A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Connectivity proven in large rank Gromov boundary of free factor complex.
Develops a statistical framework to measure uncertainty in model rankings based on human preferences.
We prove an obstruction at the level of rational cohomology in small degrees to the existence of positively curved metrics with large symmetry rank. The symmetry rank bound is logarithmic in the dimension of the manifold. As an application, we provide evidence for a generalized conjecture of Hopf that says that no symm…
Recall that a group is called large if it has a finite index subgroup which surjects onto a non-abelian free group. By work of Agol and Cooper-Long-Reid, most 3-manifold groups are large; in particular, the fundamental groups of hyperbolic 3-manifolds are large. In previous work, the first author gave examples of close…
The paper analyzes deflation for estimating a low-rank spike in large tensors with noise.
New framework assesses LLMs' expertise using nonparametric ranking and confidence diagrams.
Learning to rank is a supervised learning problem where the output space is the space of rankings but the supervision space is the space of relevance scores. We make theoretical contributions to the learning to rank problem both in the online and batch settings. First, we propose a perceptron-like algorithm for learnin…
We consider the problem of personalization of online services from the viewpoint of ad targeting, where we seek to find the best ad categories to be shown to each user, resulting in improved user experience and increased advertisers' revenue. We propose to address this problem as a task of ranking the ad categories dep…
PLUMAGE improves large model training efficiency and stability.
Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still a challenge for current methods to handle datasets with both high dimensions and…
We consider training probabilistic classifiers in the case of a large number of classes. The number of classes is assumed too large to perform exact normalisation over all classes. To account for this we consider a simple approach that directly approximates the likelihood. We show that this simple approach works well o…
The paper establishes theoretical foundations for low-rank knowledge distillation in LLMs.
We address the problem of minimizing a convex function over the space of large matrices with low rank. While this optimization problem is hard in general, we propose an efficient greedy algorithm and derive its formal approximation guarantees. Each iteration of the algorithm involves (approximately) finding the left an…
We propose RoBiRank, a ranking algorithm that is motivated by observing a close connection between evaluation metrics for learning to rank and loss functions for robust classification. The algorithm shows a very competitive performance on standard benchmark datasets against other representative algorithms in the litera…
Research characterizes learnability of multilabel ranking problems.
The paper explores how the depth of neural networks affects their ability to represent data accurately.
New model predicts stock performance in large equity markets.
In this paper we construct families of homology spheres which bound 4-manifolds with intersection forms isomorphic to . We show that these families have arbitrary large correction terms. This result says that among homology spheres, the difference of the maximal rank of minimal sub-lattice of definite filling and…
PSI-LinUCB improves scalability for large recommender systems.
In this article we define and study a notion of asymptotic rank for metric spaces and show in our main theorem that for a large class of spaces, the asymptotic rank is characterized by the growth of the higher filling functions. For a proper, cocompact, simply-connected geodesic metric space of non-curvature in the sen…
Ranky solves SVD for large sparse matrices in distributed systems.
Study manifolds with positive intermediate Ricci curvature and large symmetry rank.
Paper proposes a new method to separate low rank and sparse matrices without bias.
We construct a counterexample to the Rank versus Genus Conjecture, i.e. a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. Moreover, we show that the discrepancy between rank and Heegaard genus can be arbitrarily large for hyperbolic 3-manifolds. We also constr…
Physics-inspired methods optimize SVD compression of LLMs.
GeLoRA optimizes LoRA fine-tuning by dynamically adjusting ranks based on intrinsic dimensionality.
A new method for efficiently updating large-scale matrices in real-time.
Research reveals deep networks often learn low-rank structures, leading to more efficient training and fine-tuning.
We construct a sequence of primitive-stable representations of free groups into PSL(2,C) whose ranks go to infinity, but whose images are discrete with quotient manifolds that converge geometrically to a knot complement. In particular this implies that the rank and geometry of the image of a primitive-stable representa…
This work studies low-rank approximation of a positive semidefinite matrix from partial entries via nonconvex optimization. We characterized how well local-minimum based low-rank factorization approximates a fixed positive semidefinite matrix without any assumptions on the rank-matching, the condition number or eigensp…
We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state evolution to analyze what is the information theoretically minimal mean-squared error …
CALDERA compresses large language models by approximating weight matrices with low-rank, low-precision factors.
Characterizes knots with large Dehn surgeries.
TFB simplifies Bayesian LLM uncertainty estimation without extra training.
LoRA enhances model adaptability without increasing parameters.
We revisit the use of Stochastic Gradient Descent (SGD) for solving convex optimization problems that serve as highly popular convex relaxations for many important low-rank matrix recovery problems such as \textit{matrix completion}, \textit{phase retrieval}, and more. The computational limitation of applying SGD to so…
In this paper we consider the collaborative ranking setting: a pool of users each provides a small number of pairwise preferences between possible items; from these we need to predict preferences of the users for items they have not yet seen. We do so by fitting a rank score matrix to the pairwise data, and pro…
New algorithms improve RPCA for large matrices with upper rank bounds.
Improved LoRA+ adapts large models more efficiently.
The study finds infinitely many hyperbolic 3-manifolds with large rank and generalized torsion elements.
Low-rank structure emerges in neural networks during learning.
New method corrects quantization errors in LLMs using low-rank matrices.
New algorithms estimate Jacobian matrices for large-scale machine learning.
There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more robust to outliers and nonlinearity. Unlike the Pearson's case, testing the equality…
Parallel deep learning architectures like fine-tuned BERT and MT-DNN, have quickly become the state of the art, bypassing previous deep and shallow learning methods by a large margin. More recently, pre-trained models from large related datasets have been able to perform well on many downstream tasks by just fine-tunin…
In this note we show that every (real or complex) vector bundle over a compact rank one symmetric space carries, after taking the Whitney sum with a trivial bundle of sufficiently large rank, a metric with nonnegative sectional curvature. We also examine the case of complex vector bundles over other manifolds, and give…
Study uses random matrix theory to improve tensor approximation accuracy.
The paper tackles learning true rankings from noisy, incomplete data.