Nested Least-Privilege Networks

• Nested least-privilege networks are architectures that restrict operations to the minimum required privileges using a layered, reversible control mechanism.
• They implement a monitor–allocator–enforcer stack in language models and employ lattice-based label assignments in SDNs to manage data flow securely.
• Advanced mathematical formalisms and progressive allocation policies optimize utility–privilege tradeoffs, ensuring auditable and safe deployment in diverse operational environments.

Nested least-privilege networks operationalize the principle of granting only the minimum capability necessary to accomplish a task, structuring access and computation in a granular, layered manner. These architectures emerge at the intersection of classic computer security, LLM governance, and multilevel security (MLS)-enforced network design. Across domains, the essence is that system privileges—whether model-internal computation or information flow in a network—are arranged in a nested sequence, with reversible, fine-grained controls governing the scope of reachability without collateral exposure of unneeded powers.

1. Foundations: The Principle of Least Privilege

Least privilege restricts any process, subject, or request to the lowest level of access necessary for its purpose. In LLMs, this translates to limiting the set of internal computations during inference, rather than relying on external policy gating at the level of inputs or outputs. Formally, with pretrained model parameters $\theta\in\Theta$ and policy $\pi_\theta(y \mid x)$, the introduction of a deployment-time operator $T_g$ (parameterized by privilege level $g\in\mathcal{G}$) yields effective parameters $\theta(g)=T_g(\theta)$ and a restricted policy $\pi_{\theta,g}(y \mid x)$, where privilege is measured by the reachability of internal computations during the forward pass. $T_g$ induces an ordered privilege interface if, for $g_1\leq g_2$, all computations reachable at $g_1$ remain available at $g_2$ (Rauba et al., 30 Jan 2026).

In network security, nested least-privilege takes shape as the enforcement of MLS policies, ordering information flow based on security labels arranged in a lattice. Each endpoint is assigned a minimum necessary label, and packet flows are routed through nodes whose clearances match or exceed the required privilege, enforcing “no read up, no write down” semantics (Achleitner et al., 2020).

2. System Architectures: The Monitor–Allocator–Enforcer Stack

Both LLMs and software-defined networks (SDNs) implement nested least-privilege via multilayered control stacks. For LLMs, a monitor-allocator-enforcer triad structures deployment control:

• Monitor: Extracts signals $s(x)$ from requests (e.g., risk, uncertainty) without altering model state.
• Allocator: Maps $s(x)$ to a privilege level $g$ according to a deployment policy $\phi$.
• Enforcer: Implements $T_g$, restricting the forward pass to a subspace parameterized by $g$, yielding $\theta(g)$ and an accessible function class monotone in $g$.

In SDNs, MLSNet (Achleitner et al., 2020) formalizes this process:

• Network entities (subjects, objects, forwarding nodes) are labeled.
• Policy-compliant flows are assigned via integer programs maximizing admitted, label-respecting traffic, and flow rules are installed enforcing only those paths allowed by the security lattice.

3. Mathematical Formalism and Mechanisms

3.1 Rank-Indexed, Shape-Preserving Interventions (Language Modeling)

Nested least-privilege interventions are instantiated by factorizing linear layers $W\in\mathbb{R}^{d_\text{out}\times d_\text{in}}$ as $W\approx BA$, with $A\in\mathbb{R}^{r_\max\times d_\text{in}}$, $B\in\mathbb{R}^{d_\text{out}\times r_\max}$. For privilege level $g\leq r_\max$, restricted weights are computed as $W(g)=B_gA_g$, with $A_g$ and $B_g$ the prefix submatrices selecting the first $g$ components—yielding effective rank at most $g$. For all $g_1\leq g_2$, $\mathrm{Im}(W(g_1))\subseteq\mathrm{Im}(W(g_2))$, enforcing nestedness and monotonic expandability. This construction preserves tensor shape and, through post-hoc multitask fine-tuning, ensures stable performance across privilege levels (Rauba et al., 30 Jan 2026).

3.2 Nested Privilege in SDNs

MLSNet expresses privilege nesting via security labels $L(i)=(\mathrm{level}(i),C(i))$, with levels totally ordered (e.g., Public $\leq$ Confidential $\leq$ Secret $\leq$ TopSecret) and categories forming sets. The lattice orders $L(a)\leq L(b)$ iff $\mathrm{level}(a)\leq\mathrm{level}(b)$ and $C(a)\subseteq C(b)$. Policy constraints (no read up, no write down, category containment) are encoded as ILP constraints for each flow, ensuring that only permitted connections are admitted and, when not possible, label downgrades are minimized and precisely quantified (Achleitner et al., 2020).

