Understanding and Improving Noisy Embedding Techniques in Instruction Finetuning
Authors: Abhay Yadav
Venue: COLM 2025 (2025)
Keywords: Instruction Finetuning
LLM
Domain Adaptation
Multi-Task Learning
Language Models
TL;DR: Understanding and Improving Noisy Embedding Techniques in Instruction Finetuning by symmetric noise.

Abstract: Recent advancements in instructional fine-tuning have injected noise into embeddings, with NEFTune (Jain et al., 2024) setting benchmarks using uniform noise. Despite NEFTune’s empirical findings that uniform noise outperforms Gaussian noise, the reasons for this remain unclear. This paper aims to clarify this by offering a thorough analysis, both theoretical and empirical, indicating comparable performance among these noise types. Additionally, we introduce a new fine-tuning method for language models, utilizing symmetric noise in embeddings. This method aims to enhance the model’s function by more stringently regulating its local curvature, demonstrating superior performance over the current method, NEFTune. When fine-tuning the LLaMA-2-7B model using Alpaca, standard techniques yield a 29.79% score on AlpacaEval. However, our approach, SymNoise, increases this score significantly to 69.04%, using symmetric noisy embeddings. This is a 6.7% improvement over the state-of-the-art method, NEFTune (64.69%). Furthermore, when tested on various models and stronger baseline instruction datasets, such as Evol-Instruct, ShareGPT, OpenPlatypus, SymNoise consistently outperforms NEFTune. The current literature, including NEFTune, has underscored the importance of more in-depth research into the application of noise-based strategies in the fine-tuning of language models. Our approach, SymNoise, is another significant step towards this direction, showing notable improvement over the existing state-of-the-art method.

Published as a conference paper at COLM 2025
Understanding and Improving Noisy Embedding Techniques in Instruction Finetuning
Abhay Yadav Johns Hopkins University Baltimore, MD, USA ayadav1 30jh. edu
Abstract
Recent advancements in instructional fine-tuning have injected noise into embeddings, with NEFTune (Jain et al., 2024) setting benchmarks using uni- form noise. Despite NEFTune's empirical findings that uniform noise outper- forms Gaussian noise, the reasons for this remain unclear. This paper aims to clarify this by offering thorough analysis, both theoretical and empirical, indicating comparable performance among these noise types. Additionally, introduce new fine-tuning method for language models, utilizing symmetric noise in embeddings. This method aims to enhance the model's function by more stringently regulating its local curvature, demonstrating superior performance over the current method, NEFTune. When fine-tuning the LLaMA-2-7B model using Alpaca, standard techniques yield 29.79% score on AlpacaEval. However, our approach, SymNoise, increases this score significantly 69. 69.04%, using symmetric noisy embeddings. This is a 6.7% improvement over the state-of-the-an method, NEFTune (64.69%). Fur- thermore, when tested on various models and stronger baseline instruction datasets, such as Evol-Instruct, ShareGPT, OpenPlatypus, SymNoise con- sistently outperforms NEFTune. The current literature, including NEFTune, has underscored the importance of more in-depth research into the ap- plication of noise-based strategies in the fine-tuning language models. Our approach, SymNoise, is another significant step towards this direction, showing notable improvement over the existing state-of-ther ofetth-rrtt method.
1 Introduction
For Large Language Models (Vaswani et al., 2017; Devlin et al., 2019; Radford et al., 2019; Raffel et al., 2020; Zhang et al., 2022; Touvron et al., 2023b; Zhao et al., 2023) to be effective, their proficiency in executing specific instructions is crucial (Wang et al., 2022; Ouyang et al., 2022; Brown et al., 2020; Chung et al., 2022). These models typically begin with training on vast array of unfiltered web data, after which they undergo a more focused fine-tuning stage using a smaller, selectively chosen collection of instructional data. The fine-tuning stage, centered on instructions, is fundamental in unlocking and controlling the full capabilities of LLMs. The practical value of these models is predominantly dependent how efficiently we can leverage these concise instructional data sets for optimal performance.
In recent years, noise injection (Nukrai al., 2022; Zang al., 2021; Akbiyik, 2020) has been focal point in computer vision research, yielding methods that enhance model robustness and accuracy. This strategy has recently been adapted for fine-tuning Large Language Models (LLMs), exemplified by the NEFTune method (Jain et al., 2024), which applies uniform random noise to improve model performance on diverse datasets. Despite NEFTune's efficacy surpassing traditional fine-tuning techniques, the reasons behind its success, particularly against the commonly used Gaussian noise, are not entirely understood. Our work demystifies this by presenting a detailed theoretical and empirical analysis that reveals comparable results between noise types when appropriately scaled. Moreover, introduce novel noise injection approach which not only facilitates more intuitive
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Table 1: AlpacaEval Win Rate against Text-Davincil when applied with LLaMA-2, trained across diverse datasets. SymNoise shows an overall improvement throughout all datasets, outperforming NEFTune on all datasets. The noise scaling factor for the Gaussian distribution is divided by V3, resulting in similar performance for both methods.
