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DTA-GT: Direction- and Topology-Aware Graph Transformer for Neural Network Representation Learning
Yuxiang Zeng, Kun Xie, Yang Wang, Jigang Wen, Xiaocan Li, Guangxing Zhang, Gaogang Xie, Jiannong Cao
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Abstract
Abstract:Architecture attribute predictors reduce the cost of neural architecture search by estimating accuracy or latency from a small set of evaluated candidates. The key difficulty is that neural architectures are operation-labeled DAGs: edge direction defines computational flow, but existing predictors often treat direction as a local structural cue. We propose DTA-GT, a Direction- and Topology-Aware Graph Transformer based on encoder-wide directional consistency, which preserves directed computational semantics across node initialization, global spectral encoding, pairwise interaction, and feature update. DTA-GT realizes this principle with direction- and topology-aware node initialization, Magnetic Laplacian spectral encoding, direction-dual structural attention, and a Direction-Sensitive MoE-FFN. Across accuracy and latency prediction on NAS-Bench-101 and NAS-Bench-201, DTA-GT consistently outperforms representative sequence-, GNN-, Transformer-, and hybrid predictors under limited-budget settings. Ablations and Magnetic spectral controls show that the improvements come from coordinated direction-aware stages and edge-orientation-sensitive spectral information, while mechanistic diagnostics confirm that the modules exhibit the intended directional behavior. These results support encoder-wide directional consistency as an effective design principle for architecture DAG representation.
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- Source: https://arxiv.org/abs/2610.16822v1
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DTA-GT: Direction- and Topology-Aware Graph Transformer for Neural Network Representation Learning ∗ Yuxiang Zeng 1 ,Kun Xie 1† ,Yang Wang 1 ,Jigang Wen 2 ,Xiaocan Li 1 , Guangxing Zhang 3 ,Gaogang Xie 3 ,Jiannong Cao 4 1 Hunan University 2 Hunan University of Science and Technology 3 Chinese Academy of Sciences 4 The Hong Kong Polytechnic University zengyuxiang@hnu.edu.cn, xiekun@hnu.edu.cn Abstract Architecture attribute predictors reduce the cost of neural architecture search by estimating accuracy or latency from a small set of evaluated candidates. The key difficulty is that neural architectures are operation-labeled DAGs: edge direction defines computational flow, but existing predictors often treat direction as a local structural cue. We propose DTA-GT, a Direction- and Topology-Aware Graph Transformer based on encoder-wide directional consistency, which preserves directed computational semantics across node initialization, global spectral encod- ing, pairwise interaction, and feature update. DTA-GT realizes this principle with direction- and topology-aware node initialization, Magnetic Laplacian spectral encoding, direction-dual structural attention, and a Direction-Sensitive MoE-FFN. Across accuracy and latency prediction on NAS-Bench-101 and NAS-Bench-201, DTA-GT consistently outperforms representative sequence-, GNN-, Transformer-, and hybrid predictors under limited-budget settings. Ablations and Magnetic spec- tral controls support the contribution of the direction-aware stages and orientation- sensitive spectral information, while mechanistic diagnostics characterize module behavior. These results support encoder-wide directional consistency as an effective design principle for architecture DAG representation. Code: https://github.com/ZengYuXiang7/DTA-GT 1 Introduction Deep learning has been widely applied across various fields [1–6]. Neural architecture design is central to task performance and deployment efficiency, and Neural Architecture Search (NAS) automates this process by searching a candidate architecture space for models that meet performance and deployment constraints [7–12]. However, evaluating candidates during search is expensive: accuracy typically requires full network training, while latency requires hardware measurement or profiling. A practical way to reduce this cost is to train predictors under a limited evaluation budget, where only a small subset of candidate architectures is evaluated and the remaining unseen candidates are estimated by the predictor [13–16]. ∗ This is a preprint of a paper accepted at NeurIPS 2026. This version may contain errors. Each revised preprint supersedes earlier preprint versions. The forthcoming camera-ready version will supersede all preprints and should be treated as authoritative. † Kun Xie is the corresponding author. 40th Conference on Neural Information Processing Systems (NeurIPS 2026). arXiv:2610.16822v1 [cs.LG] 12 Oct 2026 Table 1: Topology and direction modeling in representative architecture predictors. Category Representative Methods Modeling Paradigm Topology Encoding Local Direction Cues Global Direction Prior Direction- Specific Update Sequence-based[8, 17, 18]Sequence/vector serialization GNN-based[13, 19–21]GNN-based message passing Transformer-based[14, 24–26]Topology-aware token-attention Hybrid[15, 16, 27]GNN–Transformer hybrid ProposedDTA-GT Direction- and Topology-Aware Graph Transformer Note: Symbols indicate whether each dimension is explicitly and centrally modeled (), partially or locally modeled (), or absent/non-central (). The comparison is qualitative and design-oriented rather than a performance ranking. Global direction prior refers to an explicit graph-level direction-aware structural or spectral prior, not merely local edge-direction cues. Learning-based predictors therefore rely on continuous representations of candidate architectures. This representation problem is nontrivial be- cause a neural architecture is an operation-labeled directed acyclic graph (DAG), rather than a mere undirected connectivity pattern. A directed edgeu→ vindicates that the output of operationufeeds into operationv, so the representation should preserve directed information flow. For accu- racy and latency prediction, this requires capturing operator composition along directed paths, branch splitting and merging, and reachability- related dependencies. If direction is discarded, the graph skeleton may still be retained, but upstream/downstream roles, split/merge structures, and forward dependencies can be blurred. Reversing a single edge in Fig. 1 swaps the split/merge roles of operations A and B without changing the undirected skeleton. G₁: A splits · B merges Op A Op B st G₂: A merges · B splits Op A Op B st Discard direction ↓ Same undirected skeleton Figure 1: Discarding direction obscures node roles. Their undirected skeletons match. Table 1 provides a design-oriented comparison of representative predictor families with respect to explicit topology and direction modeling. Despite the need to preserve directed computational semantics, existing predictors cover these aspects only partially. Sequence-based methods [8,17,18] linearize architectures and can obscure explicit DAG topology and edge-direction semantics. GNN- based predictors [13,19–22] explicitly model architecture graphs and local edge directions, but higher- order topology and long-range directed dependencies rely on repeated local message passing, where global structural and directional patterns can be weakened. Transformer and hybrid methods [14– 16,23–25] use self-attention to capture long-range interactions and inject topology-aware cues through operation/topology tokenization, graph-aided attention, relation masks, or bidirectional aggregation. However, these designs still treat direction as scattered structural cues rather than a coordinated modeling principle. They provide partial directional signals, but usually leave them local or stage-specific rather than combining topology encoding, local direction cues, a global direction prior, and direction-aware updates in one encoder. Thus, the main gap is not whether graph structure is used, but whether directional semantics are modeled consistently across the encoder. The challenge is therefore to preserve the asymmetry induced by directed computation while still capturing DAG topology, motivating the following question: How can a neural architecture encoder explicitly model directed computational semantics while capturing DAG topology? Our key insight is that directionality in architecture DAGs should be preserved throughout represen- tation learning, rather than injected once as a structural cue. We define encoder-wide directional consistency as the requirement that directed computational semantics be preserved across node-role encoding, global direction-aware spectral encoding, pairwise interaction, and feature update. Without such consistency, direction-aware cues introduced at one stage may be diluted by later direction- agnostic transformations. This motivates preserving direction across the main encoder stages rather than relying on an isolated structural signal. We propose DTA-GT, a Direction- and Topology-Aware Graph Transformer designed to preserve directed computational semantics throughout the encoder. DTA-GT realizes encoder-wide directional consistency through four coordinated modules: direction- and topology-aware node initialization 2 makes directed node roles available from the input stage; Magnetic Laplacian spectral encoding supplies a global edge-orientation-sensitive spectral prior; direction-dual structural attention guides pairwise interaction with separated directional relation channels; and a Direction-Sensitive MoE-FFN preserves predecessor/successor distinctions during feature update. Together, these modules prevent directional information from being reduced to an isolated structural cue. We evaluate DTA-GT on four prediction settings spanning accuracy and latency prediction over NAS-Bench-101 and NAS-Bench- 201. Across multiple limited-budget settings and evaluation metrics, DTA-GT consistently improves over representative predictors. Stage-wise ablations assess the contribution of the coordinated direction-aware stages, Magnetic spectral controls isolate the effect of the edge-orientation-sensitive spectral prior, and mechanistic diagnostics examine whether the internal behaviors align with the intended directed computational semantics. Our contributions are: •We formulate encoder-wide directional consistency as a design principle for architecture DAG representation, shifting direction modeling from isolated structural cues to coordinated preservation of directed computational semantics throughout the encoder. •We introduce DTA-GT, which integrates direction- and topology-aware node initialization, Magnetic Laplacian spectral encoding, direction-dual structural attention, and a Direction- Sensitive MoE-FFN. These modules jointly model directed node roles, a global edge- orientation-sensitive spectral prior, relation-aware interactions, and predecessor/successor- aware updates, thereby strengthening topology-aware architecture representations and pro- viding a stronger inductive bias for limited-budget prediction. •We conduct a unified evaluation on accuracy and latency prediction over standard NAS benchmarks, with stage-wise ablations, Magnetic spectral controls, and mechanistic diag- nostics to analyze the contribution and behavior of the proposed direction-aware stages. 