arXiv research

Study phase transitions with prescribed mean curvature in Riemannian manifolds.

This paper identifies and estimates the label noise transition matrix without ground truth labels.

We develop a topology data analysis-based method to detect early signs for critical transitions in financial data. From the time-series of multiple stock prices, we build time-dependent correlation networks, which exhibit topological structures. We compute the persistent homology associated to these structures in order…

Defines SETR to measure carbon transition risk for investors.

In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which encompasses both Cartan geometries and G-structures.

Beta diffusion generates bounded data using multiplicative transitions.

Just like Atiyah Lie algebroids encode the infinitesimal symmetries of principal bundles, exact Courant algebroids are believed to encode the infinitesimal symmetries of $S^1$-gerbes. At the same time, transitive Courant algebroids may be viewed as the higher analogue of Atiyah Lie algebroids, and the non-commutative a…

The paper develops a non-transitive Cartan connection for sub-Riemannian manifolds.

The goal of system identification is to learn about underlying physics dynamics behind the time-series data. To model the probabilistic and nonparametric dynamics model, Gaussian process (GP) have been widely used; GP can estimate the uncertainty of prediction and avoid over-fitting. Traditional GPSSMs, however, are ba…

Proposes a method for approximating transition densities of SDEs driven by gamma processes.

New STH distance finds patterns in event timeseries without resampling.

Deep conditional generative models are developed to simultaneously learn the temporal dependencies of multiple sequences. The model is designed by introducing a three-way weight tensor to capture the multiplicative interactions between side information and sequences. The proposed model builds on the Temporal Sigmoid Be…

In the Information Bottleneck (IB), when tuning the relative strength between compression and prediction terms, how do the two terms behave, and what's their relationship with the dataset and the learned representation? In this paper, we set out to answer these questions by studying multiple phase transitions in the IB…

Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. However, this leads to an extensive increase in the computational complexity of the training procedure. We present…

Persistent entropy detects phase transitions in complex systems.

NERS improves RL by sampling diverse transitions considering local and global contexts.

This thesis extends Yang-Mills theory to Lie groupoids and algebroids, overcoming integrability and transitivity constraints.

A novel multi-resolution Gaussian process model for efficient time traversal.

TempLe learns transition templates for efficient multi-task RL.

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

We study unsupervised multilingual alignment, the problem of finding word-to-word translations between multiple languages without using any parallel data. One popular strategy is to reduce multilingual alignment to the much simplified bilingual setting, by picking one of the input languages as the pivot language that w…

Existing approaches to combine both additive and multiplicative neural units either use a fixed assignment of operations or require discrete optimization to determine what function a neuron should perform. This leads either to an inefficient distribution of computational resources or an extensive increase in the comput…

The principal aim of this work is the evidence on empirical way that catastrophic bifurcation breakdowns or transitions, proceeded by flickering phenomenon, are present on notoriously significant and unpredictable financial markets. Overall, in this work we developed various metrics associated with catastrophic bifurca…

A new approach uses circuit topology to study complex polymer interactions.

Study on phase transitions on surfaces using Allen-Cahn equation.

Improves GCNNs with node transition probabilities and DropNode regularization.

New model for pairwise comparisons without stochastic transitivity.

Study shows surfaces sound the same everywhere if they have a transitive isometry group.

The paper studies complex genera and related geometric applications, deriving formulas for multiple zeta values.

Study on detecting hierarchical community structures in networks.

The paper tackles joint learning of linear systems, improving accuracy with pooled data.

Model place cells as spatial embeddings for efficient path planning and cognitive map construction.

We study learning latent models with multi-instance weak supervision.

A critical decision point when training predictors using multiple studies is whether studies should be combined or treated separately. We compare two multi-study prediction approaches in the presence of potential heterogeneity in predictor-outcome relationships across datasets: 1) merging all of the datasets and traini…

UCB-TQL learns from multiple tasks with shared dynamics and adapts to task-specific variations.

Study improves cross-modal bike-share and transit demand prediction.

New sampling-based approach for filtering problems using multiplicative Gaussian functions.

Machine learning detects regime shifts in online game-experiments with high accuracy.

Solves complex clustering and rotation synchronization problem.

In learning with noisy labels, for every instance, its label can randomly walk to other classes following a transition distribution which is named a noise model. Well-studied noise models are all instance-independent, namely, the transition depends only on the original label but not the instance itself, and thus they a…

We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of c…

Log-Normal Multiplicative Dynamics improves low-precision training of neural networks.

Paper detects gradual changes in cluster structure using MC fusion.

This work improves transferability of rewards inferred from expert demonstrations.

Recursive Feature Machines show grokking in modular arithmetic without neural networks.

Unified approach to tensor PCA and related problems using tensor cumulants.

Long-term human motion can be represented as a series of motion modes---motion sequences that capture short-term temporal dynamics---with transitions between them. We leverage this structure and present a novel Motion Transformation Variational Auto-Encoders (MT-VAE) for learning motion sequence generation. Our model j…

We analyze an $N+1$-player game and the corresponding mean field game with state space $\{0,1\}$. The transition rate of $j$-th player is the sum of his control $α^j$ plus a minimum jumping rate $η$. Instead of working under monotonicity conditions, here we consider an anti-monotone running cost. We show that the mean …