Alpaca Eval-Inntruct ShanGPTT OpenPPlayypus Average
LLaMA-2
70.34
68.74
62.00
57.71
+NEFT
64.89
79.60
76.28
70.61
72.80
+Gaussian
78.88
75.94
72.49
+SymNoise
69.04
81.38
78.67
72.23
75.33
understanding but also achieves superior empirical results, outperforming NEFTune and other established fine-tuning methods by considerable margin.
In particular, our objective is to regularize the curvature of the function learned during train- ing. Curvature regularization has been used in domains such computer vision (Moosavi- Dezfooli et al., 2019; Lee & Park, 2023), graph embedding (Pei et al., 2020), and deep neural networks (Huh, 2020). Specifically, gradually when the input is modified slightly by noise. In more technical terms, our goal to have the gradient approach zero the immediate vicinity of input altered by minimal amount. This represents a more stringent condition than merely requiring small values for the Hessian or gradient. However, considering computational efficiency, we opt to avoid the direct computation of gradients or Hessians. Instead, we employ this stringent condition, which, as our experiments on real-world benchmark datasets demonstrate, is effective in practical scenarios.
aim to ensure that the function's response changes
In this paper, we unveil Symmetric Noise Fine Tuning (SymNoise), new technique that leverages symmetric Bernoulli distribution-based noise applied to the embedding vectors of training data during the finetuning stage. Each noise component is generated with an equal probability of for the values -1 and 1. This method significantly enhances instruction finetuning outcomes, often with remarkable gains, while avoiding additional computational or data resources. While maintaining simplicity, SymNoise has a profound impact on downstream conversational output quality. We show that when large langudage model like LLaMA-2-7B (Touvron et al., 2023c) is finetuned using SymNoise se, its performance on AlpacaEval (Dubois al., 2023) rises from 29.79% 69. 59.04% a substantial increase of about 39.25 percentage points.
Importantly, when compared to the existing NEFTune method (which uses random uniform noise), SymNoise demonstrates superior performance edge, outperforming NEFTune by approximately 6.7%. Thus, SymNoise not only represents a valuable advancement over traditional finetuning methods but also establishes new benchmark in efficiency and effectiveness for LLM finetuning.
Contributions. In comprehensive study, we conduct a detailed theoretical and empir- ical examination, demonstrating that Gaussian and uniform random noise exhibit func- tional equivalence when adjusted with appropriate scaling factor, leading to similar performance on real-world datasets. This insight holds significant importance, especially considering that the creators of the NEFTune method, leading approach employing uniform noise, have openly recognized gaps in their understanding of the method's 's superior perfor- mance, notably in comparison the extensively studied Gaussian noise. By establishing connection with Gaussian noise, our study helps demystify the NEFTune method. Moreover, we introduce an innovative noise injection method that exceeds the capabilities of NEFTune and existing alternatives. Our contributions thus propel the momentum for continued exploration in this field.
Background and Related Work
In the evolving landscape of instruction finetuning for Large Language Models (LLMs), ini- tial efforts like FLAN and TO marked the beginning of cross-task generalization (Sanh et al.,
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Table 2: AlpacaEval Win Rate with and without NEFTune, SymNoise on LLaMA-2, LLaMA-1, and OPT on various datasets. SymNoise shows improved performance across these datasets and models.
Method/Datee Dataset
Alpaca
Evol-Instruct
OpenPlatypus
ShareG
OPT-6.7B
41.4
52.2
45.7
53.4
+NEFTune:
48.7
55.5
45.8
54.3
+SymNoi se
50.8
57.6
46.9
55.6
L-aMA-1-7B
48.5
62.3
51.2
62.9
*NEFTune
61.7
67.5
56,9
63.6
+SymNoise
58.5
LLaMA-2-7B
48.3
62.5
57.2
63.5
62.5
61.7
+SymNoiss
64.9
69.6
62.1
66.1
2021; Wei et al., 2021). These models, involving encoder-decoder language architectures, underwent finetuning across diverse spectrum of thousands NL.P tasks. This progression, detailed in studies by Chung et al. (2022) and Xu et al. (2022) demonstrated the adaptability of LLMs variety of standard NLP tasks.
Following this trajectory, OpenAl's InstructGPT (Ouyang et al., 2022) emerged as pioneer- ing model adept at handling open-ended questions with remarkable efficiency. This model, an iteration of GPT-3 (Brown et al., 2020), incorporated reinforcement learning from human feedback (RLHF), leading to the development of advanced models like ChatGPT (OpenAI, 2022). ChatGPT, in particular, gained widespread attention for generating more coherent and extended texts compared InstructGPT.
Building on these developments, Wang et al. (2022) introduced the Self-Instruct approach, utilizing InstructGPT to generate instructional pairs for further finetuning of foundational models like LLaMA into specialized variants such as Alpaca (Taori et al., 2023). Concurrently, the trend towards distilled models, as discussed by Taori al. (2023) and Xu et al. (2023), led to the creation of diverse datasets. These datasets, including works by Xu et al. (2023) and Lee et al. (2023), focused on refining specific model capabilities like STEM question answering and logical reasoning. Another notable advancement was AlpaGasus by Chen et al. (2023), which employed guality-filteriin mechanism based on GPT-4 evaluations to enhance model performance. In different methodology, ShareGP'I, described by Chiang et al. (2023), was developed through the crowd sourcing of real user interactions sourced from ChatGPT.
