SGNN_LLM_SH: Unified ISAC Optimization

• The paper introduces SGNN_LLM_SH, a unified framework that integrates CSI-induced graph neural networks and an LLM backbone with LoRA adapters to achieve permutation- and size-invariant representations in ISAC systems.
• It details an end-to-end architecture combining self-graph construction, transformer-based processing, and task-specific heads for optimized antenna deployment, segment partitioning, and beamforming.
• The method enables efficient policy transfer across heterogeneous user and target configurations, reducing retraining costs while satisfying stringent communication and sensing constraints.

The SGNN_LLM_SH model is a unified learning framework designed for joint antenna deployment, segment partitioning, and beamforming in segmented pinching antenna-assisted integrated sensing and communication (ISAC) systems. By leveraging channel state information (CSI)-induced graph neural networks (GNNs) and a LLM backbone augmented with LoRA adapters, SGNN_LLM_SH achieves permutation- and size-invariant representations while delivering high adaptability to varying user and sensing target configurations. It supports end-to-end trainability under stringent communication-sensing constraints and enables efficient policy transfer across heterogeneous user and target scenarios (Gao et al., 11 Apr 2026).

1. CSI-Induced Self-Graph Construction

SGNN_LLM_SH formulates each communication user and sensing target as a node in a CSI-induced self-graph $G=(V, E, A)$, where the node set $V=\{v_1, \ldots, v_{K_c+K_s}\}$ comprises $K_c$ users and $K_s$ targets. Each node $i$ is characterized by a feature vector,

$$x_i = [\|h_i\|_2,\, \angle(\sum_{n=1}^N [h_i]_n),\, \tau_i]^\top,$$

with $h_i \in \mathbb{C}^{N \times 1}$ as the near-field antenna-to-node channel, and $\tau_i\in\{0,1\}$ denoting user (1) or target (0) status.

Edge weights are defined by the normalized CSI similarity,

$$A_{ij} = \frac{|\langle h_i, h_j \rangle|}{\|h_i\|_2\,\|h_j\|_2 + \epsilon},$$

where $\epsilon > 0$ provides numerical stability, and each row of $V=\{v_1, \ldots, v_{K_c+K_s}\}$0 is normalized to sum to one. GNN propagation proceeds as: $V=\{v_1, \ldots, v_{K_c+K_s}\}$1 for $V=\{v_1, \ldots, v_{K_c+K_s}\}$2. Final node embeddings are pooled to produce a global, permutation-invariant graph embedding,

$V=\{v_1, \ldots, v_{K_c+K_s}\}$3

This construction guarantees that the downstream pipeline remains agnostic to user and target ordering, and is functionally robust to variable-sized interaction sets.

2. LLM Backbone with LoRA Adaptation

The model reshapes the $V=\{v_1, \ldots, v_{K_c+K_s}\}$4-antenna CSI tensor into a length-$V=\{v_1, \ldots, v_{K_c+K_s}\}$5 token sequence $V=\{v_1, \ldots, v_{K_c+K_s}\}$6 by stacking real and imaginary parts across all channels for each antenna. Token embeddings are projected via LayerNorm and an affine map, then conditioned on the pooled graph embedding: $V=\{v_1, \ldots, v_{K_c+K_s}\}$7 The sequence $V=\{v_1, \ldots, v_{K_c+K_s}\}$8 is fed into a pretrained GPT-style transformer backbone. LoRA (Low-Rank Adaptation) modules are integrated into every projection layer to enable efficient, parameter-light fine-tuning. The final hidden matrix,

$V=\{v_1, \ldots, v_{K_c+K_s}\}$9

serves as the feature substrate for task-specific heads.

LoRA facilitates rapid adaptation to new tasks or data domains while minimizing update overhead compared to full transformer retraining.

3. Task-Specific Heads: Deployment, Partitioning, and Beamforming

Following LLM backbone processing, the output sequence is aggregated via mean pooling and fed into two separate heads:

• Deployment & Partition Head: Produces raw antenna positions $K_c$0 and segment logits $K_c$1 ($K_c$2 is the number of possible antenna segments). After activation and projection,

$K_c$3

with a differentiable non-overlap projection layer enforcing deployment geometry constraints ($K_c$4, $K_c$5). The $K_c$6 highest logit segments in $K_c$7 are designated for transmission; the remainder for reception.

