ATLAS: Adaptive TDA-guided Landscape-Aware Transistor Sizing

1 Introduction

• Disconnected feasible regions can arise from operating-regime transitions, conflicting specification trade-offs, and nonconvex device physics, challenging sample-efficient search.Standard acquisition functions may concentrate queries on one predicted region, risking wasted budget if it is a false positive.Source: §1 · p. 2
• At each iteration, ATLAS builds a Mapper graph over the surrogate-predicted feasible region to estimate disconnected islands before any feasible design is observed.Source: §1 · p. 2
• Bridge and frontier candidates receive an exploration bonus because they may reveal new feasible regions.Interior candidates lie within a known region; the bonus directs search toward possible connections or unexplored areas.Source: §1 · p. 2
• When multiple regions are found, ATLAS discounts candidates in frequently queried regions to distribute sampling across the discovered islands.The discount is scaled by 1/√(1 + v_k), where v_k is the region’s visit count.Source: §1 · p. 2
• ATLAS generates local candidates around each region centroid, allocating more candidates to under-explored regions.Its exploration bonus, region-visit discount, and centroid-guided search are unified in an acquisition function that decays toward standard weighted EI as the budget progresses.Source: §1 · p. 2
• ATLAS finds successful designs with fewer simulations than other baselines, including RL methods.The introduction presents this as the framework’s experimental validation.Source: §1 · p. 2

Metaheuristic approaches and reinforcement learning

• Genetic algorithms and simulated annealing handle nonconvex, multimodal landscapes but typically need thousands of SPICE evaluations; RL methods also require thousands of training simulations.Source: §2 · pp. 2–3

Bayesian optimization for analog sizing

• Analog-sizing BO methods include WEIBO, GASPAD, MACE, ADO-LLM, DarBO, TuRBO, and SCBO, but do not account for feasible-region topology.Their acquisition functions treat the design space as structurally homogeneous, despite the possibility of disconnected feasible regions.Source: §2 · p. 3

Topological data analysis in optimization

• Prior TDA methods use topology as surrogate features, objectives, RL representations, or diversity criteria, while ATLAS uses the surrogate-predicted feasible set to guide query placement.The closest cited BO work, Shiraishi et al., uses persistence diagrams of structured inputs and does not address constrained or multi-output settings; ATLAS adapts Mapper for efficient region detection.Source: §2 · p. 3

3 Proposed Method: ATLAS

• Figure 2 sketches the framework, while Figure 3 details its pipeline.Source: §3 · p. 3

3.1 Problem Formulation

• A circuit design is represented by a vector of d parameters, including transistor dimensions and compensation capacitors.Source: §3.1 · p. 3
• Each of the S performance metrics has a specification constraint, such as a lower bound for gain or bandwidth or an upper bound for power or settling time.Source: §3.1 · p. 3
• Because evaluating the metrics requires expensive SPICE simulation, the objective is to find any design in the success set with as few evaluations as possible.Source: §3.1 · p. 3

• An independent Gaussian process for each specification provides predictive means and standard deviations.Source: §3.2 · p. 3
• The predicted feasibility score summarizes whether a candidate is expected to satisfy the specifications, with signs adjusted for upper-bound specifications.Source: §3.2 · p. 4
• Because feasibility is inferred from surrogate predictions rather than true evaluations, a predicted feasible point may be infeasible.Source: §3.2 · p. 4

3.3.1 Motivation.

• Applying TDA to the surrogate-predicted near-success set yields a dense point cloud for estimating topology, unlike sparse observed evaluations.This provides topological guidance from the first BO iteration.Source: §3.3.1 · p. 4

3.3.2 Feasible set.

• The feasible-set approximation selects the top κ% of candidates by predicted feasibility, avoiding a strict feasibility threshold that could leave too few early points.Candidates are normalized to [0, 1]^d before distance comparisons.Source: §3.3.2 · p. 4

3.3.3 Mapper graph construction.

• Mapper forms a graph by clustering points within overlapping filter intervals and linking clusters that share points; its connected components, not DBSCAN clusters, estimate feasible regions.A shared setting is used across circuits, seeds, and iterations without per-circuit tuning; Mapper is preferred to persistent homology for efficiency and interpretability.Source: §3.3.3 · p. 4
• Topological sensitivity marks candidates as bridges or frontiers when querying them may change the estimated region count, while interiors receive no topological score.The distance threshold is the Mapper graph’s median inter-node distance and is recomputed when the graph is refreshed.Source: §3.3.4 · p. 4

3.4.1 Feasibility-weighted acquisition (wEI).

• Feasibility-weighted expected improvement multiplies expected improvement by the joint probability of satisfying all specifications, with a feasibility-search fallback before a feasible incumbent exists.The acquisition is aimed at finding any design that meets the constraints rather than optimizing a separate figure of merit.Source: §3.4.1 · pp. 4–5

