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Inference-Time Steering Across Scaffolds and Epitopes for Sample-Efficient De Novo Nanobody Design
Mason Minot, Simon Friedensohn, Cédric R. Weber
TL;DR
Nanobody design depends on scaffold and epitope choices whose viability is unknown, while existing steering optimizes within a fixed configuration. This paper combines inference-time steering with joint SMC or decoupled BaSE allocation, reporting higher designable-candidate throughput without sacrificing diversity across runs.
Problem
Nanobody scaffold and epitope choices have variable, unknown yield, while steering methods optimize within fixed configurations, making condition selection a compute-allocation challenge.
Source: §1 · p. 1Method
The paper pairs in-loop inference-time steering with either a joint Global SMC allocator across configurations or decoupled Batched Successive Elimination.
Source: §2.1 · p. 2, §2.3 · p. 3Results
Adaptive global SMC achieved nearly 5× more designable backbones per GPU-hour, while decoupled SH yielded a 2.4–3.1× throughput improvement without sacrificing global conformational diversity across independent runs.
Source: §3.2 · pp. 4–5Takeaways & Limitations
Dynamic allocation makes scaffold and epitope constraints active optimization variables while increasing in-silico nanobody yield without sacrificing structural diversity.
Source: §4 · p. 5SMC allocated 53% of particles to the 8z8v-derived framework yet yielded zero terminal AF2-M passes, and both evaluation metrics remain in-silico surrogates.
Source: §3.3 · p. 5
Abstract
from arXiv · showhide
Generative molecular design typically relies on over-generation and post-hoc filtering. Inference-time steering methods like Feynman-Kac (FK) steering improve efficiency by biasing trajectories toward high-reward candidates, yet they optimize within a single fixed configuration. In de novo nanobody design, upfront commitment to conditioning choices like scaffold identity or target epitope creates a bottleneck. Since yield varies across these conditions, steering unpromising setups wastes compute. We recast generative condition selection as an inference-time resource-allocation problem. We propose two dynamic budget allocators: a joint Global Sequential Monte Carlo (SMC) formulation that steers and allocates compute across configurations concurrently, and a decoupled approach adapting Batched Successive Elimination (BaSE). Empirically, these dynamic allocators increase the yield of designable candidates per GPU-hour nearly 5$\times$ without sacrificing diversity across distinct therapeutic targets and generative configurations.
1 Introduction
Generative design often spends compute on post-hoc filtering, while inference-time steering has typically optimized within a single configuration. For nanobodies, scaffold and conditioning choices vary in viability, making condition selection a budget-allocation problem.
1 Introduction
- Over-generation followed by computationally expensive post-hoc scoring and filtering can leave campaigns evaluating many true negatives.The passages identify this as a computational bottleneck.Source: §1 · p. 1
- Feynman-Kac steering integrates scoring into sampling, but prior protein-design applications optimize within a single generative configuration.The passages also note that scaffold-driven formats remain largely unexplored.Source: §1 · p. 1
- Nanobody framework identity affects paratope geometry, stability, immunogenicity, and generative yield, so scaffold identity must be treated as a variable.Nanobody methods design antigen-binding CDRs onto a fixed, user-specified framework.Source: §1 · p. 1
- Because scaffold, epitope, and hotspot viability is unknown a priori, committing to an unproductive condition wastes steering budget and leaves viable conditions under-sampled.The passages frame this as a budget-allocation problem.Source: §1 · p. 1
2 Methods
The methods define fixed-scaffold generation and FK steering using in-loop ipTM, then allocate compute across configurations with either joint SMC or decoupled successive elimination.
2.1 Fixed-Scaffold Nanobody Generation
- BoltzGen samples 3D CDR coordinates conditioned on a fixed scaffold, and the target trajectory distribution reweights unsteered trajectories by path reward.Post-hoc designability is assessed by sampling eight ProteinMPNN sequences per backbone, refolding with AF2-M, and applying AlphaProteo criteria; the in-loop oracle is orthogonal to validation.Source: §2.1 · p. 2
2.2 Feynman-Kac Steering via In-Loop ipTM
- FK steering interleaves denoising with quality-guided cloning and culling, scoring predicted terminal backbones through BoltzIF sequences, ESMFold2 refolding, and ipTM.The methods consider fixed-cadence and adaptive resampling, with the adaptive trigger set at ESS ≤ 0.5N.Source: §2.2 · pp. 2–3
2.3 Condition Allocation Algorithms
- Global SMC uses one joint particle population and cumulative reward weights, allowing resampling to extinguish weak particles and replicate successful ones across conditions.It evaluates raw in-loop ipTM and does not assign an explicit budget to each condition.Source: §2.3 · p. 3
- Decoupled BaSE steers configurations independently, evenly budgets surviving arms each round, ranks them by 90th-percentile terminal AF2-M ipTM, and eliminates half per round.The study also evaluates unsteered SH and fixed-cadence SMC ablations.Source: §2.3 · p. 3
3 Results and Discussion
Steering and dynamic condition allocation improve designable-backbone yield, while the results also expose trade-offs between structural diversity, throughput, and reward reliability. The paper compares fixed-condition steering, allocation across configurations, and oracle divergence.
