#01Nov 12, 2026
cs.IR
Sheaf-Inspired Structured Scoring Extensions of LightGCN for Collaborative Filtering
Ksenia Belkovskaya, Timur Lidzhiev, Maria Stebliy and 1 more
Graph-based collaborative filtering learns user and item representations by propagating embeddings over a user--item interaction graph. We investigate a modular, sheaf-inspired scoring extension placed on top of a three-layer LightGCN backbone. The motivation comes from cellular sheaves, where local vector spaces are related by linear restriction maps; here, this idea motivates structured, pair-dependent transformations of user and item embeddings rather than a change to graph propagation. We compare the identity inner-product scorer, diagonal, rank-one low-rank, and full matrix residual scorers, and a parameter-matched residual MLP baseline (\texttt{mlp\_full}) on Amazon-Book, Gowalla, MovieLens-1M, and Yelp2018. We report ranking quality and catalog coverage at cutoffs 10 and 20. The selected structured variants show modest, dataset-dependent changes in ranking quality and sometimes substantial changes in coverage. Our method is inspired by sheaf geometry but does not construct a cellular sheaf or implement sheaf-Laplacian diffusion; the experiments therefore do not establish a causal benefit from sheaf geometry itself.
#02Nov 12, 2026
cs.DS
Sketching Language Models for Context Attribution
Christopher Liaw, Aranyak Mehta, Grigoris Velegkas and 1 more
Context attribution asks how removing parts of a prompt changes a language model's output. We study leave-one-out (LOO) attribution for a prompt of $n$ tokens and a fixed measurement function. Computing all LOO values directly requires $n$ model evaluations. Under a stability assumption, our algorithm estimates all LOO values to error proportional to $\varepsilon$ with constant probability using $O(\sqrt{\log(1/\varepsilon)}/\varepsilon)$ evaluation calls. To complement our upper bound, we prove a matching $Ω(\sqrt{\log(1/\varepsilon)}/\varepsilon)$ lower bound on the number of evaluation calls in an oracle model. Empirically, we verify coefficient decay consistent with stability and evaluate the performance of our sketching algorithm on a small language-model retrieval task. Technically, our result is based on a sketching algorithm for arithmetic circuits whose Taylor coefficients satisfy the stability condition recently introduced by Gunn [Gun26]. A direct adaptation of their forward differentiation sketches would require $\widetilde{O}(\log(n)/\varepsilon^2)$ evaluation calls. Our key observation is that we can apply forward differentiation to the backpropagation circuit, with only constant overhead over a forward sketch of the same Taylor degree. This reduces the variance of the sketches and is key to our improved evaluation bound. Our lower bound builds on the techniques of Amsel, Chen, Duman Keles, Halikias, Musco, and Musco [ACDH+26, SIAM Journal on Matrix Analysis and Applications] for lower bounding the number of matrix-vector queries to estimate the diagonal elements of random matrices.
#03Nov 12, 2026
cs.LG
AeroZoo: A Benchmark of Well-Posed Flow Problems for Foundation Models of Aerodynamics
Peter Sharpe, Carmelo Gonzales, Corey Adams and 2 more
Neural surrogates for computational fluid dynamics (CFD) are trained and ranked on datasets that each vary one design family in one flow domain. Such datasets cannot test the least that an aerodynamic foundation model must do: predict CFD-quality incompressible flow in seconds for new shapes in new enclosures. On DrivAerML, larger models and longer training barely lower Transolver's error; doubling the training cases cuts it by about 12% up to 400 cases, exhausting the dataset. We introduce AeroZoo, a benchmark and training corpus of 3,815 time-mean solutions to the unsteady Reynolds-averaged Navier--Stokes (RANS) equations with a transition model, across seven geometry families, eight enclosure configurations and Reynolds numbers from $10^3$ to $10^8$. Each sample poses a well-posed PDE problem in the form a solver receives it: the boundary meshes grouped by condition type, the prescribed values and the fluid properties. The 2,816 samples with a stable time mean form the canonical benchmark: two tasks, engineering metrics and 22 frozen splits, disjoint in geometry, that hold out geometry families, enclosures, boundary-condition layouts and Reynolds ranges. On the random split, boundary-condition tokens cut GeoTransolver's median velocity error from 76.9% to 8.4% of the inlet speed in single-seed runs (uniform inlet flow: 11.0%). ISLA, a transformer for boundary-driven PDEs, reaches 5.3% over four seeds, about 4 times the change from a finer mesh. On the same test samples, a held-out geometry family barely changes ISLA's error relative to uniform flow, and a held-out enclosure or boundary-condition layout raises it 2.4 to 9.2 times. The data and the scoring code will be released.
#04Nov 12, 2026
cs.LG
Symmetry in Time: A Representation Theory of Linear Recurrent Memory
Anif N. Shikder, Ramit Dey, Jan Minac and 1 more
State space models (SSMs) are an emerging alternative to Transformers. SSMs offer linear-time inference and parallel training, but most implementations make the parallel scan efficient by making the recurrence diagonal: each channel of the hidden state is multiplied by an input-dependent real or complex number. These numbers commute, so the state records which inputs occurred but not their order. We formalize this with representation theory, which explains and fixes the state-tracking failures previously reported for SSMs. The state update defines a linear representation of the monoid of input sequences, and we show that an SSM tracks a group at every sequence length exactly when that group is a quotient of the group generated by its transition matrices. Two consequences follow. Diagonal real- and complex-valued SSMs can track only commutative groups, while the transition matrices of any SSM that can track a group must split into independent blocks over the real, complex, and quaternion numbers. We then introduce HyperSSM, which adds quaternion channels while keeping linear-time inference and parallel training. Trained only on final answers, HyperSSM solves the group tasks of recent state-tracking benchmarks exactly with at most five state numbers. This includes $S_5$ with 32 generators, where previous SSMs are at chance, and HyperSSM generalizes to sequences 25 times longer than those seen in training. Because the theory says what the transitions must encode, the learned weights of the linear recurrence can be interpreted directly. We demonstrate this by recovering the calibration of a real gyroscope, the rotations of imperfect qubit gates and the geometry of protein backbones.
#05Nov 12, 2026
cs.LG
Two mathematical models of knowledge distillation
Audrey Xie, Ludwig Schmidt, John Duchi
Many hypotheses compete to explain the successes of knowledge distillation. To help address this, we propose and analyze a mathematical model of distillation, which suggests that distillation's performance comes not from obtaining better models but from easier to optimize landscapes. For generalized linear models trained with stochastic gradient descent, we prove that distillation fits performant student models asymptotically more quickly than non-distilled models. In rank-1 matrix approximation, we characterize conditions on the target matrix under which gradient descent with distillation converges strictly faster than training on the supervised objective. The theory helps delineate the ways distillation provides benefits (i.e., in optimization speed, not in generalization), and experiments on real datasets corroborate the theoretical predictions.