ConsNoTrainLoRA: Data-driven Weight Initialization of Low-rank Adapters

using Constraints

Debasmit Das *Hyoungwoo Park *Munawar Hayat Seokeon Choi Sungrack Yun Fatih Porikli

Qualcomm AI Research †

Abstract

Foundation models are pre-trained on large-scale

datasets and subsequently ﬁne-tuned on small-scale

datasets using parameter-efﬁcient ﬁne-tuning (PEFT) tech-

niques like low-rank adapters (LoRA). In most previous

works, LoRA weight matrices are randomly initialized with

a ﬁxed rank across all attachment points. In this paper, we

improve convergence and ﬁnal performance of LoRA ﬁne-

tuning, using our proposed data-driven weight initializa-

tion method, ConsNoTrainLoRA (CNTLoRA). We express

LoRA initialization as a domain shift problem where we

use multiple constraints relating the pre-training and ﬁne-

tuning activations. By reformulating these constraints, we

obtain a closed-form estimate of LoRA weights that de-

pends on pre-training weights and ﬁne-tuning activation

vectors and hence requires no training during initializa-

tion. This weight estimate is decomposed to initialize the

up and down matrices with proposed ﬂexibility of variable

ranks. With the proposed initialization method, we ﬁne-

tune on downstream tasks such as image generation, im-

age classiﬁcation and image understanding. Both quan-

titative and qualitative results demonstrate that CNTLoRA

outperforms standard and data-driven weight initialization

methods. Extensive analyses and ablations further eluci-

date the design choices of our framework, providing an op-

timal recipe for faster convergence and enhanced perfor-

mance.

1. Introduction

Foundation models (FMs) [6] generally undergo an ini-

tial phase of large-scale pre-training, followed by task-

speciﬁc ﬁne-tuning to address domain shift [28] between

pre-training and task-speciﬁc data. This two-step approach

has led to advances across multiple applications in natural

language processing [1,40,41], computer vision [11,32]

and others [7,8]. However, as the size scales up vastly (or

signiﬁcantly), ﬁne-tuning all parameters of the FM would

*These authors contributed equally to this work.

†Qualcomm AI Research is an initiative of Qualcomm Technologies, Inc.

Figure 1. The DINO score plot of different initialization methods

with increasing steps of training on the Dreambooth [37] dataset.

require much more computational complexity and memory.

Parameter-efﬁcient ﬁne-tuning (PEFT) methods provide

a promising solution e.g. Low-Rank Adaptation (LoRA)

[18] only adds a trainable adapter with fewer parameters

while keeping the pre-trained model frozen. To expedite the

convergence of PEFT models, recent works [9,29,33,47]

explore adapter initialization from model weights or data

to encapsulate pre-trained knowledge or task information.

Among the adapter initialization methods, PiSSA [29] and

OLoRA [9] are the most popular. PiSSA uses SVD decom-

position of pre-trained matrices to initialize LoRA weights,

while OLoRA [9] uses QR decomposition. Neither method

uses ﬁne-tuning data for initialization. EVA [33] addresses

this by minimizing the reconstruction error of LoRA layer

input activations and initializing down matrices from SVD

of input activations. However, up matrices are initial-

ized with zeros, making it difﬁcult to balance pre-training

knowledge with ﬁne-tuning data. To encapsulate both pre-

vious and novel knowledge, CORDA [47] uses low-rank

SVD on the interaction between LoRA weight matrices and

the covariance of input activations to initialize up and down

matrices. While effective for language tasks, its application

to visual tasks remains untested, and the selection of inter-

action is rather unclear. This paper presents a systematic,

constraint-based framework for LoRA weight initialization,

which promotes faster convergence, improves performance,

arXiv:2507.08044v1 [cs.CV] 9 Jul 2025

Figure 2. Generation evolution for different initialization methods on Dreambooth [37] dataset. The prompts from left to right are (a) A S*

toy ﬂoating on top of water. (b) A S* teapot with the Eiffel tower in the background. (c) A S* dog with a city in the background.

and also provides a uniﬁed paradigm for existing methods.

We motivate our proposed LoRA initialization method

through the lens of domain shift [14,39,42,43], which

LoRA is proposed to address and resolve the problem. Do-

main shift in each LoRA layer can be expressed through

differences between the pre-training and ﬁne-tuning activa-

tions. In the LoRA layer, the input activations are processed

by a linear weight matrix to produce output activations. Ac-

cordingly, we could consider four variables of interest in

the LoRA layer: (a) pre-training (source) input activations

(b) pre-trained (source) weights (c) ﬁne-tuning (target) in-

put activations (d) ﬁne-tuned (target) weights. We propose

domain shift constraints to relate all these four variables of

interest with the aim to obtain an initial estimate of the tar-

get weights. However, source input activations are not avail-

able during ﬁne-tuning. Hence, we propose using rough

assumptions or constraints about the source input activa-

tions. The domain shift constraint can be applied between

the source and target output activations. We can gather these

two constraints to form a constraint set and obtain the tar-

get weights. Depending on how to select constraints, we

have multiple variants of constraint sets. In this paper, we

consider three types of constraint sets, which we refer to as

modes for initialization, see Section 3.2 for details.

We use constraint sets to obtain target weight of each

LoRA layer. The target weight can then be subtracted from

source weight to obtain LoRA weights, which can be fur-

ther decomposed to obtain up and down matrices of ﬁxed

rank. However, having ﬁxed-rank adapters across all at-

tachment points in a network is sub-optimal. Hence, we

propose variable adapter structure (VAS) to allocate vari-

able ranks across different attachment points. The relative

ranking can be obtained from the decomposition technique,

which is generally SVD. We propose using relative variance

of singular values in SVD decomposition to select adapter

ranks. More details of the procedure are in Section 3.3.

Our proposed framework is holistic in the sense that

it can initialize both the parameters and structure of the

adapter. Our framework, as depicted in Fig. 3, provides

ﬂexible design choices and is more effective than existing

data-driven solutions. Since we use constraints with no

training for LoRA initialization, we call our framework as

ConsNoTrainLoRA (CNTLoRA). We demonstrate the ef-

fectiveness of our approach through quantitative and quali-

tative results in Fig. 1and 2. Our approach shows signiﬁcant

gains over competing methods (e.g. better DINO scores at

step 100 and 1000 in Fig. 1) and better image ﬁdelity at even

100 iterations (Fig. 2). In summary, our contributions are:

• We propose a suite of modes for data-driven initialization

of LoRA. Each mode corresponds to an unique constraint

set among activations and weights to obtain a better esti-

mate of the ﬁne-tuned weights, enabling faster and better

convergence.

• Our approach enables the ﬂexibility of variable ranks

across different adapter attachment points using relative

signiﬁcance of singular values during weight decomposi-

tion.

• We demonstrate the effectiveness of our framework

across a variety of discriminative and generative tasks in-

volving both vision and language modalities. We explore

how different design choices and variations of our frame-

work can lead to different performance outputs.

