arXiv research

Teaches sequential learners with changing inner states to improve future performance.

Neural encoding and decoding, which aim to characterize the relationship between stimuli and brain activities, have emerged as an important area in cognitive neuroscience. Traditional encoding models, which focus on feature extraction and mapping, consider the brain as an input-output mapper without inner states. In th…

We propose a quantization based approach for fast approximate Maximum Inner Product Search (MIPS). Each database vector is quantized in multiple subspaces via a set of codebooks, learned directly by minimizing the inner product quantization error. Then, the inner product of a query to a database vector is approximated …

Signature Isolation Forest removes constraints from FIF by using rough path theory's signature transform.

Quantization based techniques are the current state-of-the-art for scaling maximum inner product search to massive databases. Traditional approaches to quantization aim to minimize the reconstruction error of the database points. Based on the observation that for a given query, the database points that have the largest…

There has been substantial research on sub-linear time approximate algorithms for Maximum Inner Product Search (MIPS). To achieve fast query time, state-of-the-art techniques require significant preprocessing, which can be a burden when the number of subsequent queries is not sufficiently large to amortize the cost. Fu…

Neural network pruning reduces the computational cost of an over-parameterized network to improve its efficiency. Popular methods vary from $\ell_1$-norm sparsification to Neural Architecture Search (NAS). In this work, we propose a novel pruning method that optimizes the final accuracy of the pruned network and distil…

GPU-accelerates multiuser detection for 5G URLLC systems.

Fewer data weight updates lead to faster convergence in machine learning models.

Study higher rank inner products and their tilings to describe tori degenerations.

Characterizes quandles with abelian inner automorphisms.

New spectral functionals for Dirac operators with inner fluctuations computed.

A new algorithm tackles bilevel optimization with multiple inner minima.

The paper proposes an efficient nested simulation design using likelihood ratio method.

This paper constructs quandles with abelian inner automorphism groups from graphs, proving their homogeneity.

In general, adversarial perturbations superimposed on inputs are realistic threats for a deep neural network (DNN). In this paper, we propose a practical generation method of such adversarial perturbation to be applied to black-box attacks that demand access to an input-output relationship only. Thus, the attackers gen…

Groups with specific properties have vanishing $\ell^2$-Betti numbers.

The author reviews his results on locally compact homogeneous spaces with inner metric, in particular, homogeneous manifolds with inner metric. The latter are isometric to homogeneous (sub-)Finslerian manifolds; under some additional conditions they are isometric to homogeneous (sub)-Riemannian manifolds. The class $Ω$…

Researchers prove inner product recovery is impossible in latent space models.

We classify homotopes of classical symmetric spaces (studied in Part I of this work). Our classification uses the fibered structure of homotopes: they are fibered as symmetric spaces, with flat fibers, over a non-degenerate base; the base spaces correspond to inner ideals in Jordan pairs. Using that inner ideals in cla…

Paper proposes a new method to optimize feature coordinates for better image classification.

The paper challenges the belief that more inner iterations at test time improve performance in implicit deep learning.

In this paper we study isometry-invariant Finsler metrics on inner product spaces over $\mathbb{R}$ or $\mathbb{C}$, i.e. the Finsler metrics which do not change under the action of all isometries of the inner product space. We give a new proof of the analytic description of all such metrics. In this article the most g…

Study of Gaussian distributions using entropic Gromov-Wasserstein and inner product Gromov-Wasserstein.

A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this formulation, meta-parameters are learned in the outer loop, while task-specific m…

ANIL adapts only a subset of parameters, reducing computational cost.

We introduce a proximal version of the stochastic dual coordinate ascent method and show how to accelerate the method using an inner-outer iteration procedure. We analyze the runtime of the framework and obtain rates that improve state-of-the-art results for various key machine learning optimization problems including …

Study bounds the index of minimal submanifolds using energy measures and Yang-Mills-Higgs equations.

Quantum kernels can be efficiently embedded into classical feature spaces.

Each market has its singular characteristic. Its inner structure is directly responsible for the observed distributions of returns though this fact is widely overlooked. Big orders lead to doubling the tails. The behavior of a market maker with many or few ``friends'' who can reliably loan money or stock to him is quit…

Introduces PPMM algorithm for nonconvex robust regression problems.

Study on singularities of specific polynomial functions.

Graphs with stronger curvature grow faster.

We study one extremal problem on the product of power of generalized inner radii of non-overlapping domains in $\mathbb{C}^{n}$.

We point out that the Homfly polynomial (that is to say, Ocneanu's trace functional) contains two polynomial-valued inner products on the Hecke algebra representation of Artin's braid group. These bear a close connection to the Morton-Franks-Williams inequality. In these structures, the sets of positive, respectively n…

Study on kernel regression risk in high dimensions using Pinsker bound.

The paper explores harmonic maps and their properties in symmetric spaces.

The paper solves the Andreadakis problem for specific groups using inner automorphisms.

We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to nonsmooth problems that are difficult to optimize, and we propose in this paper a suit…

Efficient Maximum Inner Product Search (MIPS) is an important task that has a wide applicability in recommendation systems and classification with a large number of classes. Solutions based on locality-sensitive hashing (LSH) as well as tree-based solutions have been investigated in the recent literature, to perform ap…

Convex learning for diverse invariances in semi-inner-product space.

We present the first provably sublinear time algorithm for approximate \emph{Maximum Inner Product Search} (MIPS). Our proposal is also the first hashing algorithm for searching with (un-normalized) inner product as the underlying similarity measure. Finding hashing schemes for MIPS was considered hard. We formally sho…

A new method for efficient nested Monte Carlo simulations in financial modeling.

Neyshabur and Srebro proposed Simple-LSH, which is the state-of-the-art hashing method for maximum inner product search (MIPS) with performance guarantee. We found that the performance of Simple-LSH, in both theory and practice, suffers from long tails in the 2-norm distribution of real datasets. We propose Norm-rangin…

Study on naked singularities without symmetry, forming incomplete future null infinity and singular inner Cauchy horizon.

In this paper, we develop a loop group description of harmonic maps $\mathcal{F}: M \rightarrow G/K$ ``of finite uniton type", from a Riemann surface $M$ into inner symmetric spaces of compact or non-compact type. This develops work of Uhlenbeck, Segal, and Burstall-Guest to non-compact inner symmetric spaces. To be mo…

In this paper we deal with the global properties of Willmore surfaces in spheres via the harmonic conformal Gauss map using loop groups. We first derive a global description of those harmonic maps which can be realized as conformal Gauss maps of some Willmore surfaces (Theorem 3.4, Theorem 3.11 and Theorem 3.18). Then …

Automorphisms of pants complex are shown to be inner.