In the context of incorporating noise into model training, the pioneering work by Zhu al. (2019) with the FreeLB method demonstrated the effectiveness of adversarial perturba- tions in boosting MLM model performance. This method involved introducing calculated Gaussian perturbations into the embeddings and optimizing them to maximally impact model performance. Similar strategies were later applied in various domains, such as image captioning (Nukrai al., 2022), point cloud processing (Zang et al., 2021), graphs (Kong et al., 2022), and privacy mechanisms (Dwork et al., 2014). Curvature regularization has been used in domains such as computer vision (Moosavi-Dezfooli et al., 2019; Lee & Park, 2023), graph embedding (Pei et al., 2020), and deep neural networks (Huh, 2020). Noise based on the Bernoulli distribution, as opposed to Gaussian or Uniform noise, has been utilized, mentioned by Spall (1998). In this approach, each outcome, either - 1, is assigned an equal probability of
On Similarity of Uniform noise and Gaussian noise
In this section, we investigate the similarity between uniform and Gaussian noise when used for embedding perturbations. While these noise types yield different statistical properties in low dimensions, their behavior becomes increasingly similar as the number of dimensions grows. This phenomenon is especially relevant in the context of large language models (LLMss, where embeddings typically reside in high-dimensional spaces.
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Lemma 1. (Uniform Distribution L2 Norm) For P (x1 (2, xa) (111,,,)), the expected L2 norm is:
F[|| V
(1)
The proof is deferred to Appendix B.0.1.
Lemma 2. (Gaussian Distribution L2 Norm) For P (21, .., x4) ~ (0, (),1), the expected L2 norm is:
[[[[ vd.
(2)
The proof is deferred to Appendix B.0.2.
Gaussian//niiom Norm Rabo (n#256)
DermoulliUnifom Norm Ratio (nm256)
3.25
3.20
2.85
3.00
1.30
1.30
3.75
2300
4303
2330 3000
Direralon
Dimeralon
(a) Gaussian/ Uniffrmm average L2 ratio (b) Bernoulli/ Uniform average L2 ratio
Figure 1: Comparison of average L2 norm ratios for Gaussian and Bernoulli noise relative to Uniform noise as function of dimensionality.
Drawing from Lemma and Lemma 2, it is apparent that the expected noise from the Gaussian distribution is v/ times that of the Uniform distribution. Consequently, to equate the noise scales for comparison, the noise scaling factor for the Gaussian distribution should be adjusted by factor of V3.
As depicted in Figure la, a distinct pattern emerges the ratio of average noise (quantified via L2 norms) between Gaussian and Uniform distributions as dimensionality increases. Notably, the relative impact of Gaussian noise amplifies, approximating v3 times the effect induced by Uniform noise with increasing dimensions. An in-depth exploration and analysis concerning the influence of altering the sample size, while maintaining fixed dimensionality, are detailed in Appendix A.2.
Moreover, the comparative results on real-world datasets are presented in Table where all conditions are held constant except for the substitution of the Uniform distribution with Gaussian distribution. In this context, the noise scaling factor for the Gaussian distribution is adjusted by factor of /3, consistent with the discussion above, and one can notice that the performance of both methods thereafter is comparable. A more detailed ablation study is given in the Sec. 5.5.2.
4 Proposed Method: SymNoise
In the ideal scenario, our goal is to implement curvature regularization, a technique prevalent in fields such as computer vision (Moosavi-Dezfooli et al., 2019; Lee & Park, 2023), graph embedding (Pei et al., 2020), and deep neural networks (Huh, 2020). However, due to the high computational cost associated with these methods, we aim to explore an altermative approach that adheres to more stringent condition. This approach has demonstrated superior performance in practice, surpassing current state-of-the-art methodologies. Specifically,, seek to design function with a gradient (Vf) having value 0 in the
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R(x (ixte)
vicinity of the input, i.e., for X,E E RR, Vf f(x+c)= f(x-))
8, when 0, we have
2
In this formulation, the noise turns out to be based Bernoulli distribution, di- verging from the more commonly used Gaussian or Uniform noise types. Specifically, it uses values of -1 and 1 with equal probability, as in Spall (1998), provide a balanced and predictable effect on the network's s learning.
Following Jain al. (2024), we train instruction-based models using instruction-response pairs Unlike NEFTune, which adds uniform noise to token embeddings, we introduce symmetric Bernoulli noise. While we retain the same noise scaling factor, a/ Ld (with L as sequence length, d as embedding dimension, and a as a tunable parameter), our method differs how noise is applied. Details of our approach, SymNoise, are provided in Algorithm 2, alongside NEFTune in Algorithm 1 for comparison.
4.1 On Similarity of Uniform noise and Bernoulli noise
Lemma 3. (Bernoulli Distribution L2 Norm) For P (x1, X2, with x; E {-1,1} and P(x; = P(x: = -1) = 0.5, the expected L2 norm is:
E||| vd.
(3)
The proof is deferred to Appendix B.O.3.
