#01Nov 12, 2026
cs.LG
Maximizing Capacity Utilization of LoRA Adapters for Mitigating the Learning-Forgetting Trade-off
Tomohiro Sawada, Kartik Goyal
Low-Rank Adaptation (LoRA) often underperforms full fine-tuning, especially in heterogeneous and continual-learning settings in which substantial forgetting occurs. In general, it suffers from an undesirable learning-forgetting trade-off across diverse fine-tuning settings. We identify a potential contributor: LoRA adapters, especially high-rank ones, frequently fail to realize the available capacity afforded by the configured rank. Specifically, we find that standard LoRA updates have effective rank far below their configured rank, limiting how broadly the update energy is distributed. Therefore, we propose training mechanisms that optimize the original objective while maximizing adapter effective rank. Our main method adds a simple, stable, differentiable, and SVD-free Rényi-2 effective-rank regularizer to the language-modeling loss. We also connect capacity maximization to norm-bounded updates. In mixed-domain rank sweeps on three models evaluated with multiple random seeds, a penalty weight of $λ=0.01$ lowers mean Wiki perplexity at every tested rank of at least $16$ relative to unpenalized LoRA. Mean training perplexity improves or increases by at most $0.02$ in all but one model-rank comparison. Single-task and scheduling experiments further show that the balance between learning and retention depends on the configuration. We also observe that several LoRA variants in the literature also suffer from the identified capacity issue, and our approach provides a complementary axis of improvement to LoRA-based parameter-efficient fine-tuning. These results suggest that effective rank is not only a post-hoc diagnostic of adapter quality, but a trainable objective for improving the learning-forgetting frontier. Our code is available at https://github.com/tomohiro-sawada/lora-capacity-utilization
#02Nov 12, 2026
math.ST
Linear Regression with Self-Selection Bias in Polynomial Time
Felix Zhou
We revisit the problem of estimating $k$ linear regressors with self-selection bias in $n$ dimensions up to error $\varepsilon$ with the maximum self-selection criterion, as introduced by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [CDIZ23, STOC]. Our main result is a $\mathrm{poly}(n,k,1/\varepsilon)$ time algorithm for the unknown-index variant of this problem, thereby improving upon the running times of the best known algorithms due to Gaitonde and Mossel [GM24] and Kalavasis, Mehrotra, and Zhou [KMZ26, COLT] with exponential dependence on $k$. Our algorithm succeeds in the presence of correlated noise between regressors, which captures the related setting of max-affine regression. Consequently, we also give the first polynomial-time algorithm for this problem, improving on the prior works of Ghosh, Pananjady, Guntuboyina, and Ramchandran [GPGR22, IEEE Transactions on Information Theory] and Gaitonde and Mossel [GM24] with exponential dependence on $k$. Prior works exhaustively search over a $k$-dimensional subspace spanned by the regressors, using conditional moments of the response to test candidates. In contrast, our algorithm is driven by an improved understanding of the moments of the covariates. We show that, restricting to observations with large response values, the degree-$(\log n)$ Hermite moment of the covariates approximately decomposes as a sum of tensor powers of the regressors. The first step of our algorithm can be viewed as a tensor decomposition algorithm for these implicitly represented high-order tensors, which outputs unit vectors parallel to the regressors. A secondary step based on a simple variant of ordinary least squares extracts estimates for the regressors given these unit vectors. We believe our analytic insight and algorithmic components may have applications to designing efficient algorithms for other latent-variable problems.
#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.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.
#05Nov 12, 2026
cs.CL
Parsed, Plausible, Wrong: Output Format Controls Silent Errors in Small-Model Semantic Parsing
Umar Ahmed, Maxim Dunaev, Mohammad Nour Al Awad and 2 more
A small fine-tuned parser that emits a well-formed but wrong tree fails silently: nothing downstream can tell. We ask whether the output format, a free design choice, controls how often this happens. On the PIZZA ordering benchmark we fine-tune two sub-billion models (Qwen3.5-0.8B and LFM2.5-350M) with LoRA on six lossless encodings of the same target tree, from 44.3 down to 10.9 tokens per order, including two matched-length pairs that vary surface form at fixed length. Across 300 runs (5 training pool sizes, 5 seeds) with a hierarchical bootstrap and Holm correction fixed before the results were read, shortening alone never helps, but writing the target in ordinary words does. The word encoding is the most accurate format on both models (87.5% vs. 85.8% exact match for the native s-expression on Qwen) while emitting 4.1x fewer tokens, and it cuts the silent error rate by 2.3x on Qwen and 1.8x on LFM2, separating at every pool size. Error analysis locates much of the gain in negation. All runs also learn to refuse off-menu input (held out: 95.9-99.0% handled) and to apply in-utterance self-corrections. Strict refusal has a measured price: 2.1-10.1% of real, mostly polite, orders are refused.