2 Related Work Existing architecture predictors mainly follow three representation paradigms: sequence-based encodings, GNN-based graph modeling, and Transformer/hybrid architectures. These paradigms differ in how they encode topology and direction, and we focus on whether they preserve directed computational semantics beyond local structural cues. Sequence-based Methods. Peephole [17], NAO [18], and PNAS [8] encode architectures as flattened vectors or operation sequences. This paradigm prioritizes compact architecture descriptions and efficient predictor training under limited evaluation budgets. However, because the DAG is linearized, these methods do not explicitly model topology or preserve edge-direction semantics. As a result, directed computational dependencies among operations are difficult to capture. GNN-based Methods. BRP-NAS [13], Neural Predictor [19], NPENAS [22], GATES [20], Semi- NAS [28], DNNPerf [29], and NNLP [21] represent architectures as DAGs or graph-structured objects. Compared with sequence encodings, GNNs explicitly use graph topology and can exploit edge directions within local neighborhoods. However, in message-passing backbones, higher-order topology and long-range dependencies are mainly captured through repeated local propagation, where information can be mixed, over-smoothed, or over-squashed. Meanwhile, directional bias remains mostly local, and an explicit global direction-aware prior is usually absent. Transformer-based and Hybrid Methods. Transformer-based and hybrid predictors, including TNASP [24], NAR-Former [14], PINAT [25], FlowerFormer [23], NAR-Former V2 [15], and N- Former [16], use self-attention to model global interactions among architecture tokens. To compensate for the lack of explicit graph structure in vanilla self-attention, recent designs inject topology- aware signals through operation/topology tokenization, graph-aided attention, relation masks, or bidirectional aggregation. These designs improve topology-aware representation learning, but their directional cues remain mostly local or stage-specific, without jointly coordinating a global direction- aware spectral prior, relation-aware interaction, and direction-specific updates. 3 1345 Encoder-wideDirectionalConsistency node roles → direction-aware spectral encoding → pairwise interaction → feature updates 2 InputarchitectureDAG Direction-and topology-aware initialization L-layerDTA-GTEncoderAttention-basedGraphReadout PredictionHead 퐺=푉,퐸,휏 Input Conv3x3 MaxPool 3x3 Conv3x3Conv3x3 Add ReLU Output Initial Node Representations 퐻 0 =푋+푃 푃 푋 Direction-and Topology-Aware Node Initialization Magnetic Laplacian Spectral Encoding Direction-Sensitive MoE-FFN Direction-Dual Structural Attention AttentionMatrix WeightedSum 푧 퐺 =#훼 푖 ℎ 푖 퐿 푁 푖=1 푧 퐺 ∈ℝ # GraphRepresentation ReverseDepth ForwardDepth Out-degree In-degree Operation Type 훼 1 훼 2 훼 푁 ... Linear 푧 퐺 푦1 xL Nnodes × ℎ 1 퐿 ℎ 2 퐿 ℎ 푁 퐿 Targets Accuracy Latency Training Objective RankingLoss Routing Regularizer (Prediction) operation-labeled DAG Final NodeStates 퐻 ( ∈ℝ )×# Attention Weights 훼 ... Graph-level Representation Input 퐻 ! #$ SharedSuccessors/ Predecessors DirectedReachability Forward/Backward Adjacency + + Router Predecessor Expert Successor Expert ReIm Re/ImFusion + Fuse Weight Self Expert Direction-aware spectralprior Complex Eigenvectors Γ Directed Adjacency 퐴 퐋 퐦퐚퐠 퐪 =퐃 퐬 −퐀 퐬 ⊙exp푖Θ # eig. MSELoss Encode operation semantics, local in/out roles, and input- to-output positions. Provide a global edge-orientation- sensitive spectral prior. Guide pairwise interaction with separated directional relation channels. Adaptively fuse self, predecessor, and successor updates. Directed Node Roles Magnetic Spectral Encoding Direction-Dual Structural Attention Direction-Sensitive MoE-FFN Figure 2: The DTA-GT framework (will be updated). 3 Problem Formulation and Model Overview 3.1 Problem Formulation Following established conventions [14–16,21,24], letAbe the candidate architecture space. Each ar- chitecturea∈Ais represented as an operation-labeled directed acyclic graph (DAG)G = (V,E,τ), where nodes represent computational operations, directed edges encode data-flow dependencies, and τ : V →Oassigns an operation type to each node. We adopt the adjacency convention thatA u,v = 1 indicates a directed edge u→ v. Each architecture has a scalar target attributey ∈ R, such as accuracy or latency. Given a measured subsetD =(a i ,y i ) N i=1 sampled fromA, we learn a predictorf θ :A→ Rto estimate attributes for remaining unmeasured candidates in the same architecture space, without fully training or profiling each candidate. We decomposef θ into an encoderh φ and a prediction headp ψ :z G = h φ (G)and ˆy = p ψ (z G ), withθ = φ,ψ. The challenge is to preserve operation semantics, graph topology, and directed computational semantics across the encoder, rather than allowing directional information to be lost after a single encoding stage. 3.2 Overall Architecture Fig. 2 illustrates DTA-GT, which maps an architecture DAGGto a graph-level representation z G = h φ (G)under the encoder-wide directional consistency principle. Specifically, the encoder first initializes node states asH (0) = NodeEmbed(G) + DirSpecEnc(G), combining operation/local directed-role features with a global edge-orientation-sensitive spectral prior. It then appliesLresidual layers [30] alternating direction-dual structural attention and direction-sensitive MoE-FFN updates, usingR G andAfor relation-aware interaction and predecessor/successor-aware updates. Finally, attention-based readout producesz G = AttnReadout(H (L) ), which is passed top ψ for prediction without altering the original architecture DAG. 4 Method 4.1 Direction- and Topology-Aware Node Initialization Before global spectral encoding and attention-based interaction, each node should carry a basic description of its computation and its directed role in the architecture DAG. Operation labels specify the computation at each node, but they do not distinguish nodes with the same operation type that appear in different local structures or input-to-output positions. Topological-order indices can provide positional cues, but they may introduce ordering artifacts because a DAG can admit multiple 4 valid topological orders [14,15,25]. We therefore initialize nodes with topological-order-invariant attributes that encode computation, local directed roles, and input-to-output positions. Role-aware attributes. Each nodev i is described by five discrete features: operation labelτ(v i ), indegreedeg − (v i ), outdegreedeg + (v i ), forward depthℓ fwd (v i ), and reverse depthℓ rev (v i ). The forward depth is the maximum length of a directed path from an input node tov i , and the reverse depth is the maximum length of a directed path fromv i to an output node. The operation label captures computational semantics, indegree and outdegree characterize local merging and branching roles, and(ℓ fwd ,ℓ rev )locates the node along the directed input-to-output flow. This depth pair distinguishes nodes with the same forward depth but different remaining distances to the output side. These features make local in/out roles and input-to-output positions available before attention-based interaction. We embed, concatenate, and project them: x i = e τ (v i ) W op ∥ e deg − (v i ) W in ∥ e deg + (v i ) W out ∥ e ℓ fwd (v i ) W fwd ∥ e ℓ rev (v i ) W rev W fuse ,(1) wheree (·) denotes a one-hot vector, theWterms are learnable projections,∥denotes concatenation, and stacking all x i gives X∈ R n×d . 4.2 Magnetic Laplacian Spectral Encoding The node initializationXprovides operation semantics and local directed roles, but not a global direction-aware spectral prior over the architecture DAG. Existing predictors usually lack an explicit global direction-aware spectral prior [13–16,19–21,23–25], while standard Laplacian encodings capture symmetric connectivity but not the asymmetry betweenu → vandv → u. We therefore derivePfrom the Magnetic Laplacian [31,32], whose complex phase records edge orientation. This supplies the global spectral stage of encoder-wide directional consistency. Construction. Given the directed adjacency matrixA, define the symmetrized support(A s ) u,v = 1 2 (A u,v + A v,u ), the orientation phase(Θ (q) ) u,v = 2πq(A u,v − A v,u ), and the degree(D s ) u,u = P n v=1 (A s ) u,v . The Magnetic Laplacian is L (q) mag = D s − A s ⊙ exp iΘ (q) .(2) SinceA s is symmetric andΘ (q) is antisymmetric,L (q) mag is Hermitian and admitsL (q) mag = UΛU ∗ , with U containing complex eigenvectors and Λ containing real eigenvalues. Two-channel spectral features. We selectklow-frequency eigenvectors and retain their real and imaginary parts:P mag = [γ 1 ,...,γ k ] ∈ C n×k , and for each nodeuand spectral componentr, E u,r = [Re(P mag (u,r))∥ Im(P mag (u,r))], givingE∈ R n×k×2 . The real and imaginary channels provide a real-valued representation of the complex spectral signal, preserving orientation-dependent phase information. Spectral aggregation. For each node, we embed the two-channel spectral components and aggregate itskspectral modes with self-attention over the spectral dimension, producingp u ∈ R d . Stacking all node-wise spectral embeddings givesP = [p 1 ,..., p n ] ⊤ ∈ R n×d . Details of the spectral-mode aggregation are provided in Appendix A.7. The initial encoder states are then obtained by adding this global direction-aware spectral encoding to the node initialization: H (0) = X + P.(3) 4.3 Direction-Dual Structural Attention Standard self-attention [14,33] evaluates pairwise interactions from node representations. The Magnetic spectral encoding in Sec. 4.2 supplies a node-level global direction-aware spectral prior. Direction-dual structural attention complements this representation with explicit pairwise relation sup- ports, providing encoder-wide directional consistency. It organizes pairwise interactions through six directional relation channels. Each channel specifies a distinct structural context for query–key interac- tions, covering local dependencies, directed reachability, or shared-successor and shared-predecessor structures. Within each channel, content-based attention adaptively weights the admissible keys according to their node representations. 5 Direction-dual relation channels. For each direction-sensitive relation family, we construct paired channels over ordered or role-specific node-pair patterns, allowing attention to distinguish forward from backward dependencies and downstream-shared from upstream-shared branch structures. We instantiate three paired relation types, yielding six directional relation channels: (1) local adjacency, whereAandA ⊤ indicate direct forward and backward dependencies; (2) directed reachability, whereR fwd (u,v) = 1ifvis reachable fromu, andR bwd = R ⊤ fwd captures the reverse relation; and (3) shared successors/predecessors, whereAA ⊤ captures common successors andA ⊤ Acaptures common predecessors. LetR G = R (r) 6 r=1 denote the resulting relation channels. Together, these channels preserve local connectivity, multi-hop directed reachability, and higher-order branch structures as distinct structural contexts. Relation-constrained attention. For notational brevity, write the input node states of layerlas H = H (l−1) ∈ R n×d , and letd head = d/MforMattention heads. For them-th head, we compute Q m = HW Q m ,K m = HW K m , andV m = HW V m using projection matricesW Q m , W K m , W V m ∈ R d×d head . We use a fixed relation-to-head assignment: in the six-head configuration used in our experiments, headmis associated with directional relation channelρ(m) = m. The assigned relation defines the structural support of that head: we setB m (u,v) = 0whenR (ρ(m)) (u,v) > 0oru = v, and B m (u,v) =−∞ otherwise. The attention scores and multi-head output are then computed as S m = Q m K ⊤ m √ d head + B m ,StructAttn(H, R G ) = h M m=1 softmax(S m )V m i W O ,(4) where denotes concatenation over attention heads,W O ∈ R Md head ×d , and the softmax is applied row-wise over key nodes. This construction factorizes topology-aware interaction into structural admissibility and content- dependent weighting. The relation support determines which node pairs can interact, while the learned query–key compatibility determines their relative contributions within that support. The relation-specialized heads retain distinct directional semantics, and multi-head aggregation integrates their complementary representations into a unified topology-aware encoding. For NAS performance prediction, the resulting representation captures operation interactions under different dependency patterns and provides topology-conditioned features for ranking candidate architectures. 