In alignment with the discussions in Sec. 3 and corroborated by Lemmal, Lemma 2, and Fig 1b, it is evident that the noise induced by the Bernoulli distribution is amplified by a fac- tor of 333 compared to that of the Uniform distribution. To accommodate this disparity, our proposed method SymNoise incorporates this v3 scaling factor, as detailed in Algorithm 2.
Algorithm 1 NEFTune: Noisy Embedding Instruction Finetuning (Taken from the paper (Jain et al., 2024))
Input: D {x,, yi) tokenized dataset, embedding layer emb(-), rest of model f/emb( (.), model parameters f, loss(.), optimizer opt(.)
:ereerparamete: base noise scale a E IR+
Initialize 0 from a pretrained model.
repeat
(X,, Yi) D (sample minibatch of data and labels)
Xemb + embbb (X)), BRK,)RBBB. BxLxd (batch size B, seq. length I., embedding dimension d)
e~ Uniform(-1,7 R BxLxd (sample a noise vector)
X + Xemb + ( (VLa/ ) (add scaled noise to embeds !}
Ý + f/emb (Xemb) {make prediction at noised embeddings) <- opt(O, loss (Y, Y;)) (train step, e.g,, grad descent) until Stopping criteria met/ max iterations.
5
Experiments
In this section, we perform numerous experiments across various models and benchmarks to demonstrate the efficacy of our proposed method SymNoise and compare with existing approaches including NEFT.
5.1 Datasets
In this section, we delve into finetuning datasets that have either gained widespread pop- ularity have recently achieved state-of-the-art results. Due to the memory limitations

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Algorithm 2 SymNoise: Symmetric Noisy Embedding Instruction Finetuning (Proposed Method)
Input: D (xi, Vi) y tokenized dataset, embedding layer emb(.), rest of model f//mb()).
model parameters 0, loss()), optimizer opt(.) syyperparameter base noise scale a E I
Initialize 0 from a pretrained model.
repeat
(X,, Yi) D {sample minibatch of data and labels)
X Xemb f- emb( (X;), BxLdd BxLxx {batch size B, seq. length L, embedding dimension d)
e~ Bernoull(-11,11 1, BxLxd {sample a noise vector)
X
emb +- Xemb + Via
{add scaled noise to embeds 2}
X
emb +- Xemb - Vvial
(subtract same symmetric noise from embeds}
v5
y, - f/mb (concal "emb Xemb)) (make prediction at noised embeddings)
(Xeem/
B t opt( e loss( Y, Y:)) {train step)
until Stopping criteria met/ /et/max max iterations.
of our hardware setup, our focus is exclusively on single-turn datasets following similar protocol as used Jain et al. (2024). The chosen datasets are: Alpaca (Taori et al., 2023), ShareGPT (Chiang et al., 2023), Evol-Instruc (Xu et al., 2023), and Open-Platypus (Lee et al., 2023). More details about these datasets are in Appendix A.1
In the fine-tuning phase, each model, with the exception of ShareGPT, utilizes the prompt from the Alpaca system. Conversely, ShareGPT's is fine-tuned using the prompt from the Vicuna system. Our approach to hyperparameter tuning, including the selection of values, aligns with the methodologies suggested by Jain et al. (2024). We adhered strictly to the same set of hyperparameters those employed in NEFTune (Jain et al., 2024).
5.2 Models
Following Jain et al. (2024) setup for experimentation, our experiments predominantly utilize Large Language Models (LLMs) with a parameter size of 7 billion. Specifically, our focus is on models such as LLaMA-1 (Touvron al., 2023a), LLaMA-2 (Touvron al., 2023c), and OPT-6.7B (Zhang et al., 2022). These transformer-baa amount of training data they've been exposed to, with OPT-6.7B, LLaMA-1, and I.L.MA-2 being trained on 180 billion, trillion, and 2 trillion tokens, respectively. This variance in training data volume is expected to manifest in their performance across benchmarks like MMLU, where LLaMA-2 typically outperforms the others.
models primarily differ in the
5.3 Evaluation Protocols
Our experimental framework, adapted from the original NEFTune (Jain et al., 2024) setup, primarily utilizes single-turn data for training. We assess the models' conversational skills using AlpacaEval and examine their performance on tasks from the OpenLLM Leaderboard. This was done to verify that the introduction of our symnoise augmentation does not negatively impact the models' performance standard multiple-choice tasks. Notably, the results demonstrate that our augmented models consistently outperform the original neftune models, albeit by modest margin.
AlpacaEval: Introduced by Dubois et al. (2023), AlpacaEval crucial for appraising generative quality. It functions as an automated model-based evaluator, comparing Text-Davinci-003s generations with our model's 's over 805 prompts, focusing on the Win Rate. The Win Rate indicates how often our model is preferred over Text- Davinci-003, as judged by model evaluator (GPT-4, ChatGPT etc). The dataset's 805 test prompts, sourced from various platforms, ensure comprehensive testing

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scope. AlpacaEval's 's high human agreement rate (Dubois et al., 2023), validated by 20K annotations, highlights its usefulness and accuracy. We employ both GPT-4 and ChatGPT evaluators, using ChatGPT initially due to GPT-4's API limitations and costs.