2. Related Work

2.1. Low-rank adapter and its Variants

Fine-tuning using low-rank adaptation was introduced

in [18], and has garnered signiﬁcant attention. Multiple

follow-up works [4,10,13,16,20,21,26,31,50,51]

have been introduced, striving to improve latency, accuracy,

and memory efﬁciency. Some of the popular ones include

AdaLoRA [50], DoRA [24], LoRA-GA [46], and LoRA-

Figure 3. Visualization of our proposed framework. The input samples are fed to the network and the activations before the LoRA layer

are used for initialization of the LoRA weight matrix ∆Wi, which can then be decomposed to the up and down matrices.

XS [5]. AdaLoRA focuses on adaptive rank allocation for

different attachment points in the architecture. LoRA-GA

approximates the gradient of the pre-trained matrix using

SVD. LoRA-XS computes SVD of pre-trained weights for

LoRA weights and only updates the singular values for bet-

ter transferability to another model. Additionally, Rank-

stabilized LoRA (rsLoRA) [19] was proposed to adjust the

scaling factor for ﬁne-tuning compute/performance trade-

offs. In this paper, we compute the SVD of the LoRA ma-

trix to extract the up and down matrices.

2.2. Weight Initialization of Low-rank Adapter

Weight initialization of neural networks is a long-standing

topic. The early works of He et al. [17] and Glorot &

Bengio [15] developed methods to ensure stable training

of deep networks by considering activation functions and

network depth. For parameter-efﬁcient ﬁne-tuning, [18,22]

considered data-driven initialization by pre-training on a re-

lated task or unsupervised pre-training on the ﬁne-tuning

task. In [31], adaptation is done to initialize a sparse ma-

trix. Babakniya et al. [4] used SVD on weight matrices

after some ﬁne-tuning to initialize the LoRA matrices. Re-

cently, model-driven weight initialization has gained atten-

tion, and [9,29] use pre-trained weight information fol-

lowed by decomposition to initialize the LoRA weights.

EVA [33] considers initialization of down matrices using

singular vectors of activations. Recent works [46,47] also

consider data-driven initialization but do not consider adap-

tive rank allocation. Speciﬁcally, they consider the inter-

mediate activations of the LoRA layer and compute their

statistics followed by decomposition to obtain the up and

down matrices. Our proposed framework is a hybrid tech-

nique that considers both model-driven initialization and

data-driven initialization and can also seamlessly integrate

adaptive rank allocation if required.

2.3. Efﬁcient ﬁne-tuning of Low-rank adapter

Another line of work examines improving efﬁciency of

LoRA ﬁne-tuning. This includes memory-efﬁcient tech-

niques like [20], which keep LoRA matrices frozen and

only update scaling vectors. Other works improve mem-

ory and latency, including quantization techniques [12] in-

tegrated with LoRA. Interestingly, there are other vari-

ants of LoRA [12] that can integrate quantization into

their framework. Furthermore, customized initialization

has also improved the ﬁne-tuning results of quantized mod-

els [29,31,44]. In this paper, we consider improving con-

vergence and ﬁnal performance of ﬁne-tuning. While mem-

ory efﬁciency is not our primary objective, however, our

variable adapter rank is capable of achieving this efﬁciency.

3. Method

3.1. Background on LoRA

The rationale for using low-rank matrices is the assump-

tion that ﬁne-tuning data has low intrinsic dimensionality

and hence loss gradients are also low-rank [2]. The input

to the LoRA layer is: x∈Rd×1which is passed to the

pre-trained weight matrix W∈Rk×d. The LoRA layer

introduces new trainable low-rank matrices Aand Bsuch

that h=W x +BAx, where B∈Rk×rand A∈Rr×d.

The rank r≪kis a constant that needs to be ﬁxed be-

fore ﬁne-tuning. During ﬁne-tuning, Wis kept constant

but Aand Bare updated. In the original LoRA paper, it

was proposed to have Binitialized with zeros and Aini-

tialized randomly. Recent methods strive to initialize B,A

from the pre-trained weights Wand/or x. This is generally

done to improve convergence and ﬁnal performance scores.

Furthermore, a constant is used to scale BAx by α

3.2. ConsNoTrainLoRA

Our proposed initialization method is motivated by the do-

main shift between source and target activations. Here,

source activations are produced from the pre-training data,

while target activations are obtained from the ﬁne-tuning

data. Consider that the activation inputs for a LoRA layer i

from the source domain are denoted as Xi

src ∈Rd×band

those from the target domain are denoted as Xi

tar ∈Rd×b.

We consider the pre-trained weight of a LoRA layer as

src ∈Rk×d. Let the estimate of the initialization be de-

noted as Wi

tar ∈Rk×dsuch that Wi

tar =Wi

src + ∆Wi.

Our goal is to estimate Wi

tar from the variables Xi

src,

tar, and Wi

src. The caveat is that we have another un-

known Xi

src, which is not available during ﬁne-tuning.

Hence, we need to use multiple constraints on these vari-

ables so that the estimate of Wi

tar can be obtained. It

is important to note that these constraints are rough as-

sumptions just to provide a good initialization. After the

initialization, we would still constrain adapter training us-

ing standard task objectives. We can represent them as a

constraint set such that Fj(Xi

src,Xi

tar,Wi

src,Wi

tar) = 0

where j= 1,2, ....N. Since we have two unknown vari-

ables, we set N= 2. We propose three constraint sets that

are aimed to capture different statistical relations between

the source and target activations. Now, we proceed to de-

scribe the different constraint sets or modes (as we shall call

them in the paper) for initialization.

Cross Mode In this mode, we mainly consider ﬁrst or-

der matching between the source and target domain. This

is achieved through two constraints: (1) Output activations

of the source and target domain are equal. (2) Input activa-

tions of the source and target domain are highly correlated.

Constraint (1) can be realized as

F1(Xi

src,Xi

tar,Wi

src,Wi

tar) = Wi

srcXi

src−Wi

tarXi

tar =0

(1)

Constraint (2) can be realized as

F2(Xi

src,Xi

tar,Wi

src,Wi

tar) = Xi

srcXiT

tar −I=0(2)

Equation (2) can be re-arranged as Xi

srcXiT

tar =I.

Equation (1) can then be re-arranged as Wi

srcXi

src =

tarXi

tar, which when multiplied by XiT

tar on both sides,

we get

src =Wi

tarXi

tarXiT

tar (3)

Re-arranging the equation, we can obtain the least squares

pseudo-inverse [30] solution as

tar =Wi

src(Xi

tarXiT

tar)†CNTLoRA-X (4)

Self Mode In this mode, we mainly consider second or-

der matching between the source and target domain. This is

achieved through: (1) Covariances of source and target out-

put activations are equal. (2) Input activations of the source

domain are whitened. Constraint (1) can be realized as

F1(Xi

src,Xi

tar,Wi

src,Wi

tar) = 0(5)

srcXi

srcXiT

srcWiT

src −Wi

tarXi

tarXiT

tarWiT

tar =0(6)

Constraint (2) can be realized as

F2(Xi

src,Xi

tar,Wi

src,Wi

tar) = Xi

srcXiT

src −I=0(7)

Equation (7) can be re-arranged as Xi

srcXiT

src =

I. Equation (5) can then be re-arranged as

srcXi

srcXiT

srcWiT

src =Wi

tarXi

tarXiT

tarWiT

tar, which can

be rewritten as

srcWiT

src =Wi

tarXi

tarXiT

tarWiT

tar (8)

(8) is a quadratic equation, with multiple solutions for

tar. However, we consider a speciﬁc solution obtained

from SVD of Xi

tarXiT

tar. The SVD is obtained as

tarXiT

tar =PiDiPiT =PiDi

0.5Di

0.5PiT (9)

Here, Diis a diagonal matrix and Di

0.5is its square root.

