arXiv subjects

Shuxian Gao

Publications and source records attributed to Shuxian Gao.

3 recordsLinked to original sources

arXiv2026

TorchCraft: Unified binder design by inverting an all-atom structure predictor

All-atom structure predictors model diverse molecular interactions, but using their learned structural priors for binder design remains challenging. Here we present TorchCraft, a unified binder-design framework that optimizes sequence logits through a frozen all-atom predictor. Implemented in TorchFold, TorchCraft combines confidence, contact, geometric, and sequence-prior objectives within a shared optimization procedure for minibinders, framework-conditioned VHHs, cyclic peptides, and ligand-binding proteins. Using pretrained AlphaFold 3 weights, TorchCraft generated representative minibinders and VHHs with experimentally measured binding across four targets in each format, without post hoc sequence redesign. Computational benchmarks further demonstrated the framework's applicability to cyclic peptides and ligand-conditioned pocket design. TorchCraft extends predictor inversion to multiple binder formats and molecular contexts, providing a common framework for reusing all-atom structural priors in design.

cs.AI↗

arXiv2026

Sharp propagation of chaos for mean-field backward stochastic differential equations

We study propagation of chaos for decoupled mean-field forward-backward stochastic differential equations whose generators depend on the empirical laws of the forward states, backward values and diagonal martingale integrands. Under monotonicity and Lipschitz assumptions, synchronous coupling gives quantitative estimates, including an $m$-particle squared Wasserstein bound of order $m/n$ for a system of $n$ particles interacting through finitely many statistics. In the Markovian setting, assuming a sufficiently regular classical decoupling field, we obtain two sharp refinements. For constant invertible diffusion and first-order cancellation of the field's measure dependence along the limiting law flow, the squared Wasserstein error is of order $m^2/n^2$, on continuous-path space for the values and on $L^2$ for the diagonal integrands. Without imposing this cancellation, smooth weak errors have order $n^{-1}$ for every fixed marginal, allowing variable and possibly degenerate diffusion. The weak estimate is uniform on a fixed time interval for the values and integrated in time for the integrands. The argument compares the interacting BSDE with an empirical evaluation of the decoupling field, retaining the full martingale representation and controlling feedback through both backward laws. It yields a joint-path Wasserstein transfer bound with intrinsic squared error $m/n^2$, off-diagonal integrand estimates, and a weak-error transfer principle with additive error $n^{-1}$. Explicit models with feedback through both backward laws verify the cancellation assumptions. Examples distinguish the intrinsic backward error from the forward law error and establish matching lower bounds for each backward component.

math.PR↗

arXiv2026

Backward doubly stochastic differential equations with or without reflection under weak conditions

In this paper, we study the solvability of backward doubly stochastic differential equations (BDSDEs, for short), both with and without reflection, under weak conditions on the generator. First, when the generator $f$ is of general growth in $y$ and linear growth in $z$, we establish the existence, uniqueness, comparison principle, and the existence of maximal solutions. Second, when $f$ is of linear growth in $y$ and quadratic growth in $z$ with bounded terminal value, we prove the existence, uniqueness, and comparison principle. Finally, when $f$ is of general growth in $y$ and quadratic growth in $z$ with bounded terminal value, we prove the existence of maximal solutions.

math.PR↗