4.4 Direction-Sensitive Mixture-of-Experts Feed-Forward Network After structural attention, a standard position-wise FFN applies the same node-wise transformation to all nodes and does not distinguish predecessor from successor contexts. Such direction-agnostic updates can weaken the directional distinctions introduced by the preceding attention layer. We therefore replace the standard FFN with a Direction-Sensitive MoE-FFN, which uses three role- specific experts for the node’s own state, predecessor context, and successor context. A node-wise routing gate adaptively weights these experts according to the current node state. This keeps the feature-update stage direction-aware without assigning a fixed expert to every node role, since the useful predecessor/successor balance can vary across architectures and prediction targets. Directional experts. Given the post-attention states ˆ H (l) , the three expert outputs are H self = ˆ H (l) W self ,H pred = A ⊤ ˆ H (l) W pred ,H succ = A ˆ H (l) W succ .(5) Under the conventionA u,v = 1foru → v,H self transforms each node’s own state,A ⊤ ˆ H (l) aggregates predecessor contexts, andA ˆ H (l) aggregates successor contexts. The routing gate produces node-wise expert weights and fuses the expert outputs as [g self , g pred , g succ ] = softmax( ˆ H (l) W gate ), ̃ H = g self ⊙ H self + g pred ⊙ H pred + g succ ⊙ H succ (6) whereg self , g pred , g succ ∈ R n×1 , and the softmax is applied over the three experts. The layer output is H (l) = ˆ H (l) + ReLU( ̃ H)W proj ;⊙denotes broadcast multiplication, and allWterms are learnable projections. Routing regularization. To discourage overly sharp routing distributions, we use a negative-entropy regularizerL aux = 1 n P n i=1 P r∈self,pred,succ g i,r log(g i,r +ε). Since this term is the negative entropy of the routing distribution, minimizing it with a positive auxiliary weight encourages higher-entropy 6 routing and discourages overly concentrated expert assignments. The regularizer does not impose role labels on the router; it only prevents early collapse to a single expert so that directional contexts remain available during training. 4.5 Attention-based Graph Readout After direction-aware encoding, the readout summarizes final node states without adding virtual tokens, avoiding artificial topological relations that would alter structural biases and Magnetic spectral computation. This is important because the structural attention channels and Magnetic Laplacian are both computed from the original architecture topology; adding a virtual node would introduce extra edges or reachability patterns that are not part of the cell DAG. Attention pooling. We use attention-weighted pooling, withα = softmax H (L) r andz G = P n i=1 α i H (L) i ;r ∈ R d is a learnable scoring vector, and the softmax is applied over nodes. This pooling producesz G ∈ R d while keeping the original architecture node set unchanged, so graph-level prediction is separated from the topology used by the encoder. 4.6 Prediction and Training Objective Prediction Head. Given the graph-level representationz G , a linear head predicts the target scalar attribute, such as accuracy or latency, asˆy = p ψ (z G ) = w ⊤ z G + b, withψ = w,b. We keep the predictor head deliberately simple, so most modeling capacity remains in the direction-aware graph encoder rather than in a task-specific regressor. Architecture attribute prediction requires both calibrated value estimates and reliable attribute ranking, so we train with point-wise regression, pairwise ranking, and the routing regularizer introduced in Sec. 4.4. Training Objective. For a mini-batch of sizeB, the mean squared error (MSE) loss calibrates attribute values asL mse = 1 B P B i=1 (ˆy i − y i ) 2 . To preserve the relative order of candidate architectures under the target attribute, we use a pairwise ranking loss over sampled non-tied architecture pairsP: L rank = 1 |P| P (i,j)∈P log 1 + exp(−sgn(y i − y j )(ˆy i − ˆy j )) . This term encourages the predicted attribute order to match the measured order and aligns training with rank-based metrics such as Kendall’sτ. The final objective isL total = λ mse L mse +λ rank L rank +λ aux L aux , withL aux denoting the negative-entropy routing regularizer for the Direction-Sensitive MoE-FFN; theλterms control the relative weights of the three objectives. The MSE and ranking terms therefore serve different purposes: the former preserves target-scale calibration, while the latter directly constrains the ordering that predictor-based NAS relies on when selecting candidate architectures. 5 Experiments 5.1 Experimental Setup We evaluate accuracy and latency prediction on NAS-Bench-101 [34] and NAS-Bench-201 [35]; dataset statistics, latency-label sources, and splits are provided in Appendix A.2. We compare with ReNAS [36], NAO [18], BRP-NAS [13], NNLP [21], Graphormer [26], TNASP [24], NAR- Former [14], PINAT [25], GraphTrans [27], NAR-Former V2 [15], and N-Former [16], and report Kendall’sτand MAPE, where higherτand lower MAPE are better. We evaluate how well predictors trained on a small labeled subset estimate architecture attributes and recover the ranking of the full candidate pool. The main text reports means over five runs, while Appendix H provides the complete means and std. Baseline sources, reproduction strategies, hardware, and code-release information are provided in Appendix A, and DTA-GT hyperparameters and sensitivity analyses fork,L, anddare given in Appendix E. 7 5.2 Ablation Analysis Table 2: Ablation results under low-budget predictor training. Complete results with std are provided in Table 23. Component key Overall DirectionalityStage ContributionsReadout / Objective DirectedUndirectedw/o Dir. Feat.w/o Spec.w/o Attn.w/o MoECLS ReadoutMSE Only N:Dir. Node Feat.✓✗✓ P: Spec. Enc. ✓✗✓✗✓ A: Struct. Attn.✓✗✓✗✓ F: MoE-FFN✓✗✓✗✓ MetricK-TauMAPEK-TauMAPEK-TauMAPEK-TauMAPEK-TauMAPEK-TauMAPEK-TauMAPEK-TauMAPE NB101 Acc @1000.69540.03270.5882 0.04080.6522 0.03610.6894 0.03410.6552 0.03310.6542 0.03310.6701 0.03990.6720 0.0356 NB101 Lat @1000.86460.07580.8062 0.10740.8482 0.09080.8615 0.08060.8360 0.10330.8495 0.08600.8420 0.12030.8610 0.0808 NB201 Acc @1560.80150.02440.7215 0.06170.7198 0.07290.7452 0.06000.6123 0.10370.7248 0.04180.7535 0.07040.6937 0.0686 NB201 Lat @1560.83750.03050.8178 0.03490.8202 0.03260.8192 0.03250.8227 0.03170.8298 0.03130.8209 0.03480.8201 0.0321 Table 2 compares direction-aware DTA-GT (“Directed”) with its undirected counterpart, stage-wise ablations, and readout/objective controls under low-budget settings. The “w/o Directed Node Fea- tures” variant retains operation embeddings but omits in-degree, out-degree, forward-depth, and reverse-depth features from node initialization. Direction-aware DTA-GT outperforms its undirected counterpart across the reported metrics, supporting the importance of directional information in architecture representations. Removing direction-aware components at individual encoder stages also degrades performance, supporting our central principle that directionality should be preserved throughout the encoder. These results support maintaining directional information from node ini- tialization and global spectral encoding through pairwise interaction and feature update. Removing directed node features or Magnetic spectral encoding reduces performance, supporting the use of both local directed-role information and a global orientation-sensitive spectral prior. Removing structural attention or MoE-FFN also weakens performance, supporting the contribution of directional relations during node interaction and predecessor/successor contexts during feature updates. CLS readout performs worse than attention pooling, which aggregates existing nodes without introducing virtual graph connections that would alter directional structural relations and Magnetic Laplacian encoding. The MSE-only control also underperforms the proposed training objective. Combining regression with ranking supervision is appropriate for predictor-based NAS: MSE fits numerical attribute values, while the ranking term explicitly constrains their relative order for candidate selection. 5.3 Main Results Table 3 compares all methods across the four tasks and training budgets. DTA-GT achieves the highest Kendall’sτand the lowest MAPE across all four tasks and training budgets, showing consistent improvements in both candidate ranking and attribute estimation. These gains support the value of pre- serving directed computational semantics in architecture representations. Operator composition along directed paths, branch splitting and merging, and reachability-related dependencies describe how computations are organized within an architecture. DTA-GT explicitly models upstream/downstream roles and directional relations across its encoder stages, providing an inductive bias for capturing these computational semantics in both accuracy and latency prediction. Its consistent gains in both accuracy and latency prediction support encoder-wide directional modeling across architecture attributes. 5.4 Magnetic Spectral Encoding Analysis Table 4 isolates the spectral-encoding stage by comparing no directional encoding, symmetric Laplacian controls, and Magnetic Laplacian encoding in the directed encoder. Magnetic Laplacian encoding performs best on all reported metrics, whereas symmetric Laplacian encoding gives limited and task-dependent gains. Replacing Magnetic Laplacian with symmetric Laplacian inside the directed encoder also weakens performance, suggesting that the spectral benefit mainly comes from preserving edge-orientation asymmetry rather than adding generic undirected spectral information. Sensitivity to the Magnetic phase parameter q is evaluated in Appendix B.1 and Table 6. 5.5 Mechanistic Analysis Figure 3 examines Magnetic sensitivity to edge reversal, role-aligned predecessor/successor routing contrasts, and density-normalized attention over directional relation channels under the second train- 8 Table 3: Main results on NAS-Bench-101/201. Higher Kendall’sτand lower MAPE are better. Complete results with std are provided in Appendix H.1. Panel A: Accuracy prediction on NAS-Bench-101 BackboneMethodPublication Kendall’sτ (↑ ) by training budgetMAPE (↓) by training budget 0.02% (@100) 0.04% (@172) 0.1% (@424) 1% (@4236) 0.02% (@100) 0.04% (@172) 0.1% (@424) 1% (@4236) CNNReNASCVPR 20210.09630.12400.15960.51412.84090.83430.54560.0660 LSTMNAONeurIPS 20180.33950.40150.42020.44720.05770.05590.04930.0407 GNN NNLPICPP 20220.44520.49360.49870.78090.06650.04120.03990.0252 BRP-NASNeurIPS 20200.41290.43380.45490.76430.06720.05480.04240.0236 Transformer GraphormerNeurIPS 20210.22290.26100.29910.56100.05890.05360.04770.0355 TNASPNeurIPS 20210.50910.57490.64040.76630.04430.03930.03770.0250 NAR-FormerCVPR 20230.42280.49860.56990.81810.05380.04230.04060.0257 PINATAAAI 20230.34960.39940.42430.71620.13390.05160.04060.0271 Hybrid GraphTransNeurIPS 20210.43000.44380.46660.77020.27350.14010.13370.0252 NAR-Former V2NeurIPS 20230.53000.55000.60000.81500.09000.08500.03990.0220 N-FormerCVPR 20250.54280.56420.60570.82090.08950.09070.03680.0219 DTA-GT–0.69540.72780.79800.87400.03270.03120.02830.0202 Panel B: Latency prediction on NAS-Bench-101 BackboneMethodPublication Kendall’sτ (↑ ) by training budgetMAPE (↓) by training budget 0.02% (@100) 0.04% (@172) 0.1% (@424) 1% (@4236) 0.02% (@100) 0.04% (@172) 0.1% (@424) 1% (@4236) CNNReNASCVPR 20210.58030.71270.80280.92220.22320.15880.10800.0405 LSTMNAONeurIPS 20180.25690.25830.30490.39640.30570.30680.30620.2878 GNN NNLPICPP 20220.80560.83790.86850.91900.10640.08580.06950.0417 BRP-NASNeurIPS 20200.79370.84870.87020.92700.11050.08110.06820.0372 Transformer GraphormerNeurIPS 20210.35820.37110.40840.44670.28620.27150.26300.2617 TNASPNeurIPS 20210.80240.83250.87340.93940.11100.08970.06470.0311 NAR-FormerCVPR 20230.83370.86700.88360.94340.08810.06860.06060.0287 PINATAAAI 20230.83170.86210.88170.93890.08600.07040.05990.0315 Hybrid GraphTransNeurIPS 20210.81820.86190.88620.93650.09490.07100.05920.0329 NAR-Former V2NeurIPS 20230.77410.83140.87520.93800.12380.08880.06520.0317 N-FormerCVPR 20250.83850.86940.90820.94620.09070.06620.05130.0286 