01 · Exact surrogate adjoint
One reference tile
For the reported two-step refinement path, the four staircase plan factors can be reconstructed from one resident reference tile and explicit row and column modifiers.
Optimal transport / efficient attention / ML systems
Research where mathematical structure meets hardware constraints.
I work on learning systems that have to survive both theoretical scrutiny and real machines: differentiable transport, long-context attention, sparse derivatives, and implementations designed around the memory hierarchy.
Featured paper · Accepted at NeurIPS 2026 · arXiv:2605.08123
Block-Wise Differentiable Sinkhorn Attention
Tail-refinement gradients with a gap-aware dustbin bridge: a memory-efficient route to differentiating balanced entropic optimal-transport attention at long context.
Block-wise transport attention
The active tile moves through banded support while the rest of the plan stays out of memory.
02 · Hardware-aware schedule
Stream the active support
Fixed-width block-wise execution yields O((T+R)LW) work, O(Ld) input storage, and O(L) additional HBM for fixed head dimension and band width.
03 · Structured gaps
Dustbin augmentation bridge
The implemented gap-aware path is formalized as the same balanced surrogate on an augmented support, allowing the adjoint schedule to lift without claiming a general unbalanced model.
Transport topology · Preprint · September 2026
Support Topology and Gradient Mixing in Sinkhorn Layers
How does a sparse transport graph shape the gradients that pass through it? A fixed-support calculus connects Sinkhorn differentiation to two-step walks, overlap, and contraction.
From support to gradient mixing
Local overlap can spread a signal without guaranteeing contraction in one cycle.
Homogeneous cotangent
Watch a difference spread.
Start with +1 and −1 on opposite columns. Each cycle applies Mᵀ to that zero-sum signal.
Cycle 0
Remaining TV 100%
One-step coefficient τ(M) = 1.00
01 · Derivative structure
A walk behind the gradient
Each normalization cycle induces a stochastic operator on column-potential perturbations modulo constants. Its transpose carries zero-mass reverse-mode signals.
02 · Uniform guarantees
Every feasible face matters
At balanced plans, score-uniform one-step contraction requires pairwise two-hop column overlap on every feasible face of the transportation polytope.
03 · Sparse schedules
Mixing across several steps
Ordered support schedules can provide contraction over a window even when an individual layer has no global one-step guarantee.
Publications
Research record
Work on efficient transport attention and the support geometry that governs its gradients.
Earlier research threads
Problems that shaped the current work
Intrinsic quantification of domain shift
Reactive exploration methods for measuring domain-shift magnitude across controlled reinforcement-learning environments.
Multi-omics and biological representation learning
Research across biomarker discovery, protein representations, regulatory networks, and learning from heterogeneous biological signals.
Attention across volumetric MRI
Patch tokenization, self-attention, and inter-slice aggregation for volume-aware diagnostic classification.