We can substitute Xi

tarXiT

tar into equation (8) as

srcWiT

src =Wi

tarPiDi

0.5DiT

0.5PiT WiT

tar (10)

We can regroup the above equation (10) into (11) as

(Wi

src)(WiT

src) = (Wi

tarPiDi

0.5)(DiT

0.5PiT WiT

tar)(11)

Matching the groups and re-arranging the equation, we

can obtain the least squares pseudo-inverse solution as

tar =Wi

src(PiDi

0.5)†CNTLoRA-S (12)

Shift Mode For the third constraint set, we consider mod-

eling the difference in domain shift between source and tar-

get features. This is acheived through the following two

constraints: (1) Domain Shift with source and target fea-

tures vary by a constant (2) Source features are whitened.

Constraint (1) can be realized as

F1(Xi

src,Xi

tar,Wi

src,Wi

tar) = 0(13)

tarXi

srcXiT

srcWiT

src −Wi

tarXi

tarXiT

tarWiT

tar −C=0

(14)

Here, Cis a hyper-parameter we can vary. Constraint (2)

can be realized as

F2(Xi

src,Xi

tar,Wi

src,Wi

tar) = Xi

srcXiT

src −I=0(15)

Equation (15) can be re-arranged as Xi

srcXiT

src =Iand

plugged into (13) to obtain

tarWiT

src −Wi

tarXi

tarXiT

tarWiT

src −C=0(16)

Re-arranging the equation, we can obtain the least squares

pseudo-inverse solution as

tar =C(WiT

src −Xi

tarXiT

tarWiT

src)†(17)

CNTLoRA-Sh

By default, we use Cas identity.

For each of the modes, the estimate can be repeated over

all Bbatches to obtain a robust estimate Wi

est such that

est =Wi

0+PB

j=1 wj[Wi

tar]j

B+ 1 (18)

where wj(default value of 1) is the weighing amount of the

jth batch. Wi

0can be set to the pre-trained weight Wi

src as

the default value.

Here, Wi

est can be subtracted from Wi

src to obtain

∆Wi

est, which can then be decomposed with rank rto ob-

tain ∆Wi

est =Ui

est[:: r]Si

est[: r]Vi

est[: r:], where we can

fractionally allocate the singular matrix Si

est[: r]such that

Bi=Ui

est[:: r]Si(1−p)

est [: r]and Ai=Sip

est[: r]Vi

est[: r:].

By default, p= 0.5. Alternatively, ∆Wi

est can be obtained

through QR decomposition as ∆Wi

est =Qi

est[:: r]Ri

est[:

r:] with Bi=Qi

est[:: r]and Ai=Ri

est[: r:].

3.3. Special cases

Text to Image Generation For text-to-image generation,

we consider different options for feeding into UNet. Dur-

ing training, a noisy version of the image is fed into the

UNet while during inference, the denoising process starts

from a noise. For LoRA initialization, we consider in-

putting a noisy version of the image into the UNet: (a)

xt=√αtzt+√1−αt·ϵsuch that ϵ∼N(0, I), where the

latent zt=E(Iimg)and Eis the VAE encoder and Iimg is

the input image. Here, αt∈(0,1) is a variance scheduler.

(b) Alternatively, the input can just be the latent embedding

ztwithout any noise addition. We consider (b) as default.

Variable Adapter Structure (VAS) By default, we have

ﬁxed and same rank allocation across all attachment points

of the foundation model. However, for efﬁcient deploy-

ment, there might be restrictions on the adapter sizes. To

maintain efﬁciency, we need adaptive ranking across attach-

ment points. Our framework allows seamless integration

for adaptive ranks, especially for the SVD decomposition of

∆Wi

est =Ui

estSi

estVi

est for attachment point i. Here, Si

est

is the diagonal singular value matrix, where si

mis the mth

singular value corresponding to attachment point i. The rel-

ative variance vi

mof the singular value si

mis given by

m∝si2

m/||Si

est||1,(19)

and the proportion constant is obtained by summing over all

the singular values and dividing by the sum. This process

of obtaining relative variance vi

mis repeated for all attach-

ment points, and we collect them into a long list v, which

is sorted in descending order, and the top-Kvalues are ob-

tained. The value of Kis the rank budget i.e. the maximum

sum of all the ranks for that particular model. From the

Kvalues, we count the contribution from each attachment

point iand accordingly assign the count as the rank of the

corresponding attachment point i. This process of rank al-

location is described in Fig. 4, and we set the default value

of Kas the rank times the number of attachment points.

In supplementary, we also visualize VAS and analyze

how other LoRA variants can be expressed as constraints

and justify convergence of our method using gradient infor-

mation.

Figure 4. Visualization of how variable ranking is done to obtain

variable adapter structure.

4. Experiments

4.1. Experimental Settings

Image Generation We evaluate on the Dreambooth [37]

dataset, using DINO and CLIP-I for subject ﬁdelity, and

CLIP-T for prompt ﬁdelity. We use Stable Diffusion

v1.5 [36]. During ﬁne-tuning, in addition to denoising loss,

we use prior preservation loss weighted at 0.1 with 250 gen-

erated class samples. The LoRA [18] is applied to the cross

and self-attention layers of UNet and attention layers of text

encoder [34]. The default rank and batch size are 128 and 1,

respectively. We use AdamW [27] optimizer with a learning

rate of 1e-4 and ﬁne-tune over 1000 steps.

Image Classiﬁcation We consider VTAB-1K [49], which

has been the standard benchmark for evaluating PEFT

methods. The datasets in this benchmark are used to ﬁne-

tune a DINOv2-g/14 model [32], which is the same as used

in EVA [33]. For fair comparison, our default hyperparam-

eters are those used in EVA [33].

Image Understanding We consider two datasets: ﬁrst, the

Amazon Product Description dataset (APD) [38] for prod-

uct marketing. We ﬁne-tune the LoRA with the GLM-Edge

model [48] on this dataset. We further evaluate on myVLM

dataset [3], which consists of concepts for personalized cap-

tioning. For ﬁne-tuning, we use LLAVA-v1.5-7B [23]. For

the APD dataset, we report the SentSim [35] scores while

for the myVLM dataset, we report an additional Recall met-

ric to identify the concept in the generated caption.

More details about the implementation, evaluation setup,

and additional results are in the supplementary material

4.2. Results

4.2.1. Image generation

Quantitative Results We compare CNTLoRA with EVA,

CORDA, LoRA-GA, PISSA, and OLoRA for ﬁne-tuning

performance. Table 1shows that CNTLoRA methods con-

sistently outperform the others. CNTLoRA-X achieves the

Table 1. Final quantitative results (1000 iterations) of different

methods on the Dreambooth dataset using SD 1.5.