DTA-GT–0.86460.89300.90940.94900.07580.06130.05030.0271 Panel C: Accuracy prediction on NAS-Bench-201 BackboneMethodPublication Kendall’sτ (↑ ) by training budgetMAPE (↓) by training budget 1% (@156) 3% (@469) 5% (@781) 10% (@1563) 1% (@156) 3% (@469) 5% (@781) 10% (@1563) CNNReNASCVPR 20210.18160.22360.40970.71301.98220.84250.34440.1676 LSTMNAONeurIPS 20180.62540.64360.64450.65800.04780.04540.03990.0283 GNN NNLPICPP 20220.71090.73800.78240.81960.04100.02450.01720.0115 BRP-NASNeurIPS 20200.69530.71770.75750.77680.06290.05060.02110.0201 Transformer GraphormerNeurIPS 20210.70520.73110.74610.76500.02700.01850.01710.0149 TNASPNeurIPS 20210.74050.77700.80610.83140.03020.01580.01450.0110 NAR-FormerCVPR 20230.75400.78390.81880.85540.02560.01880.01410.0107 PINATAAAI 20230.70270.70840.75890.79200.03380.02730.02690.0198 Hybrid GraphTransNeurIPS 20210.69570.69590.77810.82580.09750.06130.04930.0153 NAR-Former V2NeurIPS 20230.74180.74320.80040.83910.13630.04410.03400.0256 N-FormerCVPR 20250.74000.74200.80500.84000.13500.04500.03300.0260 DTA-GT–0.80150.89250.91380.93040.02440.01250.00960.0084 Panel D: Latency prediction on NAS-Bench-201 BackboneMethodPublication Kendall’sτ (↑ ) by training budgetMAPE (↓) by training budget 1% (@156) 3% (@469) 5% (@781) 10% (@1563) 1% (@156) 3% (@469) 5% (@781) 10% (@1563) CNNReNASCVPR 20210.61660.65060.67250.68630.08440.07770.07070.0640 LSTMNAONeurIPS 20180.69630.69800.69840.70120.06280.06020.06000.0592 GNN NNLPICPP 20220.63490.64370.65270.65670.08070.07260.07160.0702 BRP-NASNeurIPS 20200.66900.68610.69230.69860.07170.06400.06150.0594 Transformer GraphormerNeurIPS 20210.67990.69720.70300.70300.06510.06000.05950.0589 TNASPNeurIPS 20210.66460.68730.69260.69900.07130.06330.06130.0595 NAR-FormerCVPR 20230.59160.60140.62750.65220.13090.12990.12290.1226 PINATAAAI 20230.68590.69920.69500.69960.06450.06070.06020.0593 Hybrid GraphTransNeurIPS 20210.64410.68710.69640.69930.07620.06430.06120.0600 NAR-Former V2NeurIPS 20230.62370.64740.65410.67810.07860.07190.06990.0680 N-FormerCVPR 20250.68190.68910.69470.69810.06950.06310.06090.0594 DTA-GT–0.83750.84090.84350.84920.03050.02930.02800.0276 ing budget of each task. These diagnostics describe module behavior rather than direct performance attribution:q = 0.25yields edge-orientation-sensitive spectral responses underA → A ⊤ , MoE routing shows the most pronounced role-aligned pattern on NAS-Bench-201 accuracy prediction, and structural attention assigns different enrichment to predefined relation channels. The performance ev- idence is provided by Tables 3–4; Appendix B provides detailed definitions, numerical interpretation, and per-module diagnostic plots for Fig. 3. 9 Table 4: Symmetric and Magnetic Laplacian spectral-encoding controls. Bold marks the best value. Complete results with std are reported in Table 24. Variant Sym. Lap.Mag. Lap. NB101 Acc @100NB101 Lat @100NB201 Acc @156NB201 Lat @156 K-TauMAPEK-TauMAPEK-TauMAPEK-TauMAPE No Directional Encoding✗0.58820.04080.80620.10740.72150.06170.81780.0349 No Direction + Symmetric Lap.✓✗0.58780.03860.80710.10660.71350.04850.82060.0330 Directed with Symmetric Lap.✓✗0.68940.03410.86150.08060.71480.07920.81920.0325 Directed with Magnetic Lap.✗✓0.69540.03270.86460.07580.80150.02440.83750.0305 NB101 Acc NB101 Lat NB201 Acc NB201 Lat 0.00 0.05 0.10 0.15 0.20 0.25 Direction sensitivity S q ( G ) (a) Spectral direction sensitivity q=0 q=0.25 Source Branch. Converg. Sink NB101 Acc @172 NB101 Lat @172 NB201 Acc @469 NB201 Lat @469 -0.006+0.000+0.009+0.016 +0.009+0.019-0.010+0.001 +0.034+0.037+0.015+0.044 -0.005-0.004+0.013+0.015 (b) Role-aligned MoE routing −0.04 0.00 0.04 Fwd edge Bwd edge Fwd reach Bwd reach Conv.Branch 1.91.81.01.02.22.7 1.91.81.01.02.22.7 2.12.01.01.01.24.7 2.11.81.01.01.24.7 (c) Directional relation-channel enrichment 1 2 3 4 Figure 3: Mechanistic analysis across four second-training-budget settings. Compact labels use NB101/NB201 for NAS-Bench-101/NAS-Bench-201 and Acc/Lat for accuracy/latency. (a) Magnetic Laplacian sensitivity to edge reversal atq = 0andq = 0.25. (b) Role-aligned MoE gate contrasts, with positive values indicating routing toward the aligned context. (c) Density-normalized relation- channel enrichment; values above 1 indicate above-density attention. 6 Discussion Limitations. Our architecture-prediction evaluation focuses on NAS-Bench-101 and NAS-Bench-201. Transfer to other search spaces requires aligned operation vocabularies and dependency semantics, since graph nodes may represent computations at different granularities. Dense directed-relation masks and pairwise attention also incur quadratic storage and attention costs as graph size grows. The effect of improved predictor ranking on end-to-end NAS remains to be evaluated. Future work. We will investigate a shared operation-level representation for cross-space pretraining and adaptation, and explore sparse or hierarchical attention with compact reachability representations to support larger computational graphs. We also plan to integrate DTA-GT into NAS pipelines and evaluate the selected architectures and total search cost under a fixed end-to-end evaluation budget. Appendix G elaborates on these directions. 7 Conclusion We presented DTA-GT, a Direction- and Topology-Aware Graph Transformer for neural architecture attribute prediction. DTA-GT is built on encoder-wide directional consistency, which preserves directed computational semantics across node initialization, global direction-aware spectral en- coding, pairwise interaction, and feature update. By combining direction- and topology-aware node initialization, Magnetic Laplacian spectral encoding, direction-dual structural attention, and a Direction-Sensitive MoE-FFN, DTA-GT strengthens topology-aware architecture representations while explicitly modeling edge-direction semantics. Experiments on NAS-Bench-101 and NAS- Bench-201 demonstrate consistent gains on accuracy and latency prediction across limited-budget settings. Ablations, Magnetic spectral controls, and mechanistic diagnostics further support the contribution and intended behavior of the proposed direction-aware stages. Version Note All preprints are provisional and provided solely for early preview. This version may contain errors. Each revised preprint supersedes earlier preprint versions. 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The large-DAG scalability experiments are conducted separately on an NVIDIA A800-SXM4-80GB GPU, with the corresponding hardware configuration and timing protocol reported in Appendix F. A.2 Datasets, Splits, and Training Budgets NAS-Bench-101 [34] contains 423,624 unique cell-based architectures with at most 7 nodes and 9 edges per cell. NAS-Bench-201 [35] contains 15,625 candidate cells with 4 nodes and 6 edges per cell. For NAS-Bench-201, we represent edge operations as nodes in the predictor input graph, whose encoding topology is fixed across operation assignments. The NAS-Bench-201 authors trained candidate architectures on CIFAR-10 for 200 epochs and recorded their validation accuracies, alongside latency measurements collected with a batch size of 256. These measurements serve as labels for our accuracy and latency prediction tasks, with accuracy averaged over the available benchmark runs for each architecture. NAS-Bench-101 provides accuracy labels but not latency labels; therefore, we measure NAS-Bench-101 latency on an NVIDIA RTX 4090 GPU using batch size 1 to complete the four-task evaluation. Because latency labels are benchmark- and device-specific, latency magnitudes are compared only within the same benchmark setting. For each task and training budget, each method is evaluated over five runs using a shared set of five random seeds. For each seed, architectures are randomly shuffled to form the training and validation partitions. The partitions vary across seeds, and all methods share the same partitions for a given seed. The @ notation in the result tables denotes the number of architectures used for predictor fitting, and the validation set contains 1,024 architectures. Because the predictor serves the candidate screening stage of NAS, its objective is to score and rank the complete architecture pool and identify promising candidates for costly downstream evaluation. We therefore compute Kendall’sτand MAPE over the full benchmark architecture set, including the training and validation architectures and all remaining candidates. A.3 Fair Comparison and Reproducibility Within each seed, all methods use the same training and validation partitions, full-set evaluation target, training budgets, and metrics. When reproducing baselines, we use the official implementations when available and preserve their original model configurations; otherwise, hyperparameters are selected by grid search within the ranges reported by the corresponding papers. DTA-GT uses one fixed default configuration across tasks and budgets. The main comparison and ablation tables report means over five runs; Appendix H also reports the corresponding standard deviations. A.4 Descriptions of Baselines We compare DTA-GT with representative sequence-, CNN-, GNN-, Transformer-, and hybrid architecture predictors. For methods with public source code, we use the released implementation as the primary reference. For methods for which we did not identify an official public implementation, we reproduce the predictor from the paper description and tune only within the reported or standard ranges under the shared split, budget, and evaluation protocol described above. Sequence- and CNN-based predictors. NAO [18] encodes architectures as operation sequences with an encoder–predictor–decoder framework and performs prediction in a continuous architecture embedding space. ReNAS [36] represents architectures with handcrafted tensor features and trains a relativistic predictor that focuses on ranking architectures rather than only regressing absolute performance. These baselines test whether explicit graph modeling is necessary beyond sequence or tensor encodings. GNN-based predictors. BRP-NAS [13] uses GCN-based architecture predictors and emphasizes binary relation prediction for comparing candidate architectures. NNLP [21] is a multi-platform neural 14 Table 5: Public source links and reproduction status for compared baselines. “Self-reproduced” denotes paper-based implementation under the shared protocol when no official public code was identified. MethodPublic source linkLicense/availabilityReproduction note ReNAS–No official public code identifiedSelf-reproduced (paper). NAOrenqianluo/NAOGPL-3.0Official code used as reference. BRP-NASzheng-ningxin/brp-nasApache-2.0Public code used as reference. NNLPModelTC/NNLQPApache-2.0Public code available. Graphormermicrosoft/GraphormerMITOfficial code used as reference. TNASP– No official public code identifiedSelf-reproduced (paper + supp.). NAR-Formeryuny220/NAR-FormerNot specified in repositoryOfficial code used as reference. PINATShunLu91/PINATMITOfficial code used as reference. GraphTransucbrise/graphtransApache-2.0Official code used as reference. NAR-Former V2yuny220/NAR-Former-V2MITOfficial code used as reference. N-FormerXuRuihan/NNFormerMITOfficial code used as reference. network latency query and prediction system built around graph-structured model representations. These baselines evaluate local message-passing predictors and latency-oriented graph predictors. Transformer-based predictors. Graphormer [26] is a general graph Transformer with structural encodings such as degree, shortest-path, and edge-related biases; we adapt it to architecture DAG prediction. TNASP [24] is a Transformer-based NAS predictor that combines operation embeddings, Laplacian positional encoding, and a self-evolution framework. NAR-Former [14] tokenizes operation and topology information into architecture sequences and uses a multi-stage fusion Transformer for holistic attribute prediction. PINAT [25] augments a Transformer-like NAS predictor with permutation-invariance modules and Laplacian positional information. These baselines test whether global self-attention and topology-aware tokenization are sufficient without encoder-wide directional consistency. Hybrid predictors. GraphTrans [27] combines a GNN module with global Transformer atten- tion to capture long-range graph context. NAR-Former V2 [15] rethinks Transformer-based neural network representation learning for broader architecture-attribute prediction. N-Former [16] com- bines topology-aware token mixing and bidirectional graph-isomorphism feed-forward updates to strengthen neural architecture representations. These baselines are closest in spirit to DTA-GT because they combine graph structure and attention, but they do not explicitly preserve direction across node initialization, spectral encoding, pairwise interaction, and feature update. A.5 Code and Data Access Code and experimental scripts are available in the public repository athttps://github.com/ ZengYuXiang7/DTA-GT. The repository contains the proposed DTA-GT implementation, experi- ment scripts, required benchmark data files, and the measured NAS-Bench-101 latency labels used for the four-task evaluation. This appendix provides the corresponding dataset, split, budget, hardware, latency-label, and hyperparameter details needed to interpret and reproduce the reported results. A.6 Direction-Aware Spectral Encoding Settings For the Magnetic Laplacian spectral encoding, we set the potential parameter toq = 0.25following prior Magnetic Laplacian practice [31,32]. The graph-scaled phase convention and the sensitivity experiment forqare described in Appendix B.1. Eigenvectors are sorted by ascending eigenvalues, and the firstk = 4eigenvectors are used as spectral components. Their real and imaginary parts are retained as two-channel spectral inputs before spectral-component self-attention. 