3.1 Steering Increases Yield Without Sacrificing Structural Diversity
- Fixed-scaffold steering shifted candidate distributions toward higher ipTM and improved designable-backbone yield per GPU-hour across PD-L1, BHRF1, and IL-7Rα.Within-trajectory CDR-H3 diversity fell, but independent seeds explored distinct high-reward conformational basins, preserving global diversity.Source: §3.1 · p. 4
- Steering’s diversity loss was localized to individual runs, while independent seeds recovered structural variation across high-reward conformational basins.This makes distributing compute across multiple starting conditions important for sampling viable paratope space.Source: §3.1 · p. 4
3.2 Dynamic Allocation Maximizes Yield Across Configurations
- Adaptive global SMC increased designable backbones per GPU-hour from 1.41 to 6.82 for BHRF1 and from 2.21 to 10.81 for PD-L1; decoupled SH yielded a 2.4–3.1× throughput improvement.The evaluations covered four BHRF1 epitope configurations and six PD-L1 scaffolds across three replicates.Source: §3.2 · pp. 4–5, Figure 3 · p. 4, Figure 4 · p. 5
- Unsteered SH improved yield over vanilla, but yielded fewer passing designs than steered SH; adaptive SMC achieved the highest throughput among the tested policies.Fixed-cadence SMC also outperformed vanilla and steered-unallocated baselines.Source: §3.2 · p. 5
3.3 Oracle Divergence and the Hierarchy of Reward Hacking
- SMC assigned 53% of particles to the 8z8v-derived framework based on high ESMFold2 ipTM, yet produced zero terminal AF2-M passes because of pose divergence.SH mitigates this vulnerability using orthogonal terminal validation scores for rank cuts; both metrics remain in-silico surrogates that do not guarantee in-vitro affinity or stability.Source: §3.3 · p. 5
4 Conclusion
Dynamic resource allocation with inference-time steering turns scaffold and epitope constraints into active optimization variables, increasing in-silico nanobody yield without sacrificing structural diversity. Global SMC maximizes throughput, while decoupled multi-armed bandits are more robust to in-loop reward hacking; wet-lab-correlated oracles remain a future direction.
4 Conclusion
- Dynamic allocation paired with inference-time steering increases in-silico nanobody yield without sacrificing structural diversity, with global SMC favoring throughput and decoupled bandits offering robustness to in-loop reward hacking.Because intermediate confidence metrics are surrogates, adapting allocators to wet-lab-correlated oracles is a primary future direction.Source: §4 · p. 5
A.1 Theoretical Considerations and Steering Implementation
The steering setup defines a reward-tilted distribution over the deployed sampler and schedules guidance in network time. Its immediate-potential choice yields higher empirical yield but does not retain standard convergence guarantees.
A.1 Theoretical Considerations and Steering Implementation
- Feynman-Kac steering tilts the deployed sampler’s trajectory distribution using accumulated per-event potentials, rather than applying the potential only at terminal generation.The deployed BoltzGen sampler is sharpened and under-noised relative to the exact reverse SDE assumed by standard guarantees, so a given temperature acts more aggressively.Source: §A.1 · p. 8
- Guidance events are scheduled uniformly in network time rather than raw diffusion steps, making the schedule invariant to the overall step budget.Because network time nonlinearly stretches the noise schedule, guidance events cluster toward lower-noise trajectory stages.Source: §A.1 · p. 8
- Steering used 16 particles for standard unallocated and SH runs, and K × 16 particles for joint allocation across K candidate conditions.Temperatures were 0.1–0.25, steering began at 60% of the diffusion trajectory, and 6–12 guidance events were used per trajectory.Source: §A.1 · p. 8
- Immediate potentials were selected for higher empirical yield, but do not form a standard telescoping Feynman-Kac path functional, so standard convergence guarantees do not apply.Independent steering and SH use memoryless weights; Global SMC recursively accumulates the increments into an additive path functional.Source: §A.1 · p. 8
A.2 Global SMC Scaffold Allocation
Global SMC places the scaffold label within the particle state and applies SMC over the resulting joint scaffold–trajectory space. Global weight normalization then allocates particle counts across candidate scaffolds dynamically.