Method DINO (↑)CLIP-I (↑)CLIP-T (↑)

LoRA 62.74 80.07 26.43

OLoRA 58.36 77.56 27.23

PISSA 52.34 74.41 27.98

EVA 62.24 79.68 25.7

CORDA 55.65 71.44 25.6

LoRA-GA 60.30 76.10 26.23

DoRA 62.98 80.81 27.04

RS-LoRA 63.12 81.07 26.98

CNTLoRA-X 64.63 80.78 25.83

CNTLoRA-S 63.91 81.7 27.07

CNTLoRA-Sh 62.95 80.97 27.87

CNTDoRA-X 64.82 81.02 27.67

CNTRS-LoRA-X 64.93 81.61 27.86

CNTLoRA-X + VAS 65.73 81.98 25.63

CNTLoRA-S + VAS 64.94 82.6 27.17

CNTLoRA-Sh + VAS 63.55 82.03 27.98

highest DINO score of 64.63. For CLIP-I, CNTLoRA-

S produces score of 81.7, while CNTLoRA-Sh produces

score of 80.97. For CLIP-T, CNTLoRA-S and CNTLoRA-

Sh produce scores of 27.07 and 27.87, respectively. Inte-

grating CNTLoRA-X with DoRA and RS-LoRA also im-

proves performance. For DINO, CNTDoRA-X produces

score of 64.82, and CNTRS-LoRA-X produces a score of

64.93. For CLIP-I, CNTRS-LoRA-X scores 81.61, and

CNTDoRA-X scores 81.02. For CLIP-T, CNTRS-LoRA-

X scores 27.86, and CNTDoRA-X scores 27.67. These

integrations balance improvements across all metrics. Ex-

periments on variable adapter structure (VAS) show perfor-

mance gains when combined with CNTLoRA. CNTLoRA-

S + VAS and CNTLoRA-Sh + VAS improves DINO, CLIP-

I, and CLIP-T scores. VAS optimizes for variable rank al-

location, enhancing overall performance.

Table 2. Cosine similarity and Spectral Norm between the initial-

ized adapters and the ﬁnal adapters for different methods.

Cosine Similarity (↑)Spectral Norm (↓)

Method Query Key Value Out Query Key Value Out

LoRA 0.515 0.356 0.366 0.522 4.490 3.953 1.907 1.408

EVA 0.583 0.492 0.434 0.783 0.614 0.627 1.022 0.791

CNTLoRA-X 0.610 0.643 0.788 0.816 0.516 0.620 0.838 0.646

CNTLoRA-S 0.519 0.610 0.623 0.785 0.517 0.621 0.946 0.738

CNTLoRA-Sh 0.586 0.535 0.613 0.760 0.574 0.726 0.925 0.631

Difference between Initial and Final Weights We eval-

uated the effectiveness of initialization methods by mea-

suring the cosine similarity and spectral norm differences

between initialized and ﬁne-tuned adapters. Higher co-

sine similarity and lower spectral norm differences indi-

cate better initialization, reducing weight adjustments dur-

ing training. Table 2shows that CNTLoRA variants con-

sistently have higher similarity than EVA and LoRA, with

CNTLoRA-X showing the strongest correlation. This sug-

gests that our method starts adapters closer to their optimal

conﬁguration, leading to more faster convergence.

Table 3. Final quantitative results i.e. DINO scores for (1000 it-

erations) on the Dreambooth dataset using SD 1.5 for different

number of training samples per concept used in the initialization.

Method n=1 n=2 n=4 All

EVA 61.23 61.26 61.84 62.24

CORDA 54.68 55.01 55.60 55.65

LoRA-GA 58.04 58.92 59.68 60.30

CNTLoRA-X 64.02 64.28 64.50 64.63

CNTLoRA-S 62.98 63.16 63.52 63.91

CNTLoRA-Sh 61.78 61.97 62.45 62.95

Effect of Number of Samples To assess the impact of

the number of training samples on initialization, we ﬁne-

tuned Stable Diffusion v1.5 using EVA, CORDA, LoRA-

GA, and CNTLoRA variants. This experiment reveals how

each method initializes with varying amounts of data. We

tested different sample sizes (n=1, 2, 4, All) to evaluate

ﬁne-tuning efﬁciency and model convergence. CNTLoRA-

X consistently outperforms other methods, especially with

fewer samples, highlighting the importance of high-quality

initialization in low-data scenarios.

Figure 5. Plot showing how the CLIP score evolves for different

initialization methods as a function of wall clock time

Convergence Study We analyzed how different initializa-

tion strategies affect the ﬁne-tuning dynamics by tracking

the progression of CLIP-I score over 1000 training steps.

Figure 5shows CLIP-I score evolution for various meth-

ods, including EVA, OLoRA, PISSA, and our proposed

CNTLoRA variants. The results show that CNTLoRA

variants achieve a steeper increase in scores compared to

baseline methods, highlighting their ability to accelerate

convergence. In the later stages of training, CNTLoRA-

X, CNTLoRA-S, and CNTLoRA-Sh consistently attain the

highest CLIP-I scores, demonstrating their effectiveness.

Time for Initialization In Table 4, we compare initializa-

tion times for various techniques over 1000 iterations on

Table 4. Time (s) required for computing the initialization of dif-

ferent techniques while training over 1000 iterations (922.19 s) of

a concept on the Dreambooth dataset using SD 1.5.

PISSA OLoRA EVA CORDA CNTLoRA-X CNTLoRA-S CNTLoRA-Sh

Init (↓) 5.9 5.51 15.9 11.8 13.1 15.1 13.1

Training 922.19 922.19 922.19 922.19 922.19 922.19 922.19

%(↓) 0.64 0.59 1.71 1.27 1.42 1.63 1.41

Dreambooth dataset using Stable Diffusion v1.5. OLoRA

has the shortest initialization time at 5.51 seconds (0.59%

of total training time), followed by PISSA at 5.9 seconds

(0.64%). Our methods, CNTLoRA-X, CNTLoRA-S, and

CNTLoRA-Sh, have competitive times of 13.1, 15.1, and

13.1 seconds, respectively. These results show balance

between initialization efﬁciency and training performance,

with OLoRA and PISSA being fastest, while CNTLoRA

methods offer good trade-off.

4.2.2. Image classiﬁcation

Table 5. Fine-tuning DINOv2-g/14 on the VTAB-1K benchmark.

We report average accuracy across ﬁve seeds.

