arXiv research

The paper proposes a deep learning technique for structured and composable representations.

Bounds on Littlestone dimension for private learning and online prediction.

We show that the Rademacher complexity of any $\mathbb{R}^{K}$-valued function class composed with an $\ell_{\infty}$-Lipschitz function is bounded by the maximum Rademacher complexity of the restriction of the function class along each coordinate, times a factor of $\tilde{O}(\sqrt{K})$.

Laundry surfaces for closed braid diagrams are presented. It is shown that braid diagrams are characterized by linking matrices obtained by lifting cycles from these surfaces. Oriented link types are then characterized by equivalence classes of linking matrices. Similar equivalence classes can be composed of Gordon and…

Meta-materials simulation sped up with energy surrogates.

Probabilistic techniques are central to data analysis, but different approaches can be difficult to apply, combine, and compare. This paper introduces composable generative population models (CGPMs), a computational abstraction that extends directed graphical models and can be used to describe and compose a broad class…

In this paper, we study a class of Finsler metrics composed by a Riemann metric $α=\sqrt{a_{ij}(x)y^i y^j}$ and a $1$-form $β=b_i(x)y^i$ called general ($α$, $β$)-metrics. We classify those projectively flat when $α$ is projectively flat. By solving the corresponding nonlinear PDEs, the metrics in this class are totall…

This paper explores the limits of Transformers in learning new patterns from scratch.

Improved code translation by preserving structure with composed fine-tuning.

Adding noise controls capacity of function compositions.

In this paper, we explicitly construct the Calabi composition of multiple affine hyperspheres possibly including some points viewing as 0-dimensional hypersheres. Then we compute all the basic affine invariants of the composed affine hyperspheres, proving that the composed affine hypersphere is symmetric one if and onl…

This work proposes a method to compose visual relations more faithfully.

Residual flows are shown to approximate MMD well.

Frameworks for writing, compiling, and optimizing deep learning (DL) models have recently enabled progress in areas like computer vision and natural language processing. Extending these frameworks to accommodate the rapidly diversifying landscape of DL models and hardware platforms presents challenging tradeoffs betwee…

Diffusion models reveal a phase transition in reconstructing high-level features.

MLJ offers a Julia package for composing machine learning models.

This paper investigates end-to-end learnable models for attributing composers to musical scores. We introduce several pooled, convolutional architectures for this task and draw connections between our approach and classical learning approaches based on global and n-gram features. We evaluate models on a corpus of 2,500…

Probabilistic models with discrete latent variables naturally capture datasets composed of discrete classes. However, they are difficult to train efficiently, since backpropagation through discrete variables is generally not possible. We present a novel method to train a class of probabilistic models with discrete late…

New mixed-platonic 3-manifolds from different polyhedra types.

Classifies surfaces for pure mapping class groups with automatic continuity.

Algorithmic fairness, and in particular the fairness of scoring and classification algorithms, has become a topic of increasing social concern and has recently witnessed an explosion of research in theoretical computer science, machine learning, statistics, the social sciences, and law. Much of the literature considers…

Novel bistable structures made from four-bar linkages, proving existence and construction.

Bardo Composer generates tabletop RPG music based on player speech.

The paper generalizes the construction by stochastic flows of consistent utility processes introduced by M. Mrad and N. El Karoui in (2010). The utilities random fields are defined from a general class of processes denoted by $\GX$. Making minimal assumptions and convex constraints on test-processes, we construct by co…

We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules. In particular, we define two classes of SympNets: the LA-SympNets composed of linear and activation modules, and the G-SympNets composed of gradient modules. Cor…

The cubic lattice stick index of a knot type is the least number of sticks necessary to construct the knot type in the 3-dimensional cubic lattice. We present the cubic lattice stick index of various knots and links, including all (p,p+1)-torus knots, and show how composing and taking satellites can be used to obtain t…

We prove an optimal systolic inequality for CAT(0) metrics on a genus~2 surface. We use a Voronoi cell technique, introduced by C.~Bavard in the hyperbolic context. The equality is saturated by a flat singular metric in the conformal class defined by the smooth completion of the curve y^2=x^5-x. Thus, among all CAT(0) …