Hugging Face OpenLLM Leaderboard: For leaderboard assessments, datasets like ARC (Clark et al., 2018), HellaSwag (Zellers et al., 2019), and MMLU (Hendryccs et al., 2020) are utilized. These verbalized multiclass classification datasets test the LLM's capability in factual questioning and reasoning. Our evaluations confirm that the SymNoise method does not diminish the models' proficiency in these domains.
5.4
Results
The methodology we employed for tuning hyperparameters and choosing their values adheres closely to the protocols proposed by Jain et al. (2024). Specifically, we meticulously adopted the identical hyperparameter set as delineated in NEFTune by Jain et al. (2024).
5.4.1 Improvement generated text quality
Our results demonstrate an enhanced metric performance compared to NEFTune terms of generated text quality. As evident from Table there is notable improvement across all datasets at the 7B size, with an average increase of 17.6% (compared to NEFTune's improve- ment of 15.1%). This indicates that the implementation of SymNoise significantly enhances conversational capabilities and answer quality. These findings are supported by evaluations using AlpacaEval, where SymNoise notably outperforms NEFTune. Furthermore, as shown in Table 2, enhancements are also observed in older models like LLaMA-1 and OPT-6.7B. with SymNoise consistently surpassing NEFTune in these models as well. An interesting observation is the comparatively smaller gain by NEFTune in ShareGPT, as per ChatGPT's analysis, a trend not mirrored in GPT-4's evaluation. However, SymNoise consistently excels over NEFTune for ShareGPT in evaluations by both GPT-4 and ChatGPT. In Table 1, the Win Rate shows a significant increase from 29. 29.79% to 69.04% for Alpaca, thereby outperforming the state-of-the-al method NEFTune by 6.7%.
5.4.2 Improvement in OpenLLM Leaderboard tasks
In addressing the potential that SymNoise could enhance conversational abilities at the expense of traditional skills, we conducted evaluations using tasks from the OpenLLM Leaderboard. Employing the L.-Evaal Harness framework (Gao et al., 2021), assessed our model's performance on benchmarks such as MMLU (Hendrycks et al., 2020), ARC (Clark et al., 2018), and HellaSwag (Zellers et al., 2019). These tests shed light on the model's knowledge base, reasoning capabilities, and adherence to factual information. As illustrated in Figure 3, the results indicate that SymNoi se not only stabilizes scores but also actively pre- serves and, in some cases, enhances the model's capabilities. Notably, SymNoise consistently outperforms NEFTune in terms of performance, highlighting its effectiveness in striking balance between conversational proficiency and traditional computational skills.
5.5 Analysis
As shown in NEFTune (Jain et al., 2024) and related work, adding noise to embeddings during training helps mitigate overfitting dataset-specific quirks like formatting or phrasing. This shifts the model from memorizing instructions to leveraging the broader capabilities of the pretrained base model. direct effect is that models produce longer, more coherent response--preferred by both human and automated evaluators (Dubois et al., 2023), While increased verbosity contributes to performance gains, our analysis shows that SymNoise improves both response quality and quantity beyond what NEFTune achieves.
Conceptually, SymNoise assigns probability mass to multiple noisy variants of instructions, encouraging the model to learn broader, more uniform distribution rather than overfitting to the training data or a single perturbed version. This promotes better generalization and reduces overfitting.
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Table 3: For OpeNLLM Leaderboard tasks, the influence of NEFTune and SymNoise is in- vestigated on LLaMA-2, encompassing Alpaca, Evol-Instruct, and OpenPlatypus datasets, alongside LLaMA-1 trained on the Evol-Instruct dataset. Comparative observations reveal uniformity in performance metrics across the diverse datasets and models, indicating negligible impact of NEFTune but slightly better performance of SymNoise se on the overall effec- tiveness. We follow the similar procedure mentioned in Jain et al. (2024), and report their results for completeness. In order to minimize computational expenses, we refrained from conducting thorough trpam-paramtter optimization, which may have further improved the results.
Task
Llama-2 7B (Alpaca)
+NEFT
+SymNoise
ARC
56.4
56.1
56.0
HellaSwag 80.0
80.1
80.2
MMLU
47.9
47.7
47.9
Llama-2 7B (OpenPlatypus)
+NEFT
+SymNoise
ARC
54.2
35.4
55.7
HellaSwag 80.4
80.6
80.8
MMLU
43.9
45.3
45.5
Llama-1 7B (Bvol-Instruct))
+NEFT
+SymNoise
ARC
53.7
54.1
56.0
HellaSwag
77.9
78.0
78,9
MMLU
38.3
38.4
39.1
5.5.1 Longer responses us repetition
In this section, objective is to determine whether the lengthier responses produced using SymNoise are a result of increased repetition or if they contribute to more diverse and detailed content.
Echoing the insights from Jain et al. (2024) and supporting evidence from leaderboard per- formances, a notable correlation emerges between extended response lengths and improved performance in the AlpacaEval task. This raises the question of whether the augmenta- tion of response length by SymNoise could lead diminished text diversity and quality. Our analysis scrutinized the frequency of N-gram repetitions in responses generated by LLaMA-2, trained on various datasets, both with and without SymNoise application.