Natural Specialized Structured

Cifar100

Caltech101

DTD

Pets

SVHN

Sun397

EuroSAT

Retinopathy

CLEVR-Count

CLEVR-Dist

DMLab

KITTI-Dist

dSpr-Ori

sNORB-Ele

Average

FFT 73.1 89.7 78.4 92.2 89.5 55.5 95.0 70.5 93.6 64.2 63.6 68.8 64.3 56.8 75.4

LoRA 85.9 92.2 82.2 94.5 64.1 63.6 92.6 76.6 97.7 65.3 62.1 83.6 63.0 52.3 76.8

AdaLoRA 85.4 92.5 81.4 95.0 90.5 62.2 96.4 76.6 94.4 64.4 60.3 83.7 61.0 46.0 77.8

PiSSA 85.5 93.6 82.3 94.6 92.8 62.3 96.6 76.3 95.0 66.3 63.2 84.9 60.1 48.6 78.7

OLoRA 85.5 93.0 82.1 95.1 78.3 62.1 96.3 76.8 94.3 66.0 62.4 71.3 60.9 49.5 76.7

EVA 85.6 93.9 82.2 95.9 93.2 63.6 96.6 76.1 96.1 65.1 61.1 83.3 61.6 55.0 79.2

DoRA 85.9 92.7 82.1 95.2 34.4 61.4 96.8 76.8 97.6 65.4 62.7 84.4 63.1 52.6 75.1

EVA+DoRA 86.2 92.1 81.9 94.9 93.8 62.4 96.6 76.7 97.2 65.5 54.1 83.7 62.3 54.5 78.7

CoRDA 84.3 89.2 80.1 94.2 93.1 63.6 96.1 76.4 97.2 64.6 61.3 81.4 63.2 55.3 78.6

CNTLoRA-X 86.1 94.0 83.1 96.1 94.2 64.2 97.3 77.0 97.8 65.6 63.7 85.1 65.3 57.0 80.5

CNTLoRA-S 86.3 94.2 83.4 96.0 94.1 64.4 97.1 77.0 97.9 66.9 64.7 85.3 65.2 57.4 80.7

CNTLoRA-Sh 86.1 94.1 83.2 96.2 94.3 64.3 97.0 77.0 97.4 66.4 64.8 85.2 65.2 57.2 80.6

Quantitative Results We ﬁne-tuned the DINOv2-g/14

model on the VTAB-1K benchmark, which includes Nat-

ural, Specialized, and Structured datasets. Various ini-

tialization methods, including our CNTLoRA methods,

were evaluated across ﬁve seeds for robustness. The re-

sults in Table 5show that CNTLoRA methods consistently

achieve high performance. CNTLoRA-X, CNTLoRA-S,

and CNTLoRA-Sh often outperform other methods like

FFT, LoRA, and AdaLoRA. CNTLoRA-S achieved the

highest average accuracy in several datasets, particularly ex-

celling in the Natural category (e.g., Cifar100, Caltech101,

DTD) and maintaining competitive performance in the Spe-

cialized and Structured categories (e.g., CLEVR-Count,

CLEVR-Dist, DMLab).

Convergence Study Figures 6illustrate the training dy-

namics of the DINOv2-g/14 model ﬁne-tuned with vari-

ous initialization methods on the Caltech101 and EuroSAT

datasets. These plots provide insights into the conver-

gence behavior and stability of the different methods. As

Figure 6. Evolution of loss & evaluation accuracy with epochs on

the Caltech & EuroSAT dataset

shown in Figure 6, the accuracy of the model on the

Caltech101 dataset increases with the number of training

steps. The CNTLoRA methods, particularly CNTLoRA-

S, exhibit a faster convergence rate compared to other

methods. CNTLoRA-S achieves higher accuracy ear-

lier in the training process, indicating its effectiveness in

LoRA ﬁne-tuning. This rapid convergence suggests that

CNTLoRA-S can effectively leverage the pre-trained fea-

tures of the DINOv2-g/14 model, leading to improved per-

formance. Figure 6shows the accuracy progression on the

EuroSAT dataset. Similar to the results on Caltech101,

the CNTLoRA methods demonstrate superior performance.

CNTLoRA-X and CNTLoRA-S consistently achieve higher

accuracy throughout the training process. The plots indicate

that these methods not only converge faster but also main-

tain higher accuracy levels compared to other methods.

4.2.3. Image understanding

Table 6. Comparison on Image Understanding task for Amazon

Product Description (APD) &myVLM (VLM) datasets.

Method SentSim (↑) (APD) SentSim (↑)(VLM) Recall (↑) (VLM)

LoRA 0.8013 0.6123 0.7134

AdaLoRA 0.8087 0.6164 0.7166

PiSSA 0.8132 0.6014 0.7143

OLoRA 0.8079 0.6115 0.7162

EVA 0.8186 0.6268 0.7250

LoRA-GA 0.8177 0.6194 0.7160

CoRDA 0.8121 0.6195 0.7180

CNTLoRA-X 0.8117 0.6355 0.7320

CNTLoRA-S 0.8256 0.6385 0.7390

CNTLoRA-Sh 0.8273 0.6336 0.7341

CNTLoRA-X + VAS 0.8192 0.6403 0.7419

CNTLoRA-S + VAS 0.8301 0.6442 0.7495

CNTLoRA-Sh + VAS 0.8324 0.6412 0.7455

Quantitative Results The results summarized in Table 6,

demonstrate that CNTLoRA methods consistently achieve

high performance across different datasets. Table 6presents

a comparison of various methods on image understanding

task for the APD and VLM datasets. The evaluation met-

rics include SentSim (Sentence Similarity) for both datasets

and Recall for VLM dataset. The best results are high-

lighted in bold, while the second-best results are underlined.

The CNTLoRA methods, particularly CNTLoRA-S and

CNTLoRA-Sh, demonstrate superior performance across

metrics. For the APD dataset, CNTLoRA-Sh achieves

the highest SentSim score of 0.8273, followed closely by

CNTLoRA-S. This indicates that these methods are highly

effective in understanding and relating visual content to

textual descriptions. In the VLM dataset, CNTLoRA-S

achieves the highest SentSim score of and the highest Re-

call score, showcasing its robustness and effectiveness in

visual language model tasks. CNTLoRA-Sh also performs

exceptionally well, with a SentSim score of 0.6336 and a

Recall score of 0.7341, both of which are among top results.

Compared to other methods, such as LoRA, AdaLoRA,

PiSSA, OLoRA, EVA, LoRA-GA, and CoRDA, the CNT-

LoRA methods consistently achieve higher scores, indicat-

ing superior capability in image understanding tasks. Fur-

thermore, as expected, when we apply VAS on top of all

variations of CNTLoRA, the performance improves due to

the optimal allocation of ranks.

Convergence Study In Fig. 7, we observe how Recall

and SentSim values evolve with the increasing number of

epochs on the myVLM dataset. Overall, our proposed

CNTLoRA variations evolve faster and also produce much

higher ﬁnal convergence scores. On this dataset, data-driven

LoRA initialization seems to be more effective, as shown by

the poor performance of random initialization. Among our

proposed variations CNTLoRA-S seems to be more effec-

tive suggesting that the covariance matching of activations

is more important on this dataset.

Figure 7. Progression of evaluation metrics over epochs on

myVLM dataset

Qualitative Results Fig. 8shows how captions on the eval-

uation set evolve for different training steps (i.e., 6, 14, 20)

for different initialization methods: LoRA (random), EVA

and CNTLoRA-X. For the <my dog>case, LoRA can-

not detect at 6 steps and hence produces a general caption.