NoLimits.jl: Flexible and Composable Nonlinear Mixed-Effects Modeling in Julia

Any generalized distance-squared mapping of equidimensional case has singularities, and their singularity types are wrapped into mystery in higher dimensional cases. Any generalized distance-squared mapping of equidimensional case is not injective. Nevertheless, in this paper, it is shown that the non-singular property…

How can we build recommender systems to take into account fairness? Real-world recommender systems are often composed of multiple models, built by multiple teams. However, most research on fairness focuses on improving fairness in a single model. Further, recent research on classification fairness has shown that combin…

This paper introduces the Differentiable Algorithm Network (DAN), a composable architecture for robot learning systems. A DAN is composed of neural network modules, each encoding a differentiable robot algorithm and an associated model; and it is trained end-to-end from data. DAN combines the strengths of model-driven …

Composing previously mastered skills to solve novel tasks promises dramatic improvements in the data efficiency of reinforcement learning. Here, we analyze two recent works composing behaviors represented in the form of action-value functions and show that they perform poorly in some situations. As part of this analysi…

Model-free deep reinforcement learning has been shown to exhibit good performance in domains ranging from video games to simulated robotic manipulation and locomotion. However, model-free methods are known to perform poorly when the interaction time with the environment is limited, as is the case for most real-world ro…

The ability to compose learned skills to solve new tasks is an important property of lifelong-learning agents. In this work, we formalise the logical composition of tasks as a Boolean algebra. This allows us to formulate new tasks in terms of the negation, disjunction and conjunction of a set of base tasks. We then sho…

Spectral variability is one of the major issue when conducting hyperspectral unmixing. Within a given image composed of some elementary materials (herein referred to as endmember classes), the spectral signature characterizing these classes may spatially vary due to intrinsic component fluctuations or external factors …

A microscopic dynamic model is here constructed and analyzed, describing the evolution of the income distribution in the presence of taxation and redistribution in a society in which also tax evasion and auditing processes occur. The focus is on effects of enforcement regimes, characterized by different choices of the …

New measure shows how LSTM models compose hierarchical representations.

Humans are able to perform a myriad of sophisticated tasks by drawing upon skills acquired through prior experience. For autonomous agents to have this capability, they must be able to extract reusable skills from past experience that can be recombined in new ways for subsequent tasks. Furthermore, when controlling com…

Inverse function theorem and homotopy description for L-infinity bundles.

Regret minimization is a powerful tool for solving large-scale problems; it was recently used in breakthrough results for large-scale extensive-form game solving. This was achieved by composing simplex regret minimizers into an overall regret-minimization framework for extensive-form game strategy spaces. In this paper…

We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we say a set $U\subseteq V$ is an $α$-spectral spanner if for all $v\in V$ there is a probability distribution $μ_v$ supported on $U$ such that $$vv^\intercal \preceq α\cdot\m…

An important property for lifelong-learning agents is the ability to combine existing skills to solve unseen tasks. In general, however, it is unclear how to compose skills in a principled way. We provide a "recipe" for optimal value function composition in entropy-regularised reinforcement learning (RL) and then exten…

It is expected that matter composed of a perfect fluid cannot be at rest outside of a black hole if the spacetime is asymptotically flat and static (non-rotating). However, there has not been a rigorous proof for this expectation without assuming spheical symmetry. In this paper, we provide a proof of non-existence of …

Study on 3D manifolds with circulant structures and their properties.

We develop the multilingual topic model for unaligned text (MuTo), a probabilistic model of text that is designed to analyze corpora composed of documents in two languages. From these documents, MuTo uses stochastic EM to simultaneously discover both a matching between the languages and multilingual latent topics. We d…

A framework for designing and evaluating new GCN variants.

New optimizers control network width scaling, improving stability and transfer across different model sizes.

A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex systems. The first paper in a series provides a detailed spectral theory of non-Hermi…