and SOLAR. Each row reports total adapter parameters for attention projections (Q and V for LoRA and NOLA; Q and K for SOLAR). Output heads and MLP layers are frozen. For LoRA, the parameter count is computed as: number of layers × ( input dimension × rank for B + rank × output dimension for A + ) . Due to differing dimensions between A and B in LoRA, the table computes the contributions for Q and V projections separately. For NOLA, it is computed as: number of layers × 2 × (number of random basis vectors), assuming separate basis sets for A and B . For SOLAR, the count is: number of layers × 2 × ( top k coefficients for B + top k for A + encoded bases for B + encoded bases for A ) , plus 1 byte to communicate or store the shared seed.
Model (Rank)
Configuration
Total Parameters
GPT-2 Small ( r =4)
12 layers (Q, V)
12×2×(768×4+4×768)=147,456$$
NOLA
12 layers (Q, V)
12×2×(1000+1000)=48,000$$
SOLAR ( r =1, 1000→300 )
12 layers (Q, V)
12×2×(300+300+321000)+1=15,150$$
SOLAR ( r =1, 100→90 )
12 layers (Q, V)
12×2×(90+90+32100)+1=4,396$$
GPT-2 Medium ( r =4)
24 layers (Q, V)
24×2×(1024×4+4×1024)=393,216$$
NOLA
24 layers (Q, V)
350,000 [ koohpayegani2024nola ]
Appendix
Table 16: Number of trainable adapter parameters for GPT-2 models using LoRA, NOLA, and SOLAR. Each row reports the total number of parameters added to the query and value projections (Q and V). All configurations freeze the output heads and MLP layers. For LoRA, the parameter count is computed as: number of layers × 2 × ( input dimension × rank for B + rank × output dimension for A ) . For NOLA, the parameter count is: number of layers × 2 × (number of random basis vectors), assuming separate basis sets for Q and V. For SOLAR, the parameter count is: number of layers × 2 × ( top k coefficients for B + top k coefficients for A + encoded bases for B + encoded bases for A ) , plus 1 for the shared seed.
Model
LLaMA-3.2 3B
LLaMA-3.1 8B (4-bit)
Method
LoRA
NOLA
SOLAR
LoRA
NOLA
SOLAR
r =1
1000 bases
SOLAR r=1(1K→0.1K)
r =1
1000 bases
SOLAR r=1(1K→0.3K)
# Params
287K
112K
16K (94% ↓ )
425K
128K
40K (91% ↓ )
Val Loss
1.02
1.31
1.04
0.89
1.01
0.90
MMLU Acc
54.0
52.7
54.0
60.9
56.1
60.9
Appendix
Table 17: Model representation efficiency for LLaMA 3B and 8B models. For the 8B model, all methods use 4-bit quantization, making the LoRA baseline equivalent to QLoRA.
Method
# Params (Adapter)
MMLU Accuracy
AdaLoRA (Baseline, 3B)
305K
54.8%
SOLAR (on AdaLoRA, 3B)
16K
54.7%
AdaLoRA (Baseline, 13B)
871K
57.9%
SOLAR (on AdaLoRA, 13B)
16K
57.7%
Appendix
Table 18: SOLAR applied to AdaLoRA adapters on intermediate-scale LLaMA models.
Method
Quantization
# Params
MMLU Acc
LoRA (QLoRA) - LLaMA-2 13B
2-bit
410K
53.1
SOLAR r=1(1K→0.3K) - LLaMA-2 13B
2-bit
51K
53.1
LoRA (QLoRA) - LLaMA-3.1 8B
2-bit
363K
58.4
SOLAR r=1(1K→0.3K) - LLaMA-3.1 8B
2-bit
40K
58.4
Appendix
Table 19: 2-bit quantization experiments comparing LoRA (QLoRA) and SOLAR.
Method
Byte Footprint
Oxford Pets
SUN397
CUB-200
ImageNet-1K
LoRA ( r =1)
74KB
93.0 ± 0.5
74.3 ± 0.3
84.7 ± 0.4
81.5 ± 0.6
SOLAR ( r =1, 500→50 )
2KB (97% ↓ )
91.2 ± 0.6
72.4 ± 0.4
81.4 ± 0.5
80.7 ± 0.4
SOLAR ( r =1, 100→10 )
0.4KB (99% ↓ )
90.3 ± 0.7
72.4 ± 0.5
81.3 ± 0.6
80.6 ± 0.5
Appendix
Table 20: Evaluation of extreme compression on ViT-B. We report bit-level representation footprint (32-bit baseline) and top-1 accuracy over 5 runs. All models are trained for 10 epochs.
Method
# Params
CIFAR-10
CIFAR-100
Food-101
T-ImageNet
LoRA ( r=4 )
492K
99.4
94.6
91.2
92.8
SOLAR ( r=4,8K→4K )
340K (31% ↓ )
99.4
94.5
91.2
92.8
Appendix
Table 21: Scalability of SOLAR on the ViT-G/14 model. Results show top-1 accuracy (%) on full datasets.