A.2 Global SMC Scaffold Allocation
- The scaffold label k is treated as part of particle state z = (k, x_t), allowing SMC to operate over the augmented scaffold–trajectory space.Each scaffold retains its frozen generative law, and the joint target is reward-tilted.Source: §A.2 · p. 8
- Global SMC uses one global weight denominator coupling particles across all candidate conditions, with the recursion accumulating immediate rewards into an additive path functional.This differs from independent steering, which does not couple weights across configurations.Source: §A.2 · p. 8
- Global normalization makes each scaffold’s particle count emerge from its component mass, with low-reward scaffolds able to reach zero particles and productive ones duplicated.The resulting count is approximately Nρ_k; no explicit computational budget is assigned.Source: §A.2 · p. 8
- At shared reward events, the allocator advances active particles, computes weights, globally resamples N ancestors, then regroups them by scaffold label.The returned population includes emergent scaffold counts and terminal weights.Source: §A.2 · p. 9
A.3 Successive Halving (SH) Schedule
The decoupled allocator adapts Batched Successive Elimination to distribute designs across configurations over successive rounds. It uses rank-based elimination, upper-quantile scores, and a uniform round budget.
A.3 Successive Halving (SH) Schedule
- The decoupled approach adapts Batched Successive Elimination, evaluating available configurations in rounds by steering small particle batches.It uses independent, memoryless FK sampling for fresh designs in each round.Source: §A.3 · p. 10
- Setting the elimination confidence width to zero prunes the bottom 50% of configurations by rank after each round.This replaces confidence-bound elimination with an unconditional rank-based cut.Source: §A.3 · p. 10
- Configurations are ranked by the 90th percentile of terminal validation scores, while the computational budget is distributed uniformly across rounds.The uniform schedule was chosen for greater robustness to varying quality and composition of the initial panel.Source: §A.3 · p. 10
A.4 Post-Hoc Designability Validation
Post-hoc designability validation combines sequence redesign, complex refolding, and structural metrics. The section also specifies plots and benchmarks for sequence-budget effects, compute costs, condition allocation, and structural diversity.
A.4 Post-Hoc Designability Validation
- The validation pipeline adapts Proteina Complexa and AlphaProteo criteria, redesigning CDR residues while keeping the scaffold sequence fixed before AF2-M complex folding.Eight ProteinMPNN sequences are sampled per backbone, and target templating plus an initial guess are enabled for folding.Source: §A.4 · p. 11
- Designability uses inter-chain ipAE, complex pLDDT, and binder scRMSD; a backbone passes if any of its eight sequences meets the AlphaProteo thresholds, including binder scRMSD < 1.5 Å.The passage specifies the scRMSD threshold but does not provide the other threshold values.Source: §A.4 · p. 11
- Figure 5 separates total GPU-hours into direct trajectory generation and in-loop or terminal refolding, inverse folding, and post-hoc filtering costs.Its breakdown spans generation methods and three targets at 1,152 backbones per target.Source: Figure 5 · p. 12
- Figure 6 plots expected designability pass rate against the number of MPNN sequences folded per backbone, from m = 1 to 8.The pass rate is the fraction of backbones yielding at least one successful design out of m folded sequences.Source: Figure 6 · p. 13
- Figure 7 compares BHRF1 epitope-conditioning approaches across ipTM, budget allocation, and designable backbone yield, with 1,728 trajectories per method.The benchmark covers three targeted epitopes and an unconditional baseline.Source: Figure 7 · p. 13
- Figures 8 and 10 show that steering restricts within-run structural diversity while exploring diverse productive basins across independent runs.They measure Cα RMSD of passing designs for BHRF1 epitope allocation and the 7eow PD-L1 scaffold allocation.Source: Figure 8 · p. 14, Figure 10 · p. 15
- Figure 9 compares PD-L1 scaffold allocation across ipTM, budget allocation, and designable backbone yield for six scaffolds, with 2,880 designs per method.The scaffold set includes frameworks from complex structures and clinical-stage antibodies.Source: Figure 9 · p. 14