Non-Fine-Tunable Foundation Models

• Non-fine-tunable foundation models are pre-trained systems engineered to block significant gains from gradient-based fine-tuning while maintaining performance on approved tasks.
• They employ mechanisms like Private Mask Pre-Training and the SOPHON framework to create structural optimization barriers, restricting adaptation in adversarial domains.
• Empirical results demonstrate that these models severely limit unauthorized fine-tuning (e.g., reduced accuracy gains) without compromising the utility of the source task.

Non-fine-tunable foundation models are pre-trained models engineered so that conventional gradient-based fine-tuning, especially by unauthorized or adversarial downstream users, yields minimal or no gains relative to either training from scratch or using the base model as-is. This paradigm seeks to preserve the foundation model’s utility for intended tasks while enforcing structural or optimization obstacles to downstream adaptation, with motivations in both AI safety and intellectual property protection. Recent research has established principled frameworks, rigorous formalizations, and empirical evidence for non-fine-tunability in large-scale deep learning systems, spanning vision, language, and generative architectures.

1. Foundational Concepts and Motivation

The principle of non-fine-tunability addresses a key risk in open-sourcing foundation models: once released, the dense parameter set enables downstream actors to adapt the model for diverse, possibly unauthorized, high-performance applications. This undermines safeguards against misuse (e.g., for privacy attacks or unsafe content generation), threatens licensors’ economic interests, and complicates regulatory compliance. The core objective is to design models or training methodologies that resist fine-tuning in restricted or adversarial domains, without sacrificing base performance on approved or original deployments (Deng et al., 2024, Wang et al., 31 Jan 2026).

Three fundamental goals characterize the non-fine-tunability paradigm (Deng et al., 2024):

• Intactness: Maintain source-domain performance (approved tasks).
• Non-transferability: Ensure poor zero-shot performance on restricted domains.
• Non-fine-tunability: After any admissible fine-tuning, accuracy on disallowed tasks does not exceed (and often underperforms) the result of training from scratch.

2. Formal Definitions and Theoretical Frameworks

Mathematically, non-fine-tunability is formalized as a constrained learning problem. Let $f_\theta$ be a parameterized model, $\mathcal{D}_S$ the source domain, $\mathcal{D}_A$ the set of restricted/adversarial domains, $\Phi$ the family of fine-tuning strategies, and $\mathcal{L}$ a task-appropriate loss function. The protected model $\theta^*$ must satisfy (Deng et al., 2024):

$$\min_\theta\, -\mathbb{E}_{x\sim\mathcal{D}_A,\,\phi\sim\Phi} \mathcal{L}(\phi(f_\theta)(x)) \quad\text{s.t.}\quad \mathbb{E}_{x\sim\mathcal{D}_S} \mathcal{L}(f_\theta(x)) \leq \lambda$$

Here, $\lambda$ quantifies the permissible accuracy drop on the source domain under protection constraints. The corresponding Lagrangian objective is

$$\min_\theta\, - \mathbb{E}_{x\sim\mathcal{D}_A,\phi\sim\Phi}\mathcal{L}(\phi(f_\theta)(x)) + \mu\,\mathbb{E}_{x\sim\mathcal{D}_S} \mathcal{L}(f_\theta(x))$$

where $\mu>0$ balances protection and intactness.

Within this space, non-fine-tunable learning embodies a robust optimization against all relevant (possibly adversarial) fine-tuning operators, not merely one specific adaptation protocol.

3. Mechanisms for Non-Fine-Tunability

3.1 Private Mask Pre-Training (PMP)

PMP leverages a sparse lottery ticket subnetwork identified via an “early-bird” phase in pre-training: the most responsive parameters are detected and grouped by a binary mask $M$. The base model is then fully trained, but all gradient updates are restricted to the parameters selected by $M$, while the rest remain fixed throughout. Post-training, only the full dense parameter vector $\theta$ is released, but not the mask $M$. This construction has the following theoretical and practical consequences (Wang et al., 31 Jan 2026):

• Intrinsic geometric mismatch: Fine-tuning without knowledge of $M$ forces gradients into “high-curvature” directions corresponding to $\theta^{\overline{M}}$, which were never adapted during pre-training, and thus destabilize learning.
• Provable bounded adaptation gains: Gradient-descent adaptation increases loss along the frozen subspace, and the maximal achievable improvement is bounded above by $O(\eta^2)$ for step size $\eta$; see the Taylor expansion and Proposition 1 in (Wang et al., 31 Jan 2026).

3.2 SOPHON Framework

SOPHON introduces a meta-learning paradigm wherein adversarial fine-tuning is simulated in inner training loops for restricted domains, followed by explicit updates to maximize post-fine-tuning error (“suppression”) while reinforcing source accuracy. Notable aspects include (Deng et al., 2024):

• Fine-Tuning Suppression (FTS): Simulate multiple adversarial fine-tuning strategies $\phi_i\in\Phi$ with various optimizers, learning rates, and update scopes—mirroring real-world downstream adaptation.
• Suppression Losses: Employ inverse cross-entropy, KL divergence from uniformity, and Denial-of-Service losses to maximize error without destabilizing training.
• Entrapment in local optima: Each FTS update flattens the loss around $\theta$ for $\mathcal{D}_A$, shrinking local gradients and making it extremely difficult for post-hoc fine-tuning to achieve any meaningful adaptation.