15 A.7 Magnetic Spectral Aggregation Details Given the two-channel spectral tensorE∈ R n×k×2 , we first map each real/imaginary component to a hidden representation: Z u,r = f elem (E u,r ).(7) For each nodeu, the resulting sequenceZ u = [Z u,1 ,..., Z u,k ]represents itskspectral modes. We aggregate this sequence with self-attention over the spectral dimension: e Z u = MHA(Z u , Z u , Z u ).(8) The aggregated spectral signal is then flattened across modes and projected to the model dimension: p u = f mix Concat k r=1 e Z u,r .(9) Stacking allp u gives the spectral encodingP∈ R n×d , which is added to the node initialization in Eq. 3. B Additional Mechanistic Diagnostics These diagnostics examine how the proposed modules encode edge orientation, adapt directional context aggregation across node roles, and distribute attention over complementary structural relations. The mechanistic diagnostics use the second training budget of each task, while the accompanying phase-parameter experiment uses the lowest training budget. The mechanistic diagnostics characterize internal module behavior and complement the main results and ablations rather than directly attribute performance gains. The Magnetic phase diagnostic checks operator-level orientation sensitivity, while the MoE and attention diagnostics describe task-dependent routing and attention allocation over predefined relation channels. The following subsections provide the definitions, numerical results, and per-module views corresponding to Fig. 3. B.1 Magnetic Phase Sensitivity and Parameter Analysis Graph-scaled phase. Equation(2)presents the Magnetic Laplacian in its standard form. In the reported graph-scaled setting, the shared parameterqis converted to the effective phase parameter q G = q/c G , wherec G = max1, min(m,n)andnandmare the numbers of nodes and edges in the encoded graph. For a directed edgeu → v, substitutingq G into Eq.(2)gives conjugate phase factors e i2πq G and e −i2πq G , whose separation is e i2πq G − e −i2πq G = 2|sin(2πq G )|.(10) The factors are+iand−iwhen the effective parameterq G = 0.25. With graph scaling, the nominal settingq = 0.25generally givesq G ̸= 0.25, so phase separation depends on bothqand the graph scale c G . Edge-reversal diagnostic. We quantify sensitivity to reversing all edges by S q (G) = ∥ e L q (A)− e L q (A ⊤ )∥ F ∥ e L q (A)∥ F .(11) Here, e L q denotes the normalized Magnetic Laplacian constructed with the effective phaseq G defined above. Larger values indicate stronger sensitivity to edge reversal. Atq = 0, removing the phase term gives zero edge-reversal sensitivity in all four settings. Atq = 0.25, the reported mean sensitivity is 0.2398on NAS-Bench-101 and0.2065on NAS-Bench-201 for both prediction targets. The variation across NAS-Bench-101 graphs reflects their different topologies, while the fixed NAS-Bench-201 encoding topology gives a constant response across operation assignments. 16 q=0q=0.25 0.0 0.1 0.2 0.3 Direction sensitivity S q ( G ) (a) NAS-Bench-101 q=0q=0.25 0.0 0.1 0.2 0.3 0.000 0.206 fixed topology (b) NAS-Bench-201 Figure 4: Magnetic spectral response to reversing all edge directions. NAS-Bench-101 yields a distribution over topology-diverse cells, whereas NAS-Bench-201 has a fixed encoding topology and therefore produces a constant response across operation assignments. Prediction sensitivity toq. We also evaluateq ∈ 0, 0.125, 0.25, 0.5under the lowest training budget of each task, keeping all other parameters at the shared configuration. Table 6 reports means over five runs. This experiment evaluates the predictive effect of the nominal phase parameter, complementing the operator-level edge-reversal diagnostic above. Table 6: Effect of the Magnetic phase parameterqunder the lowest training budget of each task. The tabulatedqis the shared nominal parameter before graph scaling. All other parameters are fixed at the shared configuration. Bold indicates the best result for each metric among the tested values. q NB101 Acc @100NB101 Lat @100NB201 Acc @156NB201 Lat @156 KT↑MAPE↓KT↑MAPE↓KT↑MAPE↓KT↑MAPE↓ 00.68940.03410.86150.08060.71480.07920.81920.0325 0.1250.67190.03300.86420.07670.73430.05280.82380.0325 0.250.69540.03270.86460.07580.80150.02440.83750.0305 0.50.67370.03370.86330.07660.73860.04610.82350.0323 The shared settingq = 0.25achieves the highest Kendall’sτand the lowest MAPE in all four evaluated tasks among the tested values. These results support its predictive effectiveness within the evaluated settings, while the phase-separation expression above makes its graph-dependent directional effect explicit. B.2 Detailed MoE Routing by Node Role We group nodes by directed structural role and summarize the learned weights of the self, predecessor, and successor experts. For source and branching nodes, the role-aligned contrast isg succ − g pred ; for converging and sink nodes, it isg pred − g succ . A positive contrast indicates greater weight on the context aligned with that role. Table 7: Mean role-aligned MoE routing contrasts under the second training budget of each task. Positive values indicate greater successor-context weight for source and branching nodes and greater predecessor-context weight for converging and sink nodes. SettingSourceBranchingConvergingSink NB101 Acc @172 −0.0063+0.0002+0.0093 +0.0156 NB101 Lat @172 +0.0094+0.0192 −0.0096 +0.0014 NB201 Acc @469 +0.0342+0.0371+0.0152 +0.0439 NB201 Lat @469 −0.0051 −0.0039+0.0134 +0.0149 NAS-Bench-201 accuracy prediction exhibits positive role-aligned contrasts for all four roles. The contrasts are0.0342,0.0371,0.0152, and0.0439for source, branching, converging, and sink nodes, respectively. Across the remaining settings, the signs and magnitudes vary with the prediction target 17 and node role. These patterns illustrate how the learned router adapts the balance between predecessor and successor context across tasks and structural roles. Source Sink Middle Branch. Converg. 0.30 0.35 0.40 Gate weight NB101 Acc @172 Source Sink Middle Branch. Converg. NB101 Lat @172 Source Sink Middle Branch. Converg. 0.30 0.35 0.40 Gate weight NB201 Acc @469 Source Sink Middle Branch. Converg. NB201 Lat @469 SelfIncomingOutgoing Figure 5: Learned MoE gate weights by directed node role across the four second-training-budget settings. Incoming/outgoing denote predecessor/successor contexts; dashed lines mark uniform gate weights of 1/3. B.3 Detailed Relation-Channel Statistics For each directional relationr, Figure 6 reports its density, the attention mass assigned to the node pairs covered by that relation, and density-normalized enrichment. Relation density is the fraction of off-diagonal node pairs in the encoded graphs covered by the binary relation indicatorM r , and attention mass is the fraction of off-diagonal attention assigned to those pairs. Enrichment is attention mass divided by relation density, averaged across evaluated runs, layers, and heads. An enrichment value of1corresponds to attention allocation proportional to relation coverage, placing local edges, directed reachability, and shared-neighbor relations on a common coverage-adjusted scale. Across the four second-budget settings, the six relation channels exhibit distinct enrichment patterns. On NAS-Bench-101, forward and backward edge relations have enrichment values of approximately 1.89–1.91and1.78–1.81, respectively, while the directed-reachability relations are close to0.98. The shared-successor and shared-predecessor relations reach approximately2.20and2.70. On NAS-Bench-201, the edge relations remain enriched, directed reachability is close to1.04, and the shared-predecessor relation reaches4.67. These statistics characterize how the learned attention weights distribute mass over the local, multi-hop, and branch-related structural supports supplied to the six directional channels. 18 Fwd edge Bwd edge Fwd reach Bwd reach Conv.Branch NB101 Acc @172 NB101 Lat @172 NB201 Acc @469 NB201 Lat @469 Relation density Fwd edge Bwd edge Fwd reach Bwd reach Conv.Branch Raw attention mass Fwd edge Bwd edge Fwd reach Bwd reach Conv.Branch Density-normalized enrichment 0.0 0.1 0.2 0.3 0.4 0.5 0.15 0.20 0.25 0.30 0.35 0.40 0.45 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Figure 6: Attention allocation over the six directional relation channels across the four second- training-budget settings. Relation density is the fraction of valid node pairs covered by a relation, attention mass is the fraction of attention assigned to those pairs, and enrichment is their ratio. C Complexity Analysis Letnandmdenote the numbers of nodes and directed edges, respectively. Letddenote the hidden dimension,kthe number of retained spectral modes, andLthe number of encoder layers. We treat the number of attention heads and the six directional relation channels as constants. C.1 Time Complexity Degrees, directed depths, and a sparse Magnetic Laplacian can be constructed inO(n+m)time from a sparse DAG representation. A dense construction of reachability and common-neighbor relations hasO(n 3 )worst-case time andO(n 2 )storage, and a full dense Hermitian eigendecomposition has the same worst-case time and storage orders. These graph-dependent quantities are computed once and reused during subsequent encoder evaluations. Aggregatingkspectral modes per node costsO(nkd 2 + nk 2 d), which becomesO(nd 2 )for fixedk. Each encoder layer usesO(nd 2 )work for feature projections andO(n 2 d)work for dense masked attention. When adjacency is represented densely, the directional context updates remain within the same O(n 2 d + nd 2 ) per-layer bound. The resulting encoder-evaluation cost is T eval = O nkd 2 + nk 2 d + L(n 2 d + nd 2 ) .(12) The first-use cost adds graph-dependent construction to encoder evaluation: T first = T relations + T spectral + T features + T eval .(13) With fixed k and dense preprocessing, the conservative first-use bound is O(n 3 + L(n 2 d + nd 2 )). C.2 Space Complexity Dense relation masks requireO(n 2 )storage, retained eigenvectors requireO(nk), node states require O(nd), and encoder parameters require O(Ld 2 ). For inference at batch size one, these terms give M inference = O(n 2 + nk + nd + Ld 2 ).