Following the methodology of Jain et al. (2024), our analysis was restricted to the initial seg- ments of each response to maintain consistency. Specifically, we examined the first 50 words for Alpaca-trained models, 100 words for Evol-Instruct, and 150 words for OpenPlatypus. ensuring that at least half of the responses exceeded these thresholds. Responses shorter than these limits were excluded from the analysis.
As delineated in Table 5, the findings reveal that SymNoise typically yields lengthier re- sponses. However, importantly, the frequency of 2-gram repetitions and overall token log-diversity remain largely consistent, paralleling the results observed with NEFTune This suggests that the increased length of responses under SymNoise is not simply due to repeti- tive content, but rather indicates the inclusion of additional, relevant information, thereby enriching the depth and value of the generated responses.
5.5.2 Ablation study with different strength of noise
In this section, we explored the efficacy of employing different noise distributions, specifi- cally uniform (NEFTune) versus Gaussian noise, versus within the SymNoise algorithm. From the Table 4, one can notice that Gaussian noise tends to produce longer outputs. However, this increased length does not correlate with a corresponding enhancement in performance. While it is generally observed that longer generations are associated with improved scor- ing, none of the generation-ting strategies employed matched the effectiveness of models trained with SymNoise. Interestingly, our innovative approach, SymNoise, se, exhibits superior
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performance, surpassing benchmark results. It demonstrates approximate improvement of 6.7% over the models utilizing NEFTune. Furthermore, we conducted a comparative analysis with Bernoulli noise to underscore the effectiveness of the symmetric opposing noise component in SymNoise.
Moreover, maintained consistent experimental conditions while substituting the Uniform distribution with a Gaussian distribution. In alignment with our theoretical framework,
we adjusted the noise scaling factor for the Gaussian distribution by dividing it by v3. This adjustment led to comparable performance between the two methods across various NEF Nuneune noise levels, reinforcing the validity of our noise scaling approach.
Table 4: AlpacaEval Win Rate and Average Character Count assessed by ChatGI'T across var- ious noise settings.
Table 5: Transposed view of average lengths and 2-gram repetition rates in AlpacaEval responses for different train- ing methods.
Setting
Alpaca
Evol-Inttuct 62.35 (864)
OpenPlatypa 57.20 (1101)
Metric
LaMAA-2 7B
#NEFT
+SynNo1se
LLaMA-2-76
48.26 (375)
Character Length
+NEFT
Alpaca
375
1061
118
Noise 5
62.55 (1062)
67.58 (1404)
60.99 (1428)
Evol-Instruct
864
1403
1700
+NEFT
OpenPlatypus
1100
1694
1689
Noise 10
(1010)
65.39 (1697)
60.62 (1834)
Whilespace Length
+NEFT
Alpaca
60
169
176
Noise 15
61.86 (820)
66.58 (1651)
61.74 (1694)
Evol-Instruct
138
225
245
62.6 (1073)
(1431)
(1437)
OpenPlatypus
170
264
270
Noise 5/ 3
2-Gram Repetition %
+Gaussian
61.01 (1211)
63.29 (1783)
60.32 (1878)
Alpaca
1.49
1.72
180
Noise 10/v3 /3
Evol-Instruct
3.87
3.79
3.80
+Gaussian
61.93 (835)
65.99 (1767)
61.38 (1806)
OpenPlatypus
273
3.21
3,30
15/
+Gaussian
60.93 (1371)
65.09 (2066)
59.13 (2061)
Noise
Bernoulli
(1272)
(1840)
60.22 (1968)
Noise 5
*yynoo1se Noise
([186)
69.62 (1700)
62.14 (1689)
CONCLUSION
In this work, we rigorously establish that Gaussian and uniform random noise are function- ally analogous, contingent on appropriate scaling, and demonstrate similar effectiveness on real-world datasets. This revelation is pivotal, particularly in light of the NEFTune creators' admission of the method's unexplained superiority, especially over the well-examined Gaussian noise. This insight not only sheds light on the previously opaque superiority of the NEFTune method but also bridges the gap with the well-understood Gaussian noise.
Furthermore, we have introduced SymNoise, a novel noise injection technique that outper- forms NEFTune and other existing methods by a large margin. The advancements showcased by SymNoise in training large language models (LLMs) emphasize the importance of in- novative algorithmic strategies and regularization techniques. Echoing the sentiments of (Jain et al., 2024), the field of LLMs, unlike its counterpart in computer vision, has often favored standardized training methods focusing on model scaling and dataset expansion. However, SymNoise underscores the potential of fine-tuning techniques in enhancing model performance, particularly in situations where overfitting to limited instruction datasets is concern.

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Published as a conference paper at COLM 2025
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A Appendix
A.1 Datasets
Alpaca Taori et al. (2023): Developed using the Self-Instruct method by Wang et al. (2022) and the Text-Davinci-003 Ouyang al. (2022) model (Ouyang et al., 2022), Alpaca leverages small set of seed tasks to generate new instruction tuning tasks and filter out ineffective ones. This dataset has been instrumental in advancing instruction-based learning.
