arXiv research

The paper addresses Dyna-style RL's value hallucination issue by proposing a new algorithm.

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents…

We propose Generative Predecessor Models for Imitation Learning (GPRIL), a novel imitation learning algorithm that matches the state-action distribution to the distribution observed in expert demonstrations, using generative models to reason probabilistically about alternative histories of demonstrated states. We show …

This paper shows that only finitely many knots can be ribbon concordant to any given knot.

The study limits the number of ribbon concordant fibered knots.

This paper extends complex Cartan geometry results to noncompact and non-Kähler manifolds.

These are lecture notes on the rigidity of submanifolds of projective space "resembling" compact Hermitian symmetric spaces in their homogeneous embeddings. Recent results are surveyed, along with their classical predecessors. The notes include an introduction to moving frames in projective geometry, an exposition of t…

This paper provides a new version of the condition of Di Nunno et al. (2003), Ankirchner and Imkeller (2005) and Biagini and \{O}ksendal (2005) ensuring the semimartingale property for a large class of continuous stochastic processes. Unlike our predecessors, we base our modeling framework on the concept of portfolio p…

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete topological base spaces associated to such orbifolds can be described and manipula…

Bidirectional attention is shown to be equivalent to a continuous bag of words model with mixture-of-experts.

We present new, unified proofs for the cell-like, $\mathbb{Z}/p$-, and $\mathbb{Q}$-resolution theorems. Our arguments employ extensions that are much simpler then those used by our predecessors. The techniques allow us to solve problems involving cohomology groups by converting them into problems about homology groups…

We consider the problem of optimising functions in the reproducing kernel Hilbert space (RKHS) of a Matérn kernel with smoothness parameter $ν$ over the domain $[0,1]^d$ under noisy bandit feedback. Our contribution, the $π$-GP-UCB algorithm, is the first practical approach with guaranteed sublinear regret for all $ν>1…

Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include compressive classification. Taking inspiration from large margin nearest neighbor class…

Numerical computations suggest that each point on a certain optimized shape called the ideal trefoil is in contact with two other points. We consider sequences of such contact points, such that each point is in contact with its predecessor and call it a billiard. Our numerics suggest that a particular billiard on the i…

A unique challenge for e-commerce recommendation is that customers are often interested in products that are more advanced than their already purchased products, but not reversed. The few existing recommender systems modeling unidirectional sequence output a limited number of categories or continuous variables. To mode…

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is numerically very challenging. We address this challenge by developing a new adaptive…

This paper extends geometric structure theory to infinite type structures.

Transformers can perform well with less long-range memory.

Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to the objective function. We show that many, including the most popular, quasi-Newto…

The natural partial ordering of the orbit types of the action of the group of local gauge transformations on the space of connections in space-time dimension d<=4 is investigated. For that purpose, a description of orbit types in terms of cohomology elements of space-time, derived earlier, is used. It is shown that, on…

We present Sequential Attend, Infer, Repeat (SQAIR), an interpretable deep generative model for videos of moving objects. It can reliably discover and track objects throughout the sequence of frames, and can also generate future frames conditioning on the current frame, thereby simulating expected motion of objects. Th…

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential…

TOLD++ improves convergence of diffusion models by critically damping the forward transition matrix.

New method identifies root causes in presence of latent confounding.

ALT transforms time series data for better classification.

Study ribbon concordance and minimal compressions, proving new results about fibered knots.

Many real-world applications require robust algorithms to learn point processes based on a type of incomplete data --- the so-called short doubly-censored (SDC) event sequences. We study this critical problem of quantitative asynchronous event sequence analysis under the framework of Hawkes processes by leveraging the …

A simple gating mechanism improves deep learning convergence.

A new contrastive MI estimator improves efficiency and tightness.

NE-VAE prevents posterior collapse in VAEs by embedding neighbors in latent space.

Boosting Nyström improves accuracy of matrix approximations.

We propose a novel deep learning method for local self-supervised representation learning that does not require labels nor end-to-end backpropagation but exploits the natural order in data instead. Inspired by the observation that biological neural networks appear to learn without backpropagating a global error signal,…

VICE embeds concepts in a vector space using human data.

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The …

We use the contact invariant defined in [2] to construct a new invariant of Legendrian knots in Kronheimer and Mrowka's monopole knot homology theory (KHM), following a prescription of Stipsicz and Vértesi. Our Legendrian invariant improves upon an earlier Legendrian invariant in KHM defined by the second author in sev…

Coherent uncertainty quantification is a key strength of Bayesian methods. But modern algorithms for approximate Bayesian posterior inference often sacrifice accurate posterior uncertainty estimation in the pursuit of scalability. This work shows that previous Bayesian coreset construction algorithms---which build a sm…

New EP variants improve inference stability and efficiency.

One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods…

We explore a new research direction in Bayesian variational inference with discrete latent variable priors where we exploit Kronecker matrix algebra for efficient and exact computations of the evidence lower bound (ELBO). The proposed "DIRECT" approach has several advantages over its predecessors; (i) it can exactly co…

This paper reviews deep time-series forecasting focusing on autocorrelation modeling.

New study shows MLE can avoid model collapse with gradual synthetic data addition.

RE enhances DL by learning model behavior, enabling iterative self-improvement.

Improved neural image compression with refined latent representations.

Kolmogorov-Arnold Networks improve deep learning adaptivity and can approximate Besov functions optimally.

Graph neural networks improve predictions on graph data.

T-distributed stochastic neighbour embedding (t-SNE) is a widely used data visualisation technique. It differs from its predecessor SNE by the low-dimensional similarity kernel: the Gaussian kernel was replaced by the heavy-tailed Cauchy kernel, solving the "crowding problem" of SNE. Here, we develop an efficient imple…

The generalized volume conjecture relates asymptotic behavior of the colored Jones polynomials to objects naturally defined on an algebraic curve, the zero locus of the A-polynomial $A(x,y)$. Another "family version" of the volume conjecture depends on a quantization parameter, usually denoted $q$ or $\hbar$; this quan…

Proposes $Π$-Nets, polynomial neural networks, for improved representation power.