3.4.2 Region-aware EI balancing.

• When multiple regions are estimated, candidates in frequently visited regions are discounted, and visit counts reset when the topology changes.The exploration weight is reduced when the estimated region count remains stable and boosted while it fluctuates.Source: §3.4.2 · p. 5, §3.4.3 · p. 5

3.4.4 TAL acquisition function.

• The TAL acquisition combines region-discounted wEI with a topological-sensitivity bonus for bridge and frontier candidates.Setting the exploration weight to zero and the region discount to one recovers wEI; the exploration schedule shifts from topology exploration toward feasibility search as the budget progresses.Source: §3.4.4 · p. 5

• The candidate pool combines Latin hypercube samples spanning the design space with Gaussian perturbations around anchor points.Source: §3.5 · p. 5
• With multiple regions, local-search anchors include each region centroid and the best multi-specification point, with budget allocated by inverse square root of region visits.With no detected multi-region structure, anchors instead use top multi-specification satisfaction points.Source: §3.5 · p. 5
• The local perturbation radius decays over the optimization budget, starting broad and narrowing toward exploitation.The initial radius is a fraction of the parameter range, and α controls its decay rate.Source: §3.5 · p. 5

3.6 Complexity

• Mapper construction is dominated by DBSCAN clustering at O(|F̂_t|^2), taking milliseconds in practice.The estimate applies to periodic Mapper construction.Source: §3.6 · p. 5
• Region assignment and visit-count bookkeeping add O(K·n) work per iteration for K regions and n candidates.Source: §3.6 · p. 5

4.1 Experimental Setup

• The benchmarks are TSA, CMA, COMP, and LDO; LDO uses SKY130, while the other three use GF180MCU.Each method runs on 10 random specification targets with a 500-evaluation SPICE budget, shared initial samples, and early stopping at feasibility.Source: §4.1 · pp. 5–6, Figure 4 · p. 6

4.2 Main Results

• ATLAS achieves the highest or tied-highest success rate on all four circuits, including 100% on CMA, TSA, and COMP.On COMP, ATLAS reaches 100% SR and converges 2.2× faster than CMA-ES (74±27 vs. 165±62 FSD); on LDO, it is 2.3× faster than SCBO (70±2 vs. 164±86 FSD).Source: §4.2 · p. 6, Table 3 · p. 7

4.3 Topology-Aware Exploration Analysis

• For CMA, the estimated component count rises from 57 at iteration 50 to 147 at 160, then falls to 13 by iteration 314, before first success at 330.The count is the Mapper-estimated number of disconnected regions in the near-feasible set.Source: §4.3 · p. 7, Figure 6 · p. 7
• CMA peaks above 200 Mapper regions, compared with about 50 for TSA, and both counts decline as specification satisfaction improves.The paper relates CMA's more fragmented topology to its 10 parameters and six tightly coupled specifications.Source: §4.3 · p. 7, Figure 7 · p. 7
• At CMA iteration 270, the five largest regions show distinct parameter profiles, including higher PMOS widths in C3 and lower overall values in C2.The next query is placed near under-explored C3; bridge and frontier candidates receive the exploration bonus.Source: Figure 8 · p. 7, §4.3 · p. 8
• On CMA, ATLAS reaches all six specifications by iteration 330, whereas WEIBO remains at one or two and never satisfies Gain.The comparison describes ATLAS exploring multiple specification-space clusters while WEIBO narrows to a band.Source: Figure 9 · p. 7, §4.3 · p. 8

4.4 Computational Overhead

• Mapper construction, classification, and bookkeeping add 1–17% total controlled overhead, with the TDA step itself below 2%.The TDA step is refreshed every three iterations and cached; reported simulation time is open-source ngspice runtime, not sign-off simulation.Source: §4.4 · p. 8, Table 4 · p. 8

4.5 Ablation Analysis

• Removing centroid guidance, λ decay, Δβ0, or region discount lowers TSA SR from 10/10 to 6/10, 9/10, 7/10, and 9/10; all 12 CMA settings retain 10/10.The reported FSD averages only successful runs, so censored failures make some variants appear faster; the sensitivity configurations use an a priori default eps of 0.30.Source: §4.5 · p. 8, Table 5 · p. 8, Table 6 · p. 8

5 Conclusion

• 100% SR on all four benchmarks across two PDKs; on CMA, only CMA-ES finds another feasible design, at 10% SR.Where baselines succeed, ATLAS converges 2.2–2.3× faster.Source: §5 · p. 8
• Mapper detects disconnected feasible regions from the first iteration, while TAL guides exploration with region-aware EI balancing and centroid-guided candidate generation.The conclusion describes ATLAS as a strict generalization of WEIBO.Source: §5 · p. 8
• Mapper/TDA takes less than 2% of per-iteration time.Source: §5 · p. 8
• The landscape map could support evolutionary or local-search restarts and initialization, or serve as an RL state feature, but these extensions remain untested.Future work will incorporate process-corner topology for PVT-aware sizing.Source: §5 · p. 8