Method
#Params
CIFAR-10
CIFAR-100
Food-101
T-ImageNet
LoRA ( r=4 )
74K
98.3
90.3
87.6
88.8
LoRA ( r=2 )
37K
97.1
89.0
85.5
87.4
SOLAR ( r=4,4K→1.6K )
41K
98.3
89.8
87.0
87.9
SOLAR ( r=4,4K→0.8K )
22K
97.0
89.0
85.2
87.4
Appendix
Table 22: Comparison of SOLAR with a budget-matched LoRA (r=2) baseline on ViT-B. While LoRA (r=2) has a similar parameter count to the compressed SOLAR adapter, it shows a clear performance degradation. SOLAR maintains performance comparable to the original, higher-rank LoRA (r=4).
Method
Byte Footprint
Oxford Pets
SUN397
CUB-200
ImageNet-1K
LoRA ( r=1 )
74KB
93.0
74.3
84.7
81.5
LoRA ( r=4 )
297KB
94.2
75.6
86.0
82.8
SVD truncation on LoRA
74KB
92.7
73.3
83.6
80.8
SOLAR on LoRA ( r=1 )
8KB
92.6
73.9
84.2
81.3
SOLAR on LoRA ( r=4 )
8KB
93.9
75.0
85.4
82.4
Appendix
Table 23: Comparison of SOLAR and simple SVD truncation against standard LoRA adapters on multiple vision datasets. The table reports classification accuracy and the corresponding byte footprint of the adapter parameters after compression. SOLAR consistently reduces the parameter size while preserving or improving performance.
Method
# Params
CIFAR-10 (IID)
CIFAR-10 (non-IID)
LoRA ( r=4 )
74K
93.7
87.4
SOLAR ( r=4,4K→2K )
51K (31% ↓ )
93.2
86.7
Appendix
Table 24: Performance of SOLAR on ViT-B under IID and non-IID data distributions in a simulated 10-client federated learning environment.
Exponential growth in the scale of modern foundation models has led to the widespread adoption of Low-Rank Adaptation (LoRA) as a parameter-efficient fine-tuning technique. However, standard LoRA implementations disregard the varying intrinsic dimensionality of model layers and enforce a uniform rank, leading to parameter redundancy. We propose Post-Optimization Adaptive Rank Allocation (PARA), a data-free compression method for LoRA that integrates seamlessly into existing fine-tuning pipelines. PARA leverages Singular Value Decomposition to prune LoRA ranks using a global threshold over singular values across all layers. This results in non-uniform rank allocation based on layer-wise spectral importance. As a post-hoc method, PARA circumvents the training modifications and resulting instabilities that dynamic architectures typically incur. We empirically demonstrate that PARA reduces parameter count by 75-90% while preserving the predictive performance of the original, uncompressed LoRA across multiple vision and language benchmarks. Code will be published upon acceptance.
Vishnuprasadh Kumaravelu, Sunil Gupta, P. K. Srijith
1Indian Institute of Technology Hyderabad · 2Deakin University
Low-Rank Adaptation (LoRA) has become a key mechanism for efficiently specializing foundation models into many task- and user-specific variants. Serving many LoRA adapters under a shared resource budget turns post-hoc compression into a two-level allocation problem: rank must be distributed across layers within each adapter and across adapters within the fleet. Although trained LoRAs contain substantial spectral redundancy, spectral reconstruction alone does not determine how much compression an adapter can functionally tolerate. We formulate fleet compression through a functional rank-distortion frontier for each adapter, followed by fleet-level minimax allocation under a shared rank budget. Given exact frontiers, this decomposition is equivalent to joint optimization over all layer ranks. We introduce Functional Rank Allocation (FRA), an unlabeled method for constructing practical frontiers. FRA measures isolated module truncations end to end, uses these measurements as an additive search surrogate solved by dynamic programming, remeasures every complete candidate, and takes the lower-risk envelope with a complementary spectral proposal before exact minimax allocation over the constructed frontiers. Across 78 adapters from three public fleets, FRA improves worst-case and tail utility over uniform spectral compression in constrained-budget regimes. Fixed-budget probes show that isolated costs rank candidates well, but their calibration shifts across proposal shapes; end-to-end verification and the spectral proposal therefore limit functional-search error.
Shenghui Li, Thiemo voigt
Uppsala University, Uppsala, Sweden · Research Institutes of Sweden, Stockholm, Sweden
Parameter-efficient fine-tuning (PEFT) reduces the cost of adapting foundation models by focusing training on a small parameter subset. Complementary to this idea, we introduce RoSA (Rotational Sparse Adaptation), which narrows adaptation to a subset of layers at a time. RoSA freezes lower layers close to the input throughout training and rotates a trainable block over later layers, progressively increasing the number of frozen layers close to the input. This design reduces optimizer-state memory, shortens backpropagation, and even forward propagation if activations at the last frozen layer are cached. Because RoSA is orthogonal to the choice of trainable parameterization, it can be combined with PEFT methods or sparse optimizers within each active block. Experiments across multiple LLM architectures and tasks show that RoSA reduces peak memory while maintaining strong fine-tuning performance.
Muhammad Azeem Lodhi, Chao Zhou, Rebekka Burkholz
Saarland University, Saarbrücken, Germany · CISPA Helmholtz Center for Information Security, Saarbrücken, Germany