On the other hand, EVA and CNTLoRA-X can identify the

Figure 8. Figure showing how image captions evolve with increas-

ing no. of steps for different input images. The samples are from

myVLM dataset. Presence of <*>in generated outputs suggests

that the concept has been identiﬁed. Furthermore, generation of

concise prompts suggest that model has been well ﬁne-tuned.

presence of the concept. However, CNTLoRA-X produces

a more appropriate response by identifying a dog bed in-

stead of a table. For <my mug>, our proposed method can

detect a personalized object at step 6, while other methods

cannot. At step 20, our method produces more descriptive

captions for mug compared to LoRA and EVA.

5. Conclusion

In conclusion, our data-driven weight initialization tech-

nique, CNTLoRA, signiﬁcantly improves convergence

speed and ﬁnal performance of LoRA in ﬁne-tuning tasks.

By treating LoRA initialization as a domain shift problem

and using activation vector constraints, we derived a closed-

form estimate for LoRA weights. This enhances perfor-

mance across tasks like image generation, classiﬁcation,

and understanding. Our analyses validate CNTLoRA’s ro-

bustness and efﬁcacy, with CNTLoRA-X achieving better

performance in few shot adaptation of the image generation

task, while CNTLoRA-S producing better performance in

the many-shot adaptation of image classiﬁcation and under-

standing. Additionally, our proposed variable adapter struc-

ture improved recognition performance by allowing optimal

rank allocation. Future work will explore more constraints

to reﬁne and expand our framework’s applicability.

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A. Additional Experimental Details

Image Generation For the image generation task, we con-

sider the Dreambooth [37] dataset. This dataset consists

of 30 image sets from 15 different categories in which each

category consists of 4 to 6 images per concept. The subjects

primarily fall into two types: living or non-living. Based on

this distinction, 25 prompts are used for evaluation across

four different seeds. For the training, we used the default

learning rate of 1e-4 (AdamW optimizer), with batch size

of 1, with prior preservation loss weight of 0.1. The LoRA

rank is set to 128 with α= 256 and is applied to atten-

tion layers of the text encoder, as well as to both the self-

attention and cross-attention layers of the UNet of Stable

Diffusion V1.5. LoRA is attached to the key, query, value,

and output projection matrices in the attention layers of both

the UNet and the text encoder. Training is conducted over

1000 iterations per concept.

Image Classiﬁcation For image classiﬁcation, we ﬁne-tune

the DINOv2-g/14 model [32] using VTAB-1K [49], which

consists of 19 classiﬁcation tasks spanning natural, special-

ized, and structured domains. In our experiments, we se-

lect 14 tasks from VTAB-1K to assess ﬁne-tuning perfor-

mance. To incorporate AdaLoRA, PiSSA, OLoRA, EVA,

DoRA, and CoRDA, we adapt their implementations from

the peft library. The classiﬁer head is initialized with

weights drawn from a normal distribution (σ= 2e−5),

while biases are set to zero. Throughout ﬁne-tuning, we

update the classiﬁcation head, LoRA matrices, and biases.

LoRA matrices are applied to most linear layers, especially

query, key, and value components of attention layers, as

well as the dense and fully connected layers. Input images

are rescaled to 224 ×224 using bicubic interpolation and

normalized according to ImageNet’s per-channel mean and

variance. Fine-tuning is performed with bﬂoat16 precision,

using AdamW (weight decay = 0.05) for 30 epochs. The

learning rate follows a cosine decay schedule, with a lin-

ear warm-up phase spanning the ﬁrst three epochs. For full

ﬁne-tuning, a layer-wise learning rate decay of 0.75 is ap-

plied.

Image Understanding For image understanding, we con-

sider Amazon Product Description dataset (APD) [38] for

product marketing. The APD dataset is a large-scale re-

source designed for product marketing and e-commerce ap-

plications, encompassing both structured metadata and un-

structured textual descriptions across a wide range of prod-

uct categories. For ﬁne-tuning, we use the GLM-Edge

model [48], incorporating LoRA-based adaptation with a

rank of 32 and α= 64, optimizing it to generate domain-

speciﬁc product descriptions. The attachment points are

done at query, key and value locations of all attention lay-

ers in the vision encoder as well as the language model.

Additionally, we utilize the myVLM dataset [3], which is

tailored for personalized vision-language modeling, focus-

ing on concept-based captioning where descriptions are tai-

lored to user-deﬁned preferences and contexts. The dataset

comprises manually annotated image-text pairs, ensuring

high-quality supervision for customized caption generation

and multimodal retrieval tasks. We ﬁne-tune LLAVA-v1.5-

7B [23], a vision-language model, applying adapters with a

rank of 128 and α= 256 to the self-attention layers in the

visual encoder and both the self-attention and feed-forward

network (FFN) layers in the language model. For the atten-

tion blocks, LoRA is attached at the query, key and value

locations. In both the models, training is conducted using

AdamW optimizer with a learning rate of 2e-4 and batch

size of 8. For the both tasks, ﬁne-tuning is performed over

20 epochs using all available samples. Fig. 9shows the in-

put prompts used in the datasets.

Figure 9. Figure showing the input prompts used in the myVLM

and Amazon Product Description datasets.

Language Understanding For language understanding, we

consider the popular GLUE Benchmark [45]. This bench-

mark consists of eight downstream tasks, such as natural

language inference, or sentiment analyses. For the base

model, we use the large version of Roberta [25]. The hy-

perparameters used are the same as EVA [33]. For the eval-

uation metrics, we report accuracy for all tasks except for

CoLA and STS-B, where we report Matthew’s correlation

and Pearson’s correlation, respectively.

B. Gradient Analysis

Our proposed initialization method requires initialization of

Ai, the down matrices and Bi, the up matrices separately.

The gradients of Aiand Biwith respect to the task loss L

is given as ∂L

∂Ai=BiT ∂L

∂YXiT

tar, where Yis the output

of the LoRA layer. Similarly, the gradient of the task loss

Lwith respect to Biis given as ∂L

∂Bi=∂L

∂YXiT

tarAiT .

From the expression, it is clear that the initial gradients

would depend on the initial values of Aiand Bi. For ran-

dom initialization, ∂L

∂Aiwould be zero as Biis initialized

to 0. This can slow down the convergence. For data-driven

initialization like EVA, Aiis initialized from data and it is

likely to assist ∂L

∂Biin the convergence. However, still Biis

initialized to 0 and hence the initial gradients of ∂L

∂Aiwould

be zero and hence affecting convergence. For our proposed

method, the initial values of Biand Aiare non-zero and

both depend on the principal components of the input acti-

vations Xi

tar. Consequently, both of the gradients have a

dependency on Xi

tar beyond ﬁrst order and hence we ex-

pect faster convergence compared to EVA.