4. Policy Models and Optimization

4.1 LLM Allocation Policies

Candidate allocators systematically trade privilege against utility, as defined by: $$\mathcal{U}(g) = \mathbb{E}_{x\sim\mathcal{X}}\left[ \mathbb{E}_{y\sim\pi_{\theta,g}(\cdot\mid x)} [r(x,y)] \right]$$ and, for a given target $u_0$,

$$\min_\phi\, \mathbb{E}_x[g(x)] \quad \text{s.t.} \quad \mathbb{E}_x\, \mathbb{E}_{y\sim\pi_{\theta,g(x)}} [r(x,y)] \ge u_0.$$

Allocators include Full-Privilege ($g=r_\max$), Min-Rank ($g=0$), Static-LP (fixed $g$), and Progressive variants (incrementing $g$ on uncertainty or risk signals). Policy-utility tradeoff "frontiers" quantify how much privilege is expended for a given level of utility, with progressive schemes achieving lower average privilege at the cost of increased forward passes (Rauba et al., 30 Jan 2026).

4.2 Flow Assignment in SDNs

Policy-compliant flow maximization solves: $\max \sum_f \alpha^f$ subject to flow conservation, capacity, path, and privilege-consistent constraints. Conflict-minimization (soft mode) minimizes the total security-violation cost: $$\min \sum_{f\in F_l} \sum_{(i,j)\in E} x_{ij}^f\cdot \gamma^{\text{conf}(\sigma_o,\sigma_s,\sigma_j)}$$ with $$\text{conf}(\sigma_o,\sigma_s,\sigma_j)=\max(0, \text{orig}(\sigma_o,\sigma_s)-\sigma_j)$$. Heuristic shortest-path algorithms are adapted to account for label constraints and violation penalties (Achleitner et al., 2020).

5. Selective Capability Suppression and Granularity

Nested least-privilege interventions provide mechanisms for granular suppression of capabilities:

• In LLMs, varying the privilege rank $g$ of individual MLP blocks modulates the model's domain proficiency. Block-rank reductions can selectively degrade performance on capabilities (e.g., chemistry or biology questions) with limited collateral impact, enabling targeted functionality suppression through combinatorial configuration search. Empirically, reductions can lower performance on targeted subjects from 90% to 40% while keeping other subjects above 85% (Rauba et al., 30 Jan 2026).
• In SDNs, flows only traverse nodes of sufficient privilege; when strict enforcement is infeasible due to network structure or congestion, the minimal necessary label downgrade is incurred and explicitly quantified per path (Achleitner et al., 2020).

The table below summarizes the mechanisms in each domain:

Domain	Privilege Control Mechanism	Granularity/Selectivity
Language LMs	Rank-indexed layer factorization	Per-layer, per-block, reversible
SDN (MLSNet)	Lattice-based label assignments	Per-flow, per-node, per-path

6. Implications for Security, Safety, and Deployment

Nested least-privilege architectures fundamentally extend the governance perimeter from external input/output filters to the system’s internal computational or routing substrate. Key implications include:

• Reversible, Auditable Control: The privilege level $g$ acts as a smooth, continuous knob, enabling per-request, per-user customization without retraining or model duplication. For LLMs, setting $g=r_\max$ exactly recovers the original model; reducing $g$ contracts its function class (Rauba et al., 30 Jan 2026).
• Authentic Capability Restriction: Unlike output-time wrappers, restricting model-internal computation excises underlying capability—internal representations at low $g$ lack the latent information needed to reconstruct suppressed abilities, as verified by probing experiments (Rauba et al., 30 Jan 2026).
• Minimal Collateral Exposure: Selective suppression mechanisms demonstrate that unwanted capabilities can be curtailed with bounded degradation to unrelated functions, supporting security and alignment requirements.
• Rigorous Access Control in Networks: In SDNs, enforcing “no read up, no write down” across the entire path, rather than only at endpoints, minimizes lateral movement and non-compliant flows post-compromise. Under tested topologies, full policy compliance admits 58–85% of flows (2–4 level lattices) under no congestion and retains low violation rates with soft conflict minimization (Achleitner et al., 2020).
• Operational Flexibility and Trade-offs: Progressive allocation strategies (in both NLPNs and MLSNet) optimize privilege cost, trading additional inference or routing overhead for higher compliance and reduced risk exposure.

7. Paradigm Shift: From Output Policing to Internal Function Class Governance

Traditional machine learning safety interventions focus either on training-data curation or output filtering, with the base computational mechanisms of the deployed model remaining universally accessible given suitable input. Nested least-privilege networks challenge this paradigm by restricting the internal function class at inference time, aligning more directly with classical access-control notions (“no more, no less” than what is required). This supports new operational regimes for safe AI deployment, offering continuous, auditable, and reversible privilege controls enforceable per-request—distinct from historical approaches that treat model weights as a static monolith (Rauba et al., 30 Jan 2026).