arXiv research

New RL method learns to skip states in linearly $q^π$-realizable MDPs, simplifying to linear MDPs.

TensorPlan algorithm finds δ-optimal policies with poly$(H,d)$ queries under linearly realizable state-value function.

Paper tackles sample-efficient RL for linearly realizable MDPs with limited revisiting.

There are known infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. In this paper we show that free periodic actions on these Brieskorn spheres do not extend smoothly over a contractible 4-manifold. We give a new infinite family of examples in which …

New method efficiently evaluates policies using trajectory data.

New research shows exponential lower bounds for planning in MDPs with linearly-realizable optimal action-value functions.

This paper examines number theoretic and topological properties of fully augmented pretzel link complements. In particular, we determine exactly when these link complements are arithmetic and exactly which are commensurable with one another. We show these link complements realize infinitely many CM-fields as invariant …

New RL difficulty shown for discounted settings.

TensorPlan shows an exponential lower bound for planning in MDPs with linearly realizable value functions.

Sine activation functions enable two-layer neural networks to learn modular addition more efficiently.

Multi-group learners suffer a penalty in transductive learning.

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary conditions. We construct multi-output Gaussian process priors with realizations in the so…

The paper classifies groups that can be isometry groups of infinite-genus hyperbolic surfaces.

We present a short exposition of the following results by S. Parsa. Let $L$ be a graph such that the join $L*\{1,2,3\}$ (i.e. the union of three cones over $L$ along their common bases) piecewise linearly (PL) embeds into $\mathbb R^4$. Then $L$ admits a PL embedding into $\mathbb R^3$ such that any two disjoint cycles…

New framework tackles stochastic latent subgroup heterogeneity in online decision-making.

The paper addresses rigid alignment of noisy patches, providing a polynomial time algorithm and convergence conditions.

New method certifies deep graph classifiers with tighter risk bounds.

This is the second paper of a series dedicated to the study of Poisson structures of compact types (PMCTs). In this paper, we focus on regular PMCTs, exhibiting a rich transverse geometry. We show that their leaf spaces are integral affine orbifolds. We prove that the cohomology class of the leafwise symplectic form va…

New study shows exponential lower bound for RL even with constant suboptimality gap.

Paper explores how unsupervised learning can be understood through linear algebra concepts.

Study on singular points of translation surfaces under linearly dependent conditions.

We propose a new method for blind system identification. Resorting to a Gaussian regression framework, we model the impulse response of the unknown linear system as a realization of a Gaussian process. The structure of the covariance matrix (or kernel) of such a process is given by the stable spline kernel, which has b…

In this paper we study a Ricci-Hessian type manifold $(\Bbb{M},g,\varphi,f,λ)$ which is closely related to the construction of almost Ricci soliton realized as a warped product. We classify certain classes of the Ricci-Hessian type manifolds and derive some implications for almost Ricci solitons and generalized $m$--qu…

We consider computational complexity of problems related to the fundamental group and the first homology group of (embeddable) $2$-complexes. We show, as an extension of an earlier work, that computing first homology of $2$-complexes is equivalent in computational complexity to matrix diagonalization. That is, the usua…

Improved LOO cross-validation for function approximation.

Trajectory data suffices for efficient RL in linear MDPs.

Universal triangulation for flat tori with 2434 triangles.

It is well known that an arbitrary closed orientable $3$-manifold can be realized as the unique boundary of a compact orientable $4$-manifold, that is, any closed orientable $3$-manifold is cobordant to zero. In this paper, we consider the geometric cobordism problem: a hyperbolic $3$-manifold is geometrically bounding…

If a closed 3-manifold M supports a closed, nonsingular, irrational 1-form which linearly deforms into contact forms, then M supports a K-contact form. On the 3-torus, a closed nonsingular 1-form deforms linearly into contact forms if and only if it is a fibration 1-form. on any other 2-torus bundle over the circle, ev…

This work improves sample efficiency in neural function approximation for reinforcement learning.

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an…

Flat minimal tori counterexamples refute Lu's second-gap conjecture.

New RL algorithms use lookahead info to maximize rewards.

The paper explores linearly free graphs and their embeddings into 3D space.

HARNet improves volatility forecasting using deep neural networks.

Optimization geometrodynamics simplifies adaptive optimizer dynamics.

A quadratic line complex is a three-parameter family of lines in projective space P^3 specified by a single quadratic relation in the Plucker coordinates. Fixing a point p in P^3 and taking all lines of the complex passing through p we obtain a quadratic cone with vertex at p. This family of cones supplies P^3 with a c…

Large scale machine learning (ML) systems such as the Alexa automatic speech recognition (ASR) system continue to improve with increasing amounts of manually transcribed training data. Instead of scaling manual transcription to impractical levels, we utilize semi-supervised learning (SSL) to learn acoustic models (AM) …

Supervised learning frequently boils down to determining hidden and bright parameters in a parameterized hypothesis space based on finite input-output samples. The hidden parameters determine the attributions of hidden predictors or the nonlinear mechanism of an estimator, while the bright parameters characterize how h…

In previous work, the authors studied the linear stability of algebraic Ricci solitons on simply connected solvable Lie groups (solvsolitons), which are stationary solutions of a certain normalization of Ricci flow. Many examples were shown to be linearly stable, leading to the conjecture that all solvsolitons are line…

In his celebrated paper "Generic projections", John Mather has given a striking transversality theorem and its applications on generic projections. On the other hand, in this paper, two transversality theorems on generic linearly perturbed $C^r$ mappings are shown $(r\geq 1)$. Moreover, some applications of the two the…

Unified framework for nonconvex matrix completion with linearly parameterized factors.

We demonstrate that SDYM equations for the Lie algebra of one-dimensional vector fields represent a natural reduction in the framework of general linearly degenerate dispersionless hierarchy. We define the reduction in terms of wave functions, introduce generating relation, Lax-Sato equations and the dressing scheme fo…

Following Cao-Hamilton-Ilmanen, in this paper we study the linear stability of Perelman's $ν$-entropy on Einstein manifolds with positive Ricci curvature. We observe the equivalence between the linear stability restricted to the transversal traceless symmetric 2-tensors and the stability of Einstein manifolds with resp…

Randomly initialized neural networks can linearly separate arbitrary sets.

New algorithms tackle robust RL with linear models, revealing unique challenges.

The paper proves hyperbolic groups are semistable and their boundaries are linearly connected.

We prove that the linearly controlled asymptotic dimension of the fundamental group of any 3-dimensional graph-manifold does not exceed 7. As applications we obtain that the universal cover of such a graph-manifold is an absolute Lipschitz retract and it admits a quasisymmetric embedding into the product of 8 metric tr…