C. Competitive Low Rank Adaptors as Con-

straints

The ﬁrst example of Native LoRA is as follows:

F1(Xi

src,Xi

tar,Wi

src,Wi

tar) = 0(20)

tar −Wi

src =0=⇒∆Wi=0(21)

=⇒Bi=0,Ai∼ N(0,I)(22)

PISSA can be expressed as:

F1(Xi

src,Xi

tar,Wi

src,Wi

tar) = 0(23)

tar −2Wi

src =0=⇒∆Wi=Wi

src (24)

∆Wi=UiSiVi=⇒Bi=Ui[:: r]Si[: r]0.5,(25)

Ai=Si[: r]0.5Vi[: r:] (26)

OLORA can be expressed as:

F1(Xi

src,Xi

tar,Wi

src,Wi

tar) = 0(27)

tar −2Wi

src =0=⇒∆Wi=Wi

src (28)

∆Wi=Qi[:: r]Ri[: r:] =⇒Bi=Qi[:: r],(29)

Ai=Ri[: r:] (30)

CORDA can be expressed as:

F1(Xi

src,Xi

tar,Wi

src,Wi

tar) = 0(31)

(Wi

tar −Wi

src)Xi

tarXiT

tar −SVD((Wi

tar)Xi

tarXiT

tar) = 0

(32)

=⇒∆WiCi

tar =SVD(Wi

tarCi

tar)(33)

=⇒∆Wi=SVD(Wi

tarCi

tar)Ci

tar

−1(34)

=⇒Ai= (Si)0.5[: r](ViCi

tar)−1[: r:] (35)

=⇒Bi=Ui[:: r](Si)0.5[: r](36)

EVA can be expressed as:

F1(Xi

src,Xi

tar,Wi

src,Wi

tar) = 0(37)

Ai=Vi[: r:] where (38)

Ui[:: r],Si[: r],Vi[: r:] = SVD(Xi

tar)(39)

D. Additional Experiments

D.1. Image generation

Effect of different ranks We also study how different

ranks affect quantitative performance of the model as shown

in Table 7. We have originally used the default rank of

128, on which our proposed method and their variations

CNTLoRA-X, CNTLoRA-S, CNTLoRA-Sh produced bet-

ter DINO scores than competitive methods. The pattern

holds true even for lower ranks of 64 and 32. In fact,

CNTLoRA-X at rank 64 produces better DINO scores than

what LoRA and EVA produces at rank of 128.

Table 7. Final quantitative results (DINO) (1000 iterations) of dif-

ferent methods on the Dreambooth dataset using SD 1.5 for differ-

ent ranks. Higher (↑) is better.

Method 128 64 32

LoRA 62.74 59.07 56.62

EVA 62.24 60.93 57.41

CNTLoRA-X 64.63 62.98 59.09

CNTLoRA-S 63.91 62.25 58.23

CNTLoRA-Sh 62.95 61.02 57.69

Effect of different learning rates We also study how dif-

ferent learning rates affect quantitative performance of the

model as shown in Table 8. We have originally used

the default learning rate of 1e-4, on which our proposed

method and their variations CNTLoRA-X, CNTLoRA-S,

CNTLoRA-Sh produce better DINO scores than compet-

itive methods. The pattern holds true even for different

learning rates of 1e-3 and 1e-5. For both these learning rates

we see a general drop in performance compared to that at

1e-3. The reason for drop at 1e-5 is because of slower learn-

ing rate and not enough iterations to converge. The reason

for drop in learning rate at 1e-3 is due to instability in the

ﬁne-tuning procedure.

Table 8. Final quantitative results (DINO) (1000 iterations) of dif-

ferent methods on the Dreambooth dataset using SD 1.5 for differ-

ent learning rates.

Method 1e-4 1e-3 1e-5

LoRA 62.74 60.51 58.42

EVA 62.24 60.26 59.01

CNTLoRA-X 64.63 61.98 60.05

CNTLoRA-S 63.91 61.92 60.22

CNTLoRA-Sh 62.95 60.81 59.10

Rank distribution in VAS In our proposed Variable

Adapter Structure (VAS) framework, we have variable

ranks across different attachment points. In Fig. 10, we

visualize this variable rank allocation across attachment

points for both the UNet and Text Encoder when ﬁnetuned

on the dog class of the Dreambooth dataset. For the UNet

Figure 10. Plot showing how the rank distribution takes place for the dog class in the Dreambooth dataset.

case, we see that the rank is distributed more or less ran-

domly across all attachment points. For the ”Out” attach-

ment point in the attention block, we see lower rank alloca-

tion in deeper layers suggesting lesser importance of LoRA

modules in that region. For the text encoder case, we see

higher rank allocation in the initial layers while lower rank

allocation in the deeper layers of the text encoder. This

suggests lesser importance of LoRA modules in the deeper

layer.

Table 9. Final quantitative results (1000 iterations) of different

variations of our method on the Dreambooth dataset using SD 1.5.

Method DINO (↑)CLIP-I (↑)CLIP-T (↑)

CNTLoRA-X-QR 65.29 78.63 27.36

CNTLoRA-X-0.75 65.78 81.34 24.91

CNTLoRA-X-0.25 63.26 79.71 27.01

CNTLoRA-X-0.1 62.41 78.23 28.34

CNTLoRA-Sh-Norm. 61.2 79.34 28.10

CNTLoRA-Sh-10 62.13 79.92 28.13

CNTLoRA-Sh-0.1 62.42 79.96 27.95

Additional Variations In Table 9, we consider different

variations of CNTLoRA. CNTLoRA-X-QR uses QR de-

composition instead of SVD for allocating the up and down

matrices. CNTLoRA-X-puses fractional allocation of p

when splitting the singular matrix Sand allocating it to

up and down matrices. By default, we use p= 0.5. Fur-

thermore, we consider different variations of CNTLoRA-

Sh where the constant Cis varied from the default value of

identity: (a) Norm where Cis normally distributed. (b) 10

where Cis 10 times identity (c) 0.1 where Cis 0.1 times

identity. Overall, we see that the DINO score and CLIP-

T score of CNTLoRA-X-QR improves over CNTLoRA-X.

This might be due to the fact that for QR decomposition,

there is no fractional allocation of singular matrix between

up and down matrices and hence there is balance between

image and text ﬁdelity quite well. In fact, the fractional

value pcan allow us to balance image and text ﬁdelity

well. As seen for higher fraction value of 0.75, DINO

score increases while CLIP-T score decreases. If we de-

crease the fraction value to 0.25, DINO score decrease to

63.26 while the CLIP-T score increases to 27.01. When the

fraction value is decreased further to 0.1, DINO score de-

creases to 62.41 while CLIP-T increases to 28.04. Hence,

our proposed fractional allocation can maintain a balance

between image and text ﬁdelity. As for different variants of

CNTLoRA-Sh, the newer hyperparameters of Cseems to

produce poorer image ﬁdelty performance. However, they

lead to better prompt ﬁdelity.

Qualitative Results We also show qualitative results on ad-

ditional prompts for the duck, teapot and dog classes in

Figs. 11,12 and 13 respectively. In Fig. 11, we observe

that at 100 iterations of training, LoRA (i.e. random ini-

tialization) produces poor performance in terms of image

ﬁdelity. However, for both EVA and CNTLoRA-X, we ob-

serve better image ﬁdelity due to data-driven initialization.

Infact, for the prompt “A S* toy ﬂoating on top of water”,

CNTLoRA-X produces better image ﬁdelity where the face

of the duck atleast appears compared to that of EVA.