ShareGPT Chiang et al. (2023): Comprising 70k voluntarily shared ChatGPT conversations Sha (2023), ShareGIT provides rich source of real-world interaction data. While originally multi-turn, we adapt it to a single-turn format using the Vicunav1.1 dataset version for consistency with our experimental setup.
Evol-Instruc Xu et al. (2023): This dataset, comprising 70k single-turn instructions, is considered more complex than Alpaca. Originating from the Alpaca dataset, Evol-Instruct employs ChatGPT to refine and evolve the initial instructions, thus broadening the scope and complexity of the tasks.
Open-Platypus Lee et al. (2023): Formed by combining 11 open-source datasets, Open-Platypus is tailored to enhance LLM performance in STEM and logical reason- ing domains. includes approximately 25k questions, with around 10% generated by LLMs and the rest by human experts. This dataset emphasizes the importance variety and complexity in question formats.
A.2 Analysis of Distributional Characteristics in High-Dimensional Spaces
In this section, we analyze the behavior of Gaussian, Bernoulli, and Uniform distributions in high-diimensional spaces. We explore how the average L2 norm ratios of these distributions change with respect to varying dimensions and sample sizes, providing insights into their geometric properties and implications for high-dimensional data analysis.
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A.2.1
Average L2 Norm Ratio with Varying Dimensionality
Gaussian/Uniform Average L2 Norm Ratio (n=256)
1.75
Gaussian/Unfform
www
1.70
Average Norm Ratio
1.65
1.60
1.55
1.50
0
500
1000
1500
2000
2500
3000
3500
4000
Dimension d
Figure 2: Gaussian/Unifee UUniform Average L2 Norm Ratio Function of Dimensionality. The plot illustrates the ratio of the average L2 norm of points drawn from a Gaussian distribution to that of a Uniform distribution, with the number of points fixed at 256 and the dimensionality varying from 1 to 4096.
Bernoulli/Uniform Average L2 Norm Ratio (n=256)
Berneull/Uniform
1.95
Average L2 Norm Ratio
1.90
1.85
1.80
1.75
wmm.mm
500
1000
1500
2000
2500
3000
3500
4000
Dimension d
Figure 3: Bernoulli/ Uuniii/nniiommmmm Average L2 Norm Ratio as a Function Dimensionality. The plot depicts the ratio of the average La norm of points drawn from Bernoulli distribution to that of a Uniform distribution, with the number points fixed at 256 and the dimensionality varying from to 4096.
A.2.2 Average L2 Norm Ratio with Varying Number of Points
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Gaussian/Uniform Average L2 Norm Ratio (d=4096)
1.738
Gaussian/Uniform
1.736
Average Norm Ratio
1.734
1.732
1.730
1.728
1.726
75
100
125
150
175
200
225
250
Number of Points
Figure 4: Crtusiaan/Unffone Average L2 Norm Ratio for Varying Number of Points. The plot illustrates the ratio of the average L2 norm of points drawn from a Gaussian distribution to that of Uniform distribution, with the dimensionality fixed at 4096 and the number of points varying from 64 to 256.
Bernoulli/nniform Average L2 Norm Ratio (d=4096)
Bernoull/Unitorm
1.735
Average Norm Ratio
1.734
1.733
1 MM 199 MM
1.732
1.731
1.730
75
100
125
150
175
200
225
250
Number of Points
Figure 5: Bernoulli/ Pernoull/Unnifomm Uniform Average L2 Norm Ratio for Varying Number of Points. The plot depicts the ratio of the average L2 norm points drawn from a Bernoulli distribution to that of Uniform distribution, with the dimensionality fixed at 4096 and the number of points varying from 64 to 256.
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B Deferred proofs
In this section, we show the proofs omitted from Sec. 3 and Sec. 4.1.
B.0.1 Proof of Lemma
We state again Lemma 1 from Sec. and present the proof.
Lemma 1. (Uniform Distribution L2 Norm) For P (2, (L111,
([[1,11), 1.), the
expected L2 norm is:
E[||P||a] 3
Proof: Each X; is uniformly distributed over [-1,1]. The second moment about the origin for 6²-0² a uniform distribution U(a, b) is given by 3(b-a) For u(-1,1), this yields E[2]] = 3. The
components x; are independent, hence the sum of their squares, which represents the L2 norm squared, is the sum of their expected values: |[]| = 1 E[x]] = d 3. Taking the square root gives the expected L2 norm: P[[] / E|| PI V
B.0.2 Proof of Lemma 2
We state again Lemma 2 from Sec. and present the proof.
Lemma 2. (Gaussian Distribution L2 Norm) For P == (2,, xa) ~ (0, 1), the expected L2 norm is:
E[[[P||]] = Vd.
Proof: Each xi is distributed according to NO, The square of standard normal variable, x?, follows a chi-squared distribution with 1 degree of freedom, for which the mean (expected value) is 1. Given the independence of the components x;, the expected value the sum of their squares,
representing the L2 norm squared, is: ||| = E' E[x?] d d. The expected L2 norm the square root of this sum: P|[[] E|I Vd.
B.0.3 Proof of Lemma' 3
We state again Lemma 3 from Sec. 4.1 and present the proof.