• Beamforming Head: Provides complex-valued beamformer matrices for communication ($K_c$8) and sensing ($K_c$9) functions. Outputs $K_s$0 are combined, with only antennas in transmit segments being active.

Head	Outputs	Role
Deployment & Partition	$K_s$1	Antenna positions, segment assignment
Beamforming	$K_s$2	Communication/sensing beamformers

This architectural separation enables hierarchical optimization over spatial layout and signal processing weights.

4. Optimization Objectives and Loss Formulation

SGNN_LLM_SH targets joint maximization of communication sum rate ($K_s$3) under sensing accuracy, power, and deployment constraints. The transmitted field,

$K_s$4

allocates total power $K_s$5 between communications ($K_s$6) and sensing ($K_s$7).

Key metrics:

• SINR at user $K_s$8: $K_s$9
• Sum rate: $i$0
• Sensing error for target $i$1: CRLB$i$2, where $i$3 is the FIM from the near-field echo model.

The model loss is a composite,

$i$4

where deployment, geometric, and performance (rate, CRLB compliance) losses are included.

The optimization is formally posed as: $i$5

$i$6

$i$7

This multi-objective differentiable approach supports constraint-satisfying, end-to-end, policy learning.

5. Training Regime and User-Count Transfer

The training regime comprises two stages:

1. Source Task Learning: All modules (self-graph encoder, LLM LoRA adapters, task-specific heads) are trained jointly via backpropagation through a differentiable simulation environment that can on-the-fly compute $i$8 and CRLB metrics for the current configuration.
2. Beamforming Head Adaptation ("Beam-Head-Only" Transfer): For a deployment with new user/target counts $i$9, the self-graph encoder, LLM backbone (including LoRA modules), and deployment & partition head are all frozen; only the beamforming head is reset and trained for the new output dimensionality:
   • This adaptation involves $$x_i = [\|h_i\|_2,\, \angle(\sum_{n=1}^N [h_i]_n),\, \tau_i]^\top,$$0 of total parameters and typically converges within approximately eight epochs.
   • The learned deployment $$x_i = [\|h_i\|_2,\, \angle(\sum_{n=1}^N [h_i]_n),\, \tau_i]^\top,$$1—including spatial antenna arrangement and transmit/receive segmentation—remains stable across reconfigurations.

This scheme yields low training cost for policy transfer and robust cross-scenario reuse.

6. End-to-End Pipeline Implementation

A concise end-to-end pipeline includes CSI processing, graph construction, LLM+LoRA forward pass, head projections, metric computation, and loss-based parameter updates.

The training and transfer processes are codified in detailed pseudocode, replicating the following high-level procedure:

$$x_i = [\|h_i\|_2,\, \angle(\sum_{n=1}^N [h_i]_n),\, \tau_i]^\top,$$2

This pipeline upholds unified, end-to-end differentiable optimization for deployment, segmentation, and beamforming operations, with supporting mechanisms for rapid environment adaptation.

7. Significance and Practical Implications

SGNN_LLM_SH establishes a new design paradigm for flexible, high-dimensional ISAC architectures, providing the following distinguishing properties:

• Unified end-to-end optimization under coupled communication–sensing constraints: All deployment, segmentation, and beamforming variables are differentiably co-optimized within a single computational graph.
• Permutation and size invariance through CSI-induced self-graph encoding: The model accommodates arbitrary permutations and cardinalities of users/targets, supporting broad ISAC deployment scenarios.
• Highly lightweight and efficient transfer learning: Beamforming adaptation under varying user/target configurations is achieved with negligible retraining overhead and rapid convergence, retaining deployment optimality.

Simulation results indicate elevated communication throughput and stable sensing performance across user/target reconfigurations, with transfer reducing the retraining cost to <1% of original parameters and typically converging in eight epochs. This suggests the deployment and partitioning policies are robust and reusable, while environment-specific adaptation of beamforming suffices for continued optimality (Gao et al., 11 Apr 2026).