(14) A conventional backward pass that retains per-layer attention and node activations addsO(L(n 2 +nd)) storage. The measured GPU memory in Appendix F.2 complements these asymptotic bounds for the profiled implementation. C.3 Design Choices for Practical Scalability The analysis above identifies two scale-dependent costs: graph-dependent construction at first use and dense pairwise storage and computation during encoder evaluation. DTA-GT addresses these costs through three complementary execution choices that preserve the same direction-aware representation. Sparse retained-mode spectral computation. The large-graph spectral path represents the Mag- netic Laplacian sparsely and uses thick-restart Lanczos to compute only the retained eigenpairs through sparse matrix-vector products in a compact Krylov subspace. It therefore constructs the spectral modes consumed by the encoder without forming a complete spectral basis, with runtime determined by graph sparsity, solver tolerance, and the iterations required for convergence. 19 Reusable graph-dependent preprocessing.The retained eigenpairs and directional relation masks depend only on the architecture graph, so they are constructed once and reused across encoder layers, training epochs, and repeated predictions of the same architecture. This design separates graph-input construction from model evaluation and amortizes structural and spectral construction whenever an architecture is revisited. Topology- and support-aware relation handling. Deployment-oriented architecture design bal- ances predictive quality against computational cost, making sparse-to-moderately-dense connectivity a practically important regime for support-aware execution. The practical motivation for support- aware relation handling is that computational graphs exhibit structured, architecture-dependent connectivity rather than a single density regime. ResNet-style architectures introduce selected shortcut edges, whereas DenseNet-style blocks create a denser support pattern by connecting each layer to all preceding layers within a block. Deriving relation supports from the observed topology preserves this variation and provides the structural basis for sparse execution whenever the graph admits it. The six directional relations expose their supported node pairs explicitly, allowing relation construc- tion to exploit known graph structure. LetSdenote the total number of supported pairs across the six relations. A support-indexed attention implementation evaluates only stored supported pairs, yielding anO(Sd)attention term, while sparse predecessor and successor aggregation costsO(md). The explicit relation supports therefore provide the execution interface for support-proportional computation as graph scale increases. Appendix D first reports model-level resource costs on NAS-Bench-201, while Appendix F profiles predictive accuracy, spectral and relation construction, model forward, and GPU memory on real and generated DAGs. The staged large-DAG profiles separately report graph-input construction costs, model-forward latency, and peak forward GPU memory. D Computational Efficiency We construct DTA-GT-S by reducing the hidden dimension to 60 and the encoder depth to four while retaining the direction-aware design. DTA-GT-S contains 0.36M parameters, compared with 0.61M for Graphormer and 6.99M for DTA-GT. We compare their prediction quality under the same lowest-budget setting of each task. Prediction results are averaged over five runs. Table 8: Parameter counts and inference measurements for the compact-model comparison. DTA-GT- S retains the direction-aware design with reduced width and depth. ModelParameters (M)Inference (ms/sample) Graphormer0.610.050 DTA-GT-S (d = 60, L = 4)0.360.049 Table 9: Prediction quality of Graphormer and DTA-GT-S under the lowest training budget of each task. Task GraphormerDTA-GT-S KT↑MAPE↓KT↑MAPE↓ NB101 Acc @1000.22290.05890.66030.0359 NB101 Lat @1000.35820.28620.86120.0777 NB201 Acc @1560.70520.02700.71140.0486 NB201 Lat @1560.67990.06510.81830.0371 DTA-GT-S uses19.4×fewer parameters than DTA-GT and remains smaller than Graphormer. It achieves higher Kendall’sτthan Graphormer in all four settings and lower MAPE in three of them. Graphormer obtains the lower MAPE on NAS-Bench-201 accuracy prediction, while DTA-GT-S retains the higher ranking correlation in that setting. The recorded inference times are0.049ms 20 per sample for DTA-GT-S and0.050ms per sample for Graphormer. These results show that the direction-aware design remains effective at a compact parameter scale. We report parameter count, inference latency, peak GPU memory usage, and training time to characterize the computational cost of representative architecture predictors on NAS-Bench-201. Latency is measured in milliseconds per architecture sample, and training time denotes the wall-clock time required to complete one training run. For each method, latency, memory, and training time are summarized over four NAS-Bench-201 training budgets: 156, 469, 781, and 1563 training samples. When a metric varies across budgets, we report its average value to obtain a compact method-level efficiency profile; for range-valued entries, the midpoint is used for aggregation. The parameter count is reported once since it is independent of the training budget. Table 10: Computational-efficiency comparison of architecture predictors. Memory denotes peak GPU usage. Latency, memory, and training time are summarized over four NAS-Bench-201 training budgets: 156, 469, 781, and 1563 training samples. For range-valued entries, the midpoint is used. MethodParams (M)↓ Avg. latency (ms/sample)↓ Avg. memory (GB)↓ Avg. training time (h)↓ NAO0.120.0400.0300.072 ReNAS1.040.0500.0480.077 NNLP0.640.0500.0400.083 BRP-NAS1.090.0500.0620.089 Graphormer0.610.0500.0550.101 TNASP0.610.0500.0550.101 GraphTrans0.930.0530.0730.123 DTA-GT6.990.1210.3200.180 NAR-Former V28.580.0870.3550.188 N-Former4.930.1200.2150.256 NAR-Former4.820.1350.1800.284 PINAT0.190.2100.0370.366 DTA-GT uses 6.99M parameters and has an average inference latency of 0.121 ms per sample under this NAS-Bench-201 profile. Its average training time is 0.180 h, compared with 0.188 h for NAR-Former V2, 0.256 h for N-Former, and 0.284 h for NAR-Former. This resource profile complements the predictive results by quantifying the computational cost of the direction-aware design. E Design Rationale and Parameter Sensitivity DTA-GT uses three structurally defined update paths for the node’s own state, predecessor context, and successor context. The number of experts follows this decomposition of directed computational context. A node-dependent router learns adaptive mixing weights over the three contexts from the current node representation. This allows each node to combine its local state with upstream and downstream information according to the prediction task. The four directional stages provide complementary information throughout the encoder. Node initial- ization represents local directed roles, and Magnetic spectral encoding supplies a global orientation- sensitive prior. Structural attention organizes interactions by directed node-pair relations, while the MoE-FFN adapts each node update to its self, predecessor, and successor contexts. Together, these stages preserve computational direction from the input representation through pairwise interaction and feature updates. Source and branching nodes distribute information along downstream paths, whereas converging and sink nodes summarize upstream computation. These roles motivate separate predecessor and successor contexts, with the learned gate adapting their relative contributions at each node. The routing diagnostics in Appendix B examine how these weights vary across node roles and prediction targets. Baseline sources and reproduction strategies are described in Appendix A. DTA-GT is optimized with AdamW using a batch size of 128, a learning rate of1× 10 −4 , and weight decay of0.01for at most 3000 epochs. For both accuracy and latency prediction, early stopping monitors validation Kendall’sτ 21 with a patience of 100, and evaluation uses the checkpoint with the highest validationτ. The learning rate is linearly warmed up over the first 10% of training steps and then follows a cosine decay schedule. The default DTA-GT model uses embedding dimensiond = 180, backbone depthL = 10, and loss weightsλ mse = 1,λ rank = 0.2, andλ aux = 0.001. This default configuration was set a priori by following the model scale and optimizer choices commonly used in closely related Transformer-based predictors, including NAR-Former [14], NAR-Former V2 [15], and N-Former [16]. We use the same configuration across all tasks and budgets without task- or budget-specific tuning. The shared configuration is(q,k,L,d) = (0.25, 4, 10, 180)for both benchmarks, both prediction targets, and all reported NAS training budgets. Theqsensitivity experiment is reported alongside the Magnetic mechanism analysis in Appendix B.1 and Table 6. That experiment and thek,L, anddexperiments below assess sensitivity around the configuration fixed a priori; we retain the same defaults for the main comparisons without task- or budget-specific parameter selection. Each experiment changes one parameter while keeping the remaining settings fixed. We evaluatek ∈ 1, 2, 4,L∈4, 7, 10, 12, andd∈150, 180, 210under the lowest training budget of each task. The tables below report means over five runs. Bold indicates the best result for each metric among the tested values. E.1 Retained Spectral Modes After decomposing the Magnetic Laplacian, we order the eigenvectors by ascending eigenvalue and retain the firstklow-frequency modes, givingP mag ∈ C n×k . Each retained mode contributes real and imaginary channels that preserve its orientation-dependent phase information, and the spectral aggregation module combines the resultingkcomponents into the node representation. The parameter ktherefore controls the resolution of the global spectral basis together with its storage and aggregation cost. We usek = 4as a compact basis for the evaluated architecture graphs and compare it with k = 1 and k = 2 below. Table 11: Effect of the number of retained Magnetic spectral modeskunder the lowest training budget of each task. All other parameters are fixed at the shared configuration. Bold indicates the best result for each metric among the tested values. k NB101 Acc @100NB101 Lat @100NB201 Acc @156NB201 Lat @156 KT↑MAPE↓KT↑MAPE↓KT↑MAPE↓KT↑MAPE↓ 10.67850.03370.86060.07950.73830.04810.81590.0343 20.68310.03350.86250.07810.74060.04290.81990.0353 40.69540.03270.86460.07580.80150.02440.83750.0305 Retaining four spectral modes achieves the highest Kendall’sτand the lowest MAPE in all four evaluated tasks among the tested values ofk. For NAS-Bench-201 accuracy prediction, increasingk from1to4changes Kendall’sτfrom0.7383to0.8015and MAPE from0.0481to0.0244. These results support the four-mode representation as the shared compact spectral basis for the evaluated benchmarks and prediction targets. E.2 Model Depth and Width The encoder depth L and hidden dimension d form the two standard model-scaling axes considered in our controlled sweeps. The former changes the number of stacked directional encoder blocks, while the latter changes the width of node states and learnable projections. Both parameters affect representational capacity and computation, and we vary them one at a time while keeping the remaining configuration fixed. Depth. Each DTA-GT encoder layer composes direction-dual structural attention with the node- adaptive self, predecessor, and successor context update. The depthLtherefore determines how many times pairwise structural interaction and direction-sensitive feature updating are repeated before graph readout. IncreasingLexpands the sequence of directional transformations as well as the corresponding computation. We useL = 10in the shared configuration and compare it with L∈4, 7, 12 below. 