A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Method optimizes knotting pathways in constrained polymers.
Neural networks simplify SDR in regression tasks.
Some natural hidden symmetries in the Verma modules over the Virasoro algebra are constructed in terms of geometric quantization. Their differential geometric meaning is established and their expression via -conformal symmetries in the Verma modules over the Lie algebra is found. The analysis and the unr…
New algorithm explains neural network extrema for better model generalization.
We present an alternative local definition of the writhe of a self-avoiding closed loop which differs from the traditional non-local definition by an integer. When studying dynamics this difference is immaterial. We employ a formula due to Aldinger, Klapper and Tabor for the change in writhe and propose a set of local,…
Without any means of interpretation, neural networks that predict molecular properties and bioactivities are merely black boxes. We will unravel these black boxes and will demonstrate approaches to understand the learned representations which are hidden inside these models. We show how single neurons can be interpreted…
MFGs explain and enhance generative models, revealing new model types.
I unravel the basic long run dynamics of the broker call money market, which is the pile of cash that funds margin loans to retail clients (read: continuous time Kelly gamblers). Call money is assumed to supply itself perfectly inelastically, and to continuously reinvest all principal and interest. I show that the rela…
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the interaction between traders and hierarchical cascade models to unravel the possi…
The developments of deep neural networks (DNN) in recent years have ushered a brand new era of artificial intelligence. DNNs are proved to be excellent in solving very complex problems, e.g., visual recognition and text understanding, to the extent of competing with or even surpassing people. Despite inspiring and enco…
The hyperbolic dodecahedral space of Weber and Seifert has a natural non-positively curved cubulation obtained by subdividing the dodecahedron into cubes. We show that the hyperbolic dodecahedral space has a 6-sheeted irregular cover with the property that the canonical hypersurfaces made up of the mid-cubes give a ver…
The paper studies how neural networks evolve representations, finding a unique fixed point for nonlinear activations.
We confirm and substantially extend the recent empirical result of Andersen et al. \cite{Andersen2015}, where it is shown that the amount of risk exchanged in the E-mini S\&P futures market (i.e. price times volume times volatility) scales like the 3/2 power of the number of trades . We show that this 3/2-law ho…
One of the most important problems of data processing in high energy and nuclear physics is the event reconstruction. Its main part is the track reconstruction procedure which consists in looking for all tracks that elementary particles leave when they pass through a detector among a huge number of points, so-called hi…
This paper discusses a novel explanation for asymmetric volatility based on the anchoring behavioral pattern. Anchoring as a heuristic bias causes investors focusing on recent price changes and price levels, which two lead to a belief in continuing trend and mean-reversion respectively. The empirical results support ou…
We document and analyze the empirical facts concerning one of the clearest evidence of speculation in financial trading as observed in the postage collection stamp market. We unravel some of the mechanisms of speculative behavior which emphasize the role of fancy and collective behavior. In our conclusion, we propose a…
Clusters asset classes to identify lead-lag relationships in market regimes.
We invoke a Gaussian mixture model (GMM) to jointly analyse two traditional emission-line classification schemes of galaxy ionization sources: the Baldwin-Phillips-Terlevich (BPT) and vs. [NII]/H (WHAN) diagrams, using spectroscopic data from the Sloan Digital Sky Survey Data Release 7 and SEAGal/STARLI…
A new method selects features for clustering without labels.
One of the most important problems of data processing in high energy and nuclear physics is the event reconstruction. Its main part is the track reconstruction procedure which consists in looking for all tracks that elementary particles leave when they pass through a detector among a huge number of points, so-called hi…
The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size when is larger than some crossover scale, providing direct evidence of the existence of sca…
In this paper, we unravel a fundamental connection between weighted finite automata~(WFAs) and second-order recurrent neural networks~(2-RNNs): in the case of sequences of discrete symbols, WFAs and 2-RNNs with linear activation functions are expressively equivalent. Motivated by this result, we build upon a recent ext…
Simplified equation predicts model sensitivity to data.
VL finds flatter solutions at edge of stability, matching theory with practice.
Deep residual networks (ResNets) and their variants are widely used in many computer vision applications and natural language processing tasks. However, the theoretical principles for designing and training ResNets are still not fully understood. Recently, several points of view have emerged to try to interpret ResNet …
Complex dynamical systems driven by the unravelling of information can be modelled effectively by treating the underlying flow of information as the model input. Complicated dynamical behaviour of the system is then derived as an output. Such an information-based approach is in sharp contrast to the conventional mathem…
Financial markets provide a natural quantitative lab for understanding some of the most advanced human behaviours. Among them is the use of mathematical tools known as financial instruments. Besides money, the two most fundamental financial instruments are bonds and equities. More than 30 years ago Mehra and Prescott f…
Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct extraction of those. In this paper, we introduce the first algorithmic approach to extra…
ClusterLOB clusters market events to identify different trading behaviors.
We present an analysis of oil prices in US$ and in other major currencies that diagnoses unsustainable faster-than-exponential behavior. This supports the hypothesis that the recent oil price run-up has been amplified by speculative behavior of the type found during a bubble-like expansion. We also attempt to unravel t…
Meta-learning improves feature extraction for few-shot tasks.
A new method estimates the number of clusters on spherical data.
Study reveals how spectral bias affects learnability on real-world data.
CRF model improves protein secondary structure prediction.
Random walks and polygons are used to model polymers. In this paper we consider the extension of writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random walks and polygons over the space of configurations as a function of their length. W…
Solves K-Means clustering's need for known cluster count.
Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and providing insights about the problem. Yet, caution should avoid using machine l…
The goal of score following is to track a musical performance, usually in the form of audio, in a corresponding score representation. Established methods mainly rely on computer-readable scores in the form of MIDI or MusicXML and achieve robust and reliable tracking results. Recently, multimodal deep learning methods h…
Unravelling hidden patterns in datasets is a classical problem with many potential applications. In this paper, we present a challenge whose objective is to discover nonlinear relationships in noisy cloud of points. If a set of point satisfies a nonlinear relationship that is unlikely to be due to randomness, we will l…
The paper improves spectral ranking methods for diverse comparison graphs.
Paper finds methods to accurately determine the number of clusters in data.
Study of knotted defects in smectic liquid crystals using topological knot theory.
The K-means algorithm is arguably the most popular data clustering method, commonly applied to processed datasets in some "feature spaces", as is in spectral clustering. Highly sensitive to initializations, however, K-means encounters a scalability bottleneck with respect to the number of clusters K as this number grow…
We study how information perturbations can destabilize two-sided matching markets. In our model, agents arrive on the market over two periods, while agents in the first period do not know the types of those arriving later. Agents already present in the market may match early or wait for the small group of new entrants.…
A new method uncovers discrete and continuous factors in gene expression data.
The large-scale organization of the world economies is exhibiting increasingly levels of local heterogeneity and global interdependency. Understanding the relation between local and global features calls for analytical tools able to uncover the global emerging organization of the international trade network. Here we an…
New method discovers causal relationships in sparse linear data.
In some sense, the world is composed of shapes and words, of continuous things and discrete things. The recognition and study of continuous objects in the form of shapes occupies a significant part of the effort of unraveling many geometric questions. Shapes can be rep- resented with great generality by objects called …