In Fig. 12, we observe that at 100 iterations of training,

LoRA (i.e. random initialization) and EVA produces poor

Figure 11. Plot showing how the generation evolves for different initialization methods on the Dreambooth dataset for the duck class. The

prompts from left to right are (a) A S* toy ﬂoating on top of water. (b) A S* toy in the snow. (c) A S* toy with a city in the background.

Figure 12. Plot showing how the generation evolves for different initialization methods on the Dreambooth dataset for the teapot class. The

prompts from left to right are (a) A S* teapot with a wheat ﬁeld in the background. (b) A S* teapot with the Eiffel tower in the background.

performance in terms of image ﬁdelity for the prompt “A S*

teapot with the Eiffel tower in the background.”. However,

for CNTLoRA-X, we observe better image ﬁdelity. The

pattern is repeated even for the prompt “A S* teapot with

a wheat ﬁeld in the background.”

In Fig. 13, we observe that at 100 iterations of training,

LoRA (i.e. random initialization) and EVA produces poor

image ﬁdelity performance for the prompts “A S* dog in a

chef outﬁt.” and “A S* dog with a city in the background.”.

However, for CNTLoRA-X, we observe better image ﬁ-

delity. Even at 400 iterations of training, CNTLoRA-X pro-

duces better image ﬁdelity for the prompt “A S* dog in the

snow”.

Figure 13. Plot showing how the generation evolves for different initialization methods on the Dreambooth dataset for the dog class. The

prompts from left to right are (a) A S* dog in a chef outﬁt. (b) A S* dog in the snow. (c) A S* dog with a city in the background.

Figure 14. Figure showing how image captions evolve with in-

creasing number of steps for different conditioning input images.

The samples are from myVLM dataset. Presence of <*>in the

generated outputs suggest that the concept has been identiﬁed.

Furthermore, generation of concise prompts suggest that the model

has been well ﬁne-tuned.

D.2. Image Understanding

Qualitative results In Fig. 14, we observe how the cap-

tions evolve for different training steps i.e. 6, 14, 20 for the

<my shoe>and <my toy>object. Our proposed frame-

work CNTLoRA-X can recognize the personalized toy even

at 6 steps. Even at 20 steps, it produces a more descriptive

caption compared to LoRA and EVA. For the personalized

shoe, our proposed method can produce more descriptive

and accurate captions at Step 14 and Step 20. At step 6,

even though the personalized object is not identiﬁed, our

method CNTLoRA-X produces more accurate descriptions.

Rank Distribution in VAS In our proposed Variable

Adapter Structure (VAS) framework, we have variable

ranks across different attachment points. In Fig. 15, we

visualize this variable rank allocation across attachment

points for both the language model and vision encoder when

ﬁne-tuned on the myVLM dataset. For the language model

case, we see that the rank is distributed more or less ran-

domly across all attachment points. For the vision encoder

case, we see higher rank allocation in the later layers while

lower rank allocation in the shallower layers of the text

encoder. This suggests that the ﬁne-tuning image dataset

has not very different distribution from pre-training dataset.

Rather, the language style is changed and adapters need to

be learned mainly for the language model.

D.3. Language Understanding

Quantitative results We compare our methods against

existing parameter-efﬁcient ﬁne-tuning approaches on the

GLUE benchmark, which includes diverse language under-

Figure 15. Plot showing how the rank distribution takes place when ﬁne-tuned on the myVLM dataset.

Table 10. Comparison of all methods for RoBERTaLarge [25] on GLUE tasks. We report Matthew’s correlation for CoLA, Pearson correla-

tion for STS-B, matched accuracy for MNLI, and accuracy for remaining tasks.

Method MNLI QNLI QQP SST2 CoLA MRPC RTE STS-B Avg

FFT 90.2 94.7 92.2 96.4 68.0 90.9 86.6 92.4 88.93

LoRA 90.7 94.8 92.0 96.2 69.1 91.1 88.1 92.3 89.29

AdaLoRA 90.5 94.8 90.6 96.1 68.2 90.7 84.4 91.8 88.39

PiSSA 90.1 94.7 92.2 96.1 68.7 90.4 87.6 92.5 88.89

OLoRA 90.9 95.0 92.0 96.3 69.0 91.0 87.9 92.4 89.32

EVA 90.8 95.0 92.1 96.2 69.5 91.4 88.8 92.6 89.55

DoRA 89.5 94.6 89.9 96.1 69.3 91.0 88.4 92.4 88.90

CNTLoRA-X-SVD 91.1 96.193.1 96.4 69.7 91.6 89.193.2 90.03

CNTLoRA-X-QR 90.996.2 92.9 95.1 69.5 91.2 88.9 92.1 89.6

CNTLoRA-S-SVD 90.2 95.9 92.2 96.170.1 91.8 88.2 92.8 89.6

CNTLoRA-S-QR 90.8 95.7 92.897.1 69.6 91.6 88.8 92.6 89.8

CNTLoRA-Sh-SVD 90.9 95.3 92.3 96.4 69.8 91.389.5 92.4 89.7

CNTLoRA-Sh-QR 90.6 95.0 92.1 96.3 69.592.4 89.1 92.5 89.7

standing tasks. Also, we compare our method combined

with QR decomposition simultaneously. As shown in Ta-

ble. 10, most of CNTLoRA variants consistently achieve

high performance. Especially, CNTLoRA-X-SVD consis-

tently achieves the best or near-best performance in various

datasets. These results highlight that CNTLoRA achieves

strong performance not only when using SVD but also when

initialized with QR decomposition, demonstrating the effec-

tiveness of both approaches in enhancing ﬁne-tuning.

Training curve We present the training curves for MRPC

dataset and RTE dataset of the GLUE Benchmark in Fig-

ures 16a and 16b, respectively showing that our method

achieves faster convergence compared to LoRA and EVA,

particularly in the early epochs. We observe that our ini-

tialization better preserves pre-trained knowledge, allowing

for a more stable adaptation to downstream tasks. We also

ﬁnd that our model maintains consistently lower training

loss curves across multiple tasks, demonstrating improved

ﬁne-tuning stability.

Performance convergence We present the performance

convergence results for MRPC and RTE of the GLUE

Benchmark in Figures 17a and 17b, showing that our

method achieves more stable performance compared to

LoRA and EVA, with reduced ﬂuctuations during ﬁne-

tuning. We observe that our initialization accelerates con-

vergence, allowing the model to reach optimal performance

with fewer ﬁne-tuning steps. We also ﬁnd that our approach

consistently achieves higher ﬁnal accuracy, demonstrating

(a) Training loss for different initialization methods on the MRPC dataset. (b) Training loss for different initialization methods on the RTE dataset.

Figure 16. Plots showing how the training loss varies with different epochs for different initialization methods on the MRPC and RTE

datasets.

(a) Accuracy for different initialization methods on the MRPC dataset. (b) Accuracy for different initialization methods on the RTE dataset.

Figure 17. Plots showing how the accuracy varies with different epochs for different initialization methods on the MRPC and RTE datasets.

its effectiveness in enhancing ﬁne-tuning efﬁciency and sta-

bility.