Lemma 3. (Bernoulli Distribution L2 Norm) For P = (x1, X2, xa), with E {-1,1} and
P(x; = Pxx; -1) 0.5, the expected L2 norm is:
E|[[ Vd.
Proof:
Each x; takes values -1 or with equal probability, leading to x² irrespective of x, actual value. Hence, E[x;] = 1. Given the independence of the components x,, the expected value of the sun of their squares, which represents the 222 norm squared, is simply the sum of the expected values: E[][ = Di_ E[x?] = = d. Therefore, the expected L2 norm is the square root of
this value: P||| v E[ll P| Vd.
15


Reviews:
[{"review_id": "g3BtHA7lhk", "reviewer": "Reviewer_5zJn", "summary": "This paper studies noise injection in embedding space for instruction fine-tuning of language models. It first analyzes why the NEFTune method, which uses uniform noise, works better than Gaussian noise, and shows that when properly scaled, both perform similarly.\n\nBuilding on this, the authors propose SymNoise, a new method that injects symmetric Bernoulli noise. The goal is to regularize the model's response to small input changes—encouraging smoother behavior without computing gradients or Hessians.\n\nExperiments across multiple datasets and models (e.g., LLaMA, OPT) show that SymNoise consistently outperforms NEFTune. For example, it improves LLaMA-2-7B’s AlpacaEval win rate from 64.69% to 69.04%.\n\nAdditional analysis shows that SymNoise produces longer, more informative responses without increasing repetition, and generalizes better across tasks.", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "1. The motivation about noise injection is very clear.\n2. The proposed method is simple and also effective (as shown in experimental results).", "reasons_to_reject": "I think this paper does not exhibit any obvious flaws.", "questions_to_authors": "1. Since the SymNoise method involves injecting noise twice, the authors should apply the same procedure to Gaussian and uniform noise for a fair comparison. I expect this may bring some performance improvements.\n\n2. I look forward to see some experimental results about testing-time computation on math or other tasks. To see whether noise injection could benefit for random sampling.", "extra_scores": {}}, {"review_id": "BORAzcDtIY", "reviewer": "Reviewer_Yag6", "summary": "This paper revisits noise injection strategies for instruction fine-tuning of large language models. It offers both theoretical and empirical insights into why NEFTune’s uniform noise works, showing that when scaled properly, Gaussian and uniform noise perform similarly. Building on this, the authors introduce SymNoise, a novel technique that uses symmetric Bernoulli noise to regularize local curvature. SymNoise leads to consistent performance gains across datasets like Alpaca, Evol-Instruct, OpenPlatypus, and ShareGPT. Compared to NEFTune, SymNoise improves AlpacaEval win rates by up to 6.7%, and yields similar or slightly better performance on other language modeling benchmarks.", "questions": "", "limitations": "", "rating": 7, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "- The theoretical grounding that Gaussian, uniform, and Bernoulli noise behave similarly in high-dimensional space is carefully laid out and empirically validated.\n- The introduction of SymNoise is intuitive, easy to implement, and effective in improving model generalization, particularly for instruction-tuned LLMs.\n- The experiments are broad and systematic. The paper covers multiple datasets, multiple models (OPT, LLaMA-1, LLaMA-2), and evaluation settings (AlpacaEval, OpenLLM Leaderboard).\n- The paper performs a detailed ablation studies that show robustness of SymNoise across different noise types and", "reasons_to_reject": "- [Minor] The core innovation, SymNoise, is somewhat modest in novelty. While well-motivated and effective, it is primarily a minor extension of NEFTune with symmetric Bernoulli noise. But, it does work well, and it is simple.\n- [Minor] The presentation of Algorithm 2 (SymNoise) could benefit from more explanation or illustrative examples. The double-noise step may confuse readers unfamiliar with this type of regularization.\n\nTypos:\n- \"langudage\" should be \"language.\"", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "KpAUzeGvsP", "reviewer": "Reviewer_7QRP", "summary": "This paper presents a well-motivated and technically sound study on noise injection methods in instruction fine-tuning for large language models. It offers both theoretical insights and practical contributions by (1) demystifying the relative effectiveness of uniform vs. Gaussian noise in embedding perturbation, and (2) introducing SymNoise, a novel symmetric Bernoulli-based noise method.\n\nThe idea is novel.\n\nThe empirical results are compelling: SymNoise outperforms NEFTune consistently across multiple datasets and models (including LLaMA-1/2 and OPT), and delivers notable gains on AlpacaEval. The ablation studies, theoretical derivations, and performance consistency across tasks strengthen the validity of the work.", "questions": "", "limitations": "", "rating": 7, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "The paper is clearly written, well-structured, and addresses a timely problem in instruction fine tuning. The insights into curvature regularization via symmetric noise are novel and could inspire further exploration in noise-based LLM training.\n\nThe contributions are meaningful, the empirical results are strong, and the paper is likely to be of interest to both academic and applied ML communities.", "reasons_to_reject": "N/A", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: This paper offers a nice analysis of different noise injection methods (during fine-tuning). Starting from a theoretical motivation, the authors motivate Symmetric Noise Fine Tuning (SymNoise). Reviewers agreed that this is a nicely executed work, drawing clear and practical connections between theory and empiricism.
Decision: Accept