22 Table 12: Effect of encoder depthLunder the lowest training budget of each task. All other parameters are fixed at the shared configuration. Bold indicates the best result for each metric among the tested values. L NB101 Acc @100NB101 Lat @100NB201 Acc @156NB201 Lat @156 KT↑MAPE↓KT↑MAPE↓KT↑MAPE↓KT↑MAPE↓ 40.66620.04090.86230.08030.73030.06450.82190.0346 70.67310.03680.86290.07960.74200.04490.82380.0335 100.69540.03270.86460.07580.80150.02440.83750.0305 120.67650.03330.86030.08270.73870.04370.82260.0332 Increasing the encoder depth from4to10improves Kendall’sτand reduces MAPE in all four evaluated tasks. AtL = 12, all eight reported metrics decline relative toL = 10, showing that additional depth does not continue the improvement observed up to ten layers. The shared ten-layer configuration therefore gives the best predictive results among the evaluated depths across both benchmarks and prediction targets. Width.The hidden dimensiondsets the width of the node states and the attention and directional- context projections throughout the encoder. We used = 180in the shared configuration and compare it with d = 150 and d = 210 below. Table 13: Effect of hidden dimensiondunder the lowest training budget of each task. All other parameters are fixed at the shared configuration. Bold indicates the best result for each metric among the tested values. d NB101 Acc @100NB101 Lat @100NB201 Acc @156NB201 Lat @156 KT↑MAPE↓KT↑MAPE↓KT↑MAPE↓KT↑MAPE↓ 1500.67930.03370.86430.07690.74300.04860.82440.0336 1800.69540.03270.86460.07580.80150.02440.83750.0305 2100.67340.03320.85830.08040.75140.04440.81850.0337 The shared widthd = 180achieves the highest Kendall’sτand the lowest MAPE in all four evaluated tasks. Increasing the width tod = 210lowers Kendall’sτand increases MAPE in all four tasks relative tod = 180. Across the evaluated settings,d = 180therefore provides the strongest overall predictive performance among the tested widths. F Evaluation on Larger DAGs F.1 Predictive Accuracy on MalNet-Derived DAGs We further evaluate the direction-aware encoder on larger DAGs derived from the five-class MalNet- Tiny graph-classification dataset [37]. The derived graphs contain 5–4,993 nodes, with a mean of 1,407 nodes. This experiment examines the effectiveness of the directional design on larger graphs under limited training supervision. We contract each strongly connected component into a node to obtain a condensation DAG. Each node receives a shared operation token, so the compared predictors must derive their graph representations from the structure of the resulting DAG. All compared methods use the same derived graphs and data partitions. We use a stratified 5%/5%/90% training/validation/test split and fit each model on the 5% training partition. All classification metrics are computed on the held-out 90% test partition. The five classes contain equal numbers of graphs, and stratification preserves their proportions in each partition. We compare DTA-GT with BRP-NAS, Graphormer, and N-Former and report accuracy, macro-F1, macro-precision, and macro-recall. Table 14 reports the mean over five runs. 23 Table 14: Classification results on DAGs derived from MalNet-Tiny using a stratified 5%/5%/90% training/validation/test split. All methods use the same derived graphs and partitions. Values are mean percentages. ModelAccuracyMacro-F1Macro-PrecisionMacro-Recall BRP-NAS57.053.156.957.0 Graphormer69.567.970.969.5 N-Former59.358.862.459.3 DTA-GT74.173.874.874.1 DTA-GT achieves 74.1% accuracy and 73.8% macro-F1, leading the compared methods on all four metrics. Its accuracy exceeds Graphormer by 4.6 percentage points and BRP-NAS by 17.1 percentage points. With a shared node token, these results support the effectiveness of the direction- and topology-aware representation on substantially larger DAGs. F.2 Computational Efficiency on Large DAGs We profile representative MalNet-derived DAGs and generated DAGs on an NVIDIA A800-SXM4 GPU with 80 GB memory. The real-graph profiles range from 16 nodes and 25 edges to 3,416 nodes and 9,215 edges, while the generated profiles range from 8 nodes and 16 edges to 32,768 nodes and 65,536 edges. The real graphs have median edge density below 0.3%. All methods use identical graphs and reported model settings with batch size one. The real-DAG comparison reports the graph preprocessing required by each method followed by one model-forward pass. The generated-DAG comparison reports the recorded prediction-path latency for each method; the DTA-GT row isolates model forward after graph-input construction, and its largest-graph first-use stages are reported separately. The real-DAG DTA-GT stage profile uses ten warm-up and thirty timed measurements for graph-input construction, followed by thirty warm-up and five hundred timed measurements for model forward. The independently instrumented profile on the largest generated DAG uses one warm-up and five timed measurements for each construction stage, followed by thirty warm-up and fifty timed measurements for model forward. The profiled DTA-GT configuration uses hidden dimension 192, ten encoder layers, six attention heads, four retained spectral modes, andq = 0.25. Graph-dependent structural masks and spectral features are constructed once per graph and shared by all encoder layers. For larger graphs, we represent the Magnetic Laplacian in sparse CSR form and compute only the retained eigenpairs using thick-restart Lanczos [38]; smaller graphs use dense eigendecomposition. We report structural-mask construction, Magnetic spectral construction, and model forward separately in Table 15. Table 15: DTA-GT stage latencies on representative MalNet-derived DAGs. Graph inputs are constructed before model forward. Columns identify node and edge counts, and entries report mean latency in milliseconds. Component16–25 88–180 362–859 1,427–3,844 3,416–9,215 Structural-mask construction0.390.390.391.2511.46 Magnetic spectral construction0.642.896.157.337.48 Model forward5.195.305.5212.1340.01 On the 3,416-node DAG, structural-mask construction, spectral construction, and model forward take 11.46 ms, 7.48 ms, and 40.01 ms, respectively. The sum of these reported stages is 58.95 ms. For repeated predictions of the same architecture, the constructed graph inputs can be reused and only the model-forward stage is executed again. Table 16 compares end-to-end method-specific preprocessing and inference latency on representative MalNet-derived DAGs. On the largest profiled real DAG, DTA-GT requires 58.95 ms, compared with 122.56 ms for PINAT and 161.20 ms for N-Former. BRP-NAS requires 4.24 ms on the same graph, showing the lower computational cost of the GCN predictor in this profile. 24 Table 16: End-to-end latency on representative MalNet-derived DAGs. Each method includes its required graph preprocessing and one inference pass. Values are mean milliseconds per graph on the A800, and columns identify node and edge counts. Method16–25 88–180 362–859 1,427–3,844 3,416–9,215 BRP-NAS0.550.550.551.354.24 PINAT10.7410.6510.5229.97122.56 NAR-Former43.50 238.11 1,339.6211,612.4455,393.56 NAR-Former V28.5830.27119.67449.761,185.62 N-Former7.297.277.4422.71161.20 DTA-GT6.228.5812.0620.71 58.95 Table 17 extends the profile to generated DAGs with up to 32,768 nodes and 65,536 edges. DTA-GT completes model forward after graph-input construction on the largest generated DAG in 3,125.11 ms and reaches 42.249 GiB of peak GPU memory. PINAT and NAR-Former V2 record 9,684.47 ms and 12,036.15 ms, respectively, on their profiled prediction paths. NAR-Former and N-Former encounter out-of-memory failures at this graph size under their reported settings, while BRP-NAS records 313.80 ms. Table 17: Recorded prediction-path latency on generated DAGs. The DTA-GT row reports model forward after graph-input construction; Table 18 reports its complete first-use stage sum on the largest graph. Values are mean milliseconds per graph on the A800. OOM denotes an out-of-memory failure under the reported settings. Method8–16 64–128 512–1,024 4,096–8,192 32,768–65,536 BRP-NAS0.560.540.586.08313.80 PINAT10.6610.5510.58191.529,684.47 NAR-Former28.23 166.742,248.0078,731.93OOM NAR-Former V26.0123.96161.231,298.0312,036.15 N-Former7.437.247.76268.80OOM DTA-GT (forward)5.205.215.4161.083,125.11 Table 18 independently profiles four DTA-GT stages on the largest generated DAG. Model forward after graph-input construction takes 3,125.117 ms and reaches 42.249 GiB of peak GPU memory. The independently measured means for feature preprocessing, spectral construction, structural-mask construction, and model forward sum to 25,601.083 ms for first use. The stage breakdown shows that graph-dependent preprocessing is a substantial part of the first-use cost at this scale. Table 18: Staged DTA-GT profile for the generated DAG with 32,768 nodes and 65,536 edges. Stage means are measured independently, and the first-use value is their arithmetic sum. Peak GPU memory refers to model forward. Stage or resourceRecorded value Feature preprocessing14,616.178 ms Magnetic spectral construction9.923 ms Structural-mask construction7,849.865 ms Model forward3,125.117 ms First-use stage sum25,601.083 ms Peak forward GPU memory42.249 GiB For generated DAGs containing a spanning directed chain, we additionally evaluate a topology- specific relation-construction procedure motivated by the support-aware design discussed in Ap- pendix C.3. On the 32,768-node graph, this procedure constructs the six masks in 33.340 ms, and the resulting dense Boolean masks occupy 6 GiB. This result separates relation-construction time from relation storage and provides measured evidence for topology-aware relation handling. 25 The MalNet classification results and A800 profiles jointly characterize representation quality and computational cost on larger DAGs. DTA-GT provides the strongest classification results among the evaluated MalNet predictors, while BRP-NAS has lower latency in the large-graph profiles. The staged A800 measurements support the intended roles of retained-mode spectral computa- tion, reusable graph-dependent preprocessing, and topology-aware relation construction within the evaluated range. The reported scaling evidence covers graphs with up to 32,768 nodes; sparse or hierarchical attention and compact reachability representations remain important directions for substantially larger computational graphs. G Extended Discussion Cross-space representation and adaptation. A node in a cell-based CNN space may denote a primitive convolution or pooling operation, whereas a node in another space may denote an entire Transformer layer or Mamba block. These different computational granularities motivate a canonical operation-level representation for cross-space adaptation. Composite blocks could be decomposed into shared semantic units or mapped to a common operation vocabulary with aligned edge definitions and target protocols. For spaces with compatible operation definitions and dependency semantics, future work can investigate reusing DTA-GT’s directional encoder and graph preprocessing, with new vocabulary entries and embeddings for additional operation types. This would enable studies of cross-space pretraining followed by adaptation on a small evaluated subset from the target space. Task adaptation and NAS evaluation.For a new DAG-level task with compatible atomic units and directed-dependency semantics, adapting the prediction head and fine-tuning the encoder on a small labeled subset provides a natural extension. This would allow the same direction-aware representation principle to be studied under different graph-level targets. A complementary direction is to integrate the predictor into a NAS search loop and evaluate how candidate ranking affects architecture selection under a fixed end-to-end evaluation budget. Relation-channel design and extension. The three paired relation families in Section 4.3 are heuristic choices motivated by DAG semantics, providing a concrete instantiation of direction-dual structural attention. They capture local dependencies, multi-hop reachability, and shared predeces- sor/successor structure. Additional directional information, such as hop-specific dependencies or directed motif patterns, can be represented by further ordered or role-specific relation supports, with a corresponding extension of the relation-to-head assignment. The relation set can therefore be tailored to the directional semantics available in a target graph domain. Our experiments evaluate the six-channel instantiation; the predictive value and computational cost of expanded relation sets remain to be studied. Computational scaling. Directed reachability can grow quadratically even when the original adjacency is sparse. For example, a directed chain hasn− 1edges butn(n− 1)/2reachable ordered pairs. Dense relation masks therefore require quadratic storage, and dense masked attention incurs quadratic pairwise computation for a fixed hidden dimension. The A800 profiles in Appendix F.2 demonstrate execution on generated DAGs with up to 32,768 nodes. Extending Graph Transformer predictors to substantially larger computational graphs calls for sparse or hierarchical attention together with compact representations of directed reachability. Combining these mechanisms with reusable spectral preprocessing could extend the encoder to larger computational graphs while retaining its direction-aware representation. Future evaluations should measure prediction quality, first-use graph-input construction, model-forward latency, and GPU memory under matched graph and hardware settings. H Complete Results with Standard Deviations This section provides the complete means and standard deviations for the prediction and ablation experiments summarized in the main text. Prediction results are summarized over five runs using the same settings as their corresponding mean-only tables. 