4. Empirical Results and Practical Effectiveness

Extensive experiments substantiate both the PMP and SOPHON paradigms:

Private Mask Pre-Training Results (Wang et al., 31 Jan 2026):

• Base performance preserved: TinyLlama and GPT-2 models retain task performance on original source datasets (GLUE average, e.g., 53.7% with PMP vs. 53.8% baseline).
• Suppression of unauthorized fine-tuning: Fine-tuning on GLUE leads to severe degradation—TinyLlama: 76.0% (baseline) → 69.4% (PMP), GPT-2: 68.1% → 56.6%.
• Restoration via authorized adaptation: Access to $M$ re-enables effective fine-tuning.
• Mask ratio as control knob: $p = 0.7$ (fraction of trainable parameters) balances adaptation suppression and base accuracy; random masks are significantly less effective than early-bird masks.

SOPHON Results (Deng et al., 2024):

• Classification (CIFAR-10): Original fine-tune achieves ≈85% after 20 epochs; SOPHON-fine-tuned model remains at 10.4% (random guess). From-scratch training reaches 62.7%.
• Generation (CelebA): Post-fine-tuning MSE with SOPHON remains much worse (0.705) than from-scratch (0.479) or baseline fine-tune (0.445).
• Robustness: SOPHON’s suppression holds across domains, architectures (ResNet, VGG, CAFormer), fine-tuning algorithms (Momentum, Adam, Nesterov), and hyperparameters.
• Training stability: Standard losses destabilize suppression (explode or NaN), but ICE, KLU, DoS losses remain smooth and effective.

Model / Task	Source Accuracy	After Fine-Tune	From Scratch
SOPHON (CIFAR-10)	96.2%	10.4%	62.7%
PMP (GLUE, TinyLlama)	53.7%	69.4%	—

These findings demonstrate the feasibility of non-fine-tunable design, robust to various attackers’ fine-tuning protocols.

5. Algorithmic and Implementation Details

The implementation of both SOPHON and PMP depends on carefully coordinated meta-learning or parameter-masking strategies.

SOPHON Pseudocode (Deng et al., 2024):

1. Alternate between Fine-Tuning Suppression (FTS) and Normal Training Reinforcement (NTR).
2. For FTS, sample diverse $\phi_i\sim\Phi$—simulate $K$ SGD steps per strategy/environment, aggregate loss with suppression loss variants.
3. For NTR, update on source batches to maintain base task accuracy.
4. Use Adam or Momentum optimizers, multiple learning rates, batch sizes, repeat over sufficient iterations (e.g., 800 outer iterations).

PMP Workflow (Wang et al., 31 Jan 2026):

1. Early training phase identifies the early-bird mask $M$ by tracking gradient statistics and mask IoU stability ($\tau=0.99$).
2. Continue pre-training with only $\theta^M$ adapted.
3. At convergence, publish $\theta$ (dense vector), keeping $M$ secret.
4. Optionally, share $M$ with trusted parties to enable authorized fine-tuning.

Overheads and Hyperparameter Sensitivity:

• PMP adds negligible inference overhead; one short warm-up plus restricted adaptation in pre-training.
• SOPHON maintains training stability by careful loss design to avoid divergence.

6. Limitations, Extensions, and Practical Guidelines

Limitations:

• Both approaches require careful balancing between base utility and transfer suppression: excessive restriction can degrade the primary utility.
• PMP achieves suppression only when mask $M$ remains secret; authorized fine-tuning requires explicit disclosure of $M$ (Wang et al., 31 Jan 2026).
• SOPHON’s adversarial fine-tuning simulation must be sufficiently diverse to anticipate potential downstream attacker strategies (Deng et al., 2024).

Possible Extensions:

• Extension to additional modalities (NLP, vision, generative models) is plausible due to the paradigm’s generality.
• For SOPHON, adapting the suppression losses to tasks beyond classification/generation may enhance coverage.
• PMP suggests mask ratio ($p$) can be tuned for custom trade-offs in non-fine-tunability.

Practical Guidelines:

• For PMP, set $p\approx0.7$ for effective trade-off; favor early-bird over random masks.
• For SOPHON, employ suppression losses (ICE/KLU/DoS) for stability; ensure simulation covers a wide $\Phi$.
• Both paradigms are compatible with black-box deployment for end-users—with authorized adaptation contingent on access control (PMP) or task/domain design (SOPHON).

7. Connections to Related Research and Benchmarks

Non-fine-tunability is closely related to model robustness, model watermarking, and responsible AI, but introduces distinct optimization and deployment constraints. Capabilities encoding approaches (Adorni et al., 6 May 2025) enable efficient benchmarking of base model performance on downstream tasks without relying on fine-tuning, providing auxiliary tools for model selection when non-fine-tunability is desired. Unlike suppression-based designs, capabilities encoding predicts model-task suitability from a shared latent space, emphasizing lightweight latent-space evaluation rather than adversarial transfer or subspace restriction.

The direct suppression of downstream adaptation, as formalized in PMP and SOPHON, constitutes a major development in foundation model governance and responsible AI management, with strong empirical evidence supporting practical deployment and adaptation resistance across architectures, optimizers, and domains (Deng et al., 2024, Wang et al., 31 Jan 2026).