26 H.1 NAS-Bench-101 and NAS-Bench-201 Prediction The complete mean and standard-deviation results for all four prediction tasks are reported in Tables 19–22. Table 19: Complete accuracy-prediction results on NAS-Bench-101. Each cell places the mean above its standard deviation. Method Kendall’s τ (↑) by training budgetMAPE (↓) by training budget 0.02% (@100) 0.04% (@172) 0.1% (@424) 1% (@4236) 0.02% (@100) 0.04% (@172) 0.1% (@424) 1% (@4236) ReNAS 0.0963 ± 0.0579 0.1240 ± 0.0453 0.1596 ± 0.0471 0.5141 ± 0.1137 2.8409 ± 2.7629 0.8343 ± 0.1109 0.5456 ± 0.1241 0.0660 ± 0.0338 NAO 0.3395 ± 0.0445 0.4015 ± 0.0218 0.4202 ± 0.0123 0.4472 ± 0.0017 0.0577 ± 0.0149 0.0559 ± 0.0030 0.0493 ± 0.0108 0.0407 ± 0.0017 NNLP 0.4452 ± 0.0188 0.4936 ± 0.0319 0.4987 ± 0.0470 0.7809 ± 0.0046 0.0665 ± 0.0192 0.0412 ± 0.0023 0.0399 ± 0.0118 0.0252 ± 0.0007 BRP-NAS 0.4129 ± 0.0116 0.4338 ± 0.0107 0.4549 ± 0.0093 0.7643 ± 0.0007 0.0672 ± 0.0079 0.0548 ± 0.0086 0.0424 ± 0.0051 0.0236 ± 0.0002 Graphormer 0.2229 ± 0.0687 0.2610 ± 0.0314 0.2991 ± 0.0202 0.5610 ± 0.0013 0.0589 ± 0.0081 0.0536 ± 0.0124 0.0477 ± 0.0054 0.0355 ± 0.0003 TNASP 0.5091 ± 0.0079 0.5749 ± 0.0125 0.6404 ± 0.0109 0.7663 ± 0.0035 0.0443 ± 0.0020 0.0393 ± 0.0010 0.0377 ± 0.0009 0.0250 ± 0.0003 NAR-Former 0.4228 ± 0.0048 0.4986 ± 0.0120 0.5699 ± 0.0097 0.8181 ± 0.0012 0.0538 ± 0.0055 0.0423 ± 0.0011 0.0406 ± 0.0017 0.0257 ± 0.0005 PINAT 0.3496 ± 0.0553 0.3994 ± 0.0050 0.4243 ± 0.0078 0.7162 ± 0.0153 0.1339 ± 0.0558 0.0516 ± 0.0101 0.0406 ± 0.0025 0.0271 ± 0.0012 GraphTrans 0.4300 ± 0.0229 0.4438 ± 0.0419 0.4666 ± 0.0067 0.7702 ± 0.0035 0.2735 ± 0.1625 0.1401 ± 0.0688 0.1337 ± 0.0583 0.0252 ± 0.0004 NAR-Former V2 0.5300 ± 0.0100 0.5500 ± 0.0040 0.6000 ± 0.0040 0.8150 ± 0.0025 0.0900 ± 0.0450 0.0850 ± 0.0300 0.0399 ± 0.0090 0.0220 ± 0.0007 N-Former 0.5428 ± 0.0107 0.5642 ± 0.0034 0.6057 ± 0.0037 0.8209 ± 0.0024 0.0895 ± 0.0472 0.0907 ± 0.0314 0.0368 ± 0.0016 0.0219 ± 0.0007 DTA-GT 0.6954 ± 0.0105 0.7278 ± 0.0047 0.7980 ± 0.0038 0.8740 ± 0.0001 0.0327 ± 0.0001 0.0312 ± 0.0006 0.0283 ± 0.0004 0.0202 ± 0.0017 Table 20: Complete latency-prediction results on NAS-Bench-101. Each cell places the mean above its standard deviation. Method Kendall’s τ (↑) by training budgetMAPE (↓) by training budget 0.02% (@100) 0.04% (@172) 0.1% (@424) 1% (@4236) 0.02% (@100) 0.04% (@172) 0.1% (@424) 1% (@4236) ReNAS 0.5803 ± 0.0108 0.7127 ± 0.0278 0.8028 ± 0.0048 0.9222 ± 0.0024 0.2232 ± 0.0051 0.1588 ± 0.0130 0.1080 ± 0.0026 0.0405 ± 0.0009 NAO 0.2569 ± 0.0372 0.2583 ± 0.0509 0.3049 ± 0.0752 0.3964 ± 0.0004 0.3057 ± 0.0016 0.3068 ± 0.0009 0.3062 ± 0.0007 0.2878 ± 0.0009 NNLP 0.8056 ± 0.0180 0.8379 ± 0.0034 0.8685 ± 0.0014 0.9190 ± 0.0024 0.1064 ± 0.0103 0.0858 ± 0.0019 0.0695 ± 0.0009 0.0417 ± 0.0013 BRP-NAS 0.7937 ± 0.0030 0.8487 ± 0.0027 0.8702 ± 0.0015 0.9270 ± 0.0006 0.1105 ± 0.0008 0.0811 ± 0.0021 0.0682 ± 0.0004 0.0372 ± 0.0003 Graphormer 0.3582 ± 0.0079 0.3711 ± 0.0094 0.4084 ± 0.0176 0.4467 ± 0.0007 0.2862 ± 0.0076 0.2715 ± 0.0015 0.2630 ± 0.0025 0.2617 ± 0.0013 TNASP 0.8024 ± 0.0082 0.8325 ± 0.0056 0.8734 ± 0.0034 0.9394 ± 0.0009 0.1110 ± 0.0046 0.0897 ± 0.0033 0.0647 ± 0.0015 0.0311 ± 0.0005 NAR-Former 0.8337 ± 0.0023 0.8670 ± 0.0031 0.8836 ± 0.0031 0.9434 ± 0.0007 0.0881 ± 0.0011 0.0686 ± 0.0011 0.0606 ± 0.0015 0.0287 ± 0.0003 PINAT 0.8317 ± 0.0119 0.8621 ± 0.0006 0.8817 ± 0.0018 0.9389 ± 0.0005 0.0860 ± 0.0050 0.0704 ± 0.0004 0.0599 ± 0.0011 0.0315 ± 0.0003 GraphTrans 0.8182 ± 0.0148 0.8619 ± 0.0026 0.8862 ± 0.0011 0.9365 ± 0.0007 0.0949 ± 0.0085 0.0710 ± 0.0008 0.0592 ± 0.0005 0.0329 ± 0.0004 NAR-Former V2 0.7741 ± 0.0115 0.8314 ± 0.0069 0.8752 ± 0.0039 0.9380 ± 0.0019 0.1238 ± 0.0069 0.0888 ± 0.0038 0.0652 ± 0.0024 0.0317 ± 0.0007 N-Former 0.8385 ± 0.0011 0.8694 ± 0.0022 0.9082 ± 0.0006 0.9462 ± 0.0006 0.0907 ± 0.0005 0.0662 ± 0.0011 0.0513 ± 0.0004 0.0286 ± 0.0003 DTA-GT 0.8646 ± 0.0036 0.8930 ± 0.0012 0.9094 ± 0.0010 0.9490 ± 0.0007 0.0758 ± 0.0009 0.0613 ± 0.0021 0.0503 ± 0.0022 0.0271 ± 0.0010 27 Table 21: Complete accuracy-prediction results on NAS-Bench-201. Each cell places the mean above its standard deviation. Method Kendall’s τ (↑) by training budgetMAPE (↓) by training budget 1% (@156) 3% (@469) 5% (@781) 10% (@1563) 1% (@156) 3% (@469) 5% (@781) 10% (@1563) ReNAS 0.1816 ± 0.1025 0.2236 ± 0.1178 0.4097 ± 0.0893 0.7130 ± 0.0338 1.9822 ± 1.7129 0.8425 ± 0.5541 0.3444 ± 0.0594 0.1676 ± 0.0185 NAO 0.6254 ± 0.0108 0.6436 ± 0.0170 0.6445 ± 0.0071 0.6580 ± 0.0100 0.0478 ± 0.0026 0.0454 ± 0.0048 0.0399 ± 0.0057 0.0283 ± 0.0016 NNLP 0.7109 ± 0.0230 0.7380 ± 0.0151 0.7824 ± 0.0332 0.8196 ± 0.0299 0.0410 ± 0.0272 0.0245 ± 0.0075 0.0172 ± 0.0070 0.0115 ± 0.0018 BRP-NAS 0.6953 ± 0.0112 0.7177 ± 0.0120 0.7575 ± 0.0113 0.7768 ± 0.0089 0.0629 ± 0.0249 0.0506 ± 0.0115 0.0211 ± 0.0025 0.0201 ± 0.0034 Graphormer 0.7052 ± 0.0039 0.7311 ± 0.0062 0.7461 ± 0.0128 0.7650 ± 0.0024 0.0270 ± 0.0044 0.0185 ± 0.0002 0.0171 ± 0.0006 0.0149 ± 0.0010 TNASP 0.7405 ± 0.0080 0.7770 ± 0.0073 0.8061 ± 0.0016 0.8314 ± 0.0013 0.0302 ± 0.0007 0.0158 ± 0.0019 0.0145 ± 0.0044 0.0110 ± 0.0006 NAR-Former 0.7540 ± 0.0107 0.7839 ± 0.0039 0.8188 ± 0.0036 0.8554 ± 0.0009 0.0256 ± 0.0017 0.0188 ± 0.0005 0.0141 ± 0.0006 0.0107 ± 0.0005 PINAT 0.7027 ± 0.0167 0.7084 ± 0.0006 0.7589 ± 0.0021 0.7920 ± 0.0034 0.0338 ± 0.0055 0.0273 ± 0.0048 0.0269 ± 0.0123 0.0198 ± 0.0110 GraphTrans 0.6957 ± 0.0056 0.6959 ± 0.0055 0.7781 ± 0.0023 0.8258 ± 0.0025 0.0975 ± 0.0510 0.0613 ± 0.0086 0.0493 ± 0.0224 0.0153 ± 0.0031 NAR-Former V2 0.7418 ± 0.0049 0.7432 ± 0.0086 0.8004 ± 0.0052 0.8391 ± 0.0055 0.1363 ± 0.0511 0.0441 ± 0.0102 0.0340 ± 0.0074 0.0256 ± 0.0062 N-Former 0.7400 ± 0.0050 0.7420 ± 0.0060 0.8050 ± 0.0040 0.8400 ± 0.0040 0.1350 ± 0.0500 0.0450 ± 0.0100 0.0330 ± 0.0070 0.0260 ± 0.0060 DTA-GT 0.8015 ± 0.0133 0.8925 ± 0.0028 0.9138 ± 0.0010 0.9304 ± 0.0011 0.0244 ± 0.0105 0.0125 ± 0.0007 0.0096 ± 0.0012 0.0084 ± 0.0022 Table 22: Complete latency-prediction results on NAS-Bench-201. Each cell places the mean above its standard deviation. Method Kendall’s τ (↑) by training budgetMAPE (↓) by training budget 1% (@156) 3% (@469) 5% (@781) 10% (@1563) 1% (@156) 3% (@469) 5% (@781) 10% (@1563) ReNAS 0.6166 ± 0.0032 0.6506 ± 0.0070 0.6725 ± 0.0005 0.6863 ± 0.0004 0.0844 ± 0.0009 0.0777 ± 0.0009 0.0707 ± 0.0004 0.0640 ± 0.0006 NAO 0.6963 ± 0.0004 0.6980 ± 0.0003 0.6984 ± 0.0002 0.7012 ± 0.0002 0.0628 ± 0.0000 0.0602 ± 0.0000 0.0600 ± 0.0001 0.0592 ± 0.0000 NNLP 0.6349 ± 0.0062 0.6437 ± 0.0016 0.6527 ± 0.0017 0.6567 ± 0.0019 0.0807 ± 0.0009 0.0726 ± 0.0007 0.0716 ± 0.0003 0.0702 ± 0.0002 BRP-NAS 0.6690 ± 0.0021 0.6861 ± 0.0005 0.6923 ± 0.0011 0.6986 ± 0.0005 0.0717 ± 0.0003 0.0640 ± 0.0001 0.0615 ± 0.0002 0.0594 ± 0.0001 Graphormer 0.6799 ± 0.0010 0.6972 ± 0.0010 0.7030 ± 0.0017 0.7030 ± 0.0006 0.0651 ± 0.0005 0.0600 ± 0.0001 0.0595 ± 0.0002 0.0589 ± 0.0001 TNASP 0.6646 ± 0.0069 0.6873 ± 0.0010 0.6926 ± 0.0008 0.6990 ± 0.0005 0.0713 ± 0.0010 0.0633 ± 0.0001 0.0613 ± 0.0001 0.0595 ± 0.0002 NAR-Former 0.5916 ± 0.0637 0.6014 ± 0.0393 0.6275 ± 0.0101 0.6522 ± 0.0027 0.1309 ± 0.0070 0.1299 ± 0.0096 0.1229 ± 0.0001 0.1226 ± 0.0001 PINAT 0.6859 ± 0.0107 0.6992 ± 0.0008 0.6950 ± 0.0019 0.6996 ± 0.0001 0.0645 ± 0.0010 0.0607 ± 0.0002 0.0602 ± 0.0003 0.0593 ± 0.0001 GraphTrans 0.6441 ± 0.0059 0.6871 ± 0.0013 0.6964 ± 0.0006 0.6993 ± 0.0008 0.0762 ± 0.0013 0.0643 ± 0.0006 0.0612 ± 0.0001 0.0600 ± 0.0003 NAR-Former V2 0.6237 ± 0.0201 0.6474 ± 0.0060 0.6541 ± 0.0032 0.6781 ± 0.0030 0.0786 ± 0.0060 0.0719 ± 0.0009 0.0699 ± 0.0002 0.0680 ± 0.0009 N-Former 0.6819 ± 0.0014 0.6891 ± 0.0012 0.6947 ± 0.0014 0.6981 ± 0.0017 0.0695 ± 0.0003 0.0631 ± 0.0003 0.0609 ± 0.0001 0.0594 ± 0.0000 DTA-GT 0.8375 ± 0.0048 0.8409 ± 0.0008 0.8435 ± 0.0025 0.8492 ± 0.0003 0.0305 ± 0.0007 0.0293 ± 0.0004 0.0280 ± 0.0010 0.0276 ± 0.0001 H.2 Ablation Analysis Table 23 reports the uncertainty estimates corresponding to the mean-only ablation results in Table 2. 28 Table 23: Complete ablation results under the lowest training budget of each task. Values are mean± standard deviation. Variant NAS-Bench-101NAS-Bench-201 AccuracyLatencyAccuracyLatency KT↑ MAPE↓ KT↑ MAPE↓ KT↑ MAPE↓ KT↑ MAPE↓ Directed DTA-GT 0.6954 ± 0.0105 0.0327 ± 0.0001 0.8646 ± 0.0036 0.0758 ± 0.0009 0.8015 ± 0.0133 0.0244 ± 0.0105 0.8375 ± 0.0048 0.0305 ± 0.0007 Undirected 0.5882 ± 0.0063 0.0408 ± 0.0016 0.8062 ± 0.0085 0.1074 ± 0.0014 0.7215 ± 0.0110 0.0617 ± 0.0253 0.8178 ± 0.0103 0.0349 ± 0.0031 w/o Directed Node Features 0.6522 ± 0.0236 0.0361 ± 0.0019 0.8482 ± 0.0056 0.0908 ± 0.0058 0.7198 ± 0.0205 0.0729 ± 0.0140 0.8202 ± 0.0050 0.0326 ± 0.0016 w/o Spec. Enc. 0.6894 ± 0.0016 0.0341 ± 0.0015 0.8615 ± 0.0008 0.0806 ± 0.0031 0.7452 ± 0.0089 0.0600 ± 0.0055 0.8192 ± 0.0003 0.0325 ± 0.0009 w/o Struct. Attn. 0.6552 ± 0.0144 0.0331 ± 0.0007 0.8360 ± 0.0202 0.1033 ± 0.0017 0.6123 ± 0.0339 0.1037 ± 0.0087 0.8227 ± 0.0033 0.0317 ± 0.0029 w/o MoE-FFN 0.6542 ± 0.0095 0.0331 ± 0.0007 0.8495 ± 0.0020 0.0860 ± 0.0022 0.7248 ± 0.0137 0.0418 ± 0.0062 0.8298 ± 0.0063 0.0313 ± 0.0024 CLS Readout 0.6701 ± 0.0101 0.0399 ± 0.0048 0.8420 ± 0.0047 0.1203 ± 0.0096 0.7535 ± 0.0141 0.0704 ± 0.0103 0.8209 ± 0.0030 0.0348 ± 0.0012 MSE Only 0.6720 ± 0.0109 0.0356 ± 0.0022 0.8610 ± 0.0056 0.0808 ± 0.0060 0.6937 ± 0.0065 0.0686 ± 0.0006 0.8201 ± 0.0021 0.0321 ± 0.0007 H.3 Magnetic Spectral Controls Table 24 provides the available repeated-run statistics corresponding to the mean-only controls in Table 4. The “Directed with Symmetric Lap.” row reports theq = 0results from the five-run phase-parameter sensitivity experiment. Table 24: Complete symmetric- and Magnetic-Laplacian control results under the lowest training budget of each task. Cells report mean± standard deviation. Variant NAS-Bench-101 @100NAS-Bench-201 @156 AccuracyLatencyAccuracyLatency KT↑ MAPE↓ KT↑ MAPE↓ KT↑ MAPE↓ KT↑ MAPE↓ No Directional Encoding 0.5882 ± 0.0063 0.0408 ± 0.0016 0.8062 ± 0.0085 0.1074 ± 0.0014 0.7215 ± 0.0110 0.0617 ± 0.0253 0.8178 ± 0.0103 0.0349 ± 0.0031 No Direction + Symmetric Lap. 0.5878 ± 0.0090 0.0386 ± 0.0018 0.8071 ± 0.0169 0.1066 ± 0.0082 0.7135 ± 0.0472 0.0485 ± 0.0123 0.8206 ± 0.0192 0.0330 ± 0.0055 Directed with Symmetric Lap. 0.6894 ± 0.0161 0.0341 ± 0.0008 0.8615 ± 0.0051 0.0806 ± 0.0014 0.7148 ± 0.0159 0.0792 ± 0.0101 0.8192 ± 0.0096 0.0325 ± 0.0042 Directed with Magnetic Lap. 0.6954 ± 0.0105 0.0327 ± 0.0001 0.8646 ± 0.0036 0.0758 ± 0.0009 0.8015 ± 0.0133 0.0244 ± 0.0105 0.8375 ± 0.0048 0.0305 ± 0.0007 29 NeurIPS Paper Checklist 1. Claims Question: Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? 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