Machine learning for discovering laws of nature

A microscopic particle obeys the principles of quantum mechanics -- so where is the sharp boundary between the macroscopic and microscopic worlds? It was this "interpretation problem" that prompted Schr\"odinger to propose his famous thought experiment (a cat that is simultaneously both dead and alive) and sparked a great debate about the quantum measurement problem, and there is still no satisfactory answer yet. This is precisely the inadequacy of rigorous mathematical models in describing the laws of nature. We propose a computational model to describe and understand the laws of nature based on Darwin's natural selection. In fact, whether it's a macro particle, a micro electron or a security, they can all be considered as an entity, the change of this entity over time can be described by a data series composed of states and values. An observer can learn from this data series to construct theories (usually consisting of functions and differential equations). We don't model with the usual functions or differential equations, but with a state Decision Tree (determines the state of an entity) and a value Function Tree (determines the distance between two points of an entity). A state Decision Tree and a value Function Tree together can reconstruct an entity's trajectory and make predictions about its future trajectory. Our proposed algorithmic model discovers laws of nature by only learning observed historical data (sequential measurement of observables) based on maximizing the observer's expected value. There is no differential equation in our model; our model has an emphasis on machine learning, where the observer builds up his/her experience by being rewarded or punished for each decision he/she makes, and eventually leads to rediscovering Newton's law, the Born rule (quantum mechanics) and the efficient market hypothesis (financial market)

Resonant response of forced complex networks: the role of topological disorder

We investigate the effect of topological disorder on a system of forced threshold elements, where each element is arranged on top of complex heterogeneous networks. Numerical results indicate that the response of the system to a weak signal can be amplified at an intermediate level of topological disorder, thus indicating the occurrence of topological-disorder-induced resonance. Using mean field method, we obtain an analytical understanding of the resonant phenomenon by deriving the effective potential of the system. Our findings might provide further insight into the role of network topology in signal amplification in biological networks.Comment: 12 pages, 4 figure

Timelike entanglement entropy and TTˉT\bar{T} deformation

In a previous work arXiv:1811.07758 about the $T\bar{T}$ deformed CFT$_2$, from the consistency requirement of the entanglement entropy theory, we found that in addition to the usual spacelike entanglement entropy, a timelike entanglement entropy must be introduced and treated equally. Inspired by the recent explicit constructions of the timelike entanglement entropy and its bulk dual, we provide a comprehensive analysis of the timelike and spacelike entanglement entropies in the $T\bar{T}$ deformed finite size system and finite temperature system. The results confirm our prediction that in the finite size system only the timelike entanglement entropy receives a correction, while in the finite temperature system only the usual spacelike entanglement entropy gets a correction. These findings affirm the necessity of a complete measure including both spacelike and timelike entanglement entropies, called general entanglement entropy, for characterizing deformed systems from the quantum information perspective.Comment: v1: 12 pages, 2 figures; v2: references added; v3: typo fixe

Timelike entanglement entropy in dS3/CFT2\text{dS}_3/\text{CFT}_2

In the context of dS$_3$/CFT$_2$, we propose a timelike entanglement entropy defined by the renormalization group flow. This timelike entanglement entropy is calculated in CFT by using the Callan-Symanzik equation. We find an exact match between this entanglement entropy and the length of a timelike geodesic connecting two different spacelike surfaces in dS$_3$.The counterpart of this entanglement entropy in AdS$_3$ is a spacelike one, also induced by RG flow and extends all the way into the bulk of AdS$_3$. As a result, in both AdS$_3$/CFT$_2$ and dS$_3$/CFT$_2$, there exist exactly three entanglement entropies, providing precisely sufficient information to reconstruct the three-dimensional bulk geometry.Comment: v1: 9 pages, 1 figure; v2: references added, fixed typo

Nucleation in scale-free networks

We have studied nucleation dynamics of the Ising model in scale-free networks with degree distribution $P(k)\sim k^{-\gamma}$ by using forward flux sampling method, focusing on how the network topology would influence the nucleation rate and pathway. For homogeneous nucleation, the new phase clusters grow from those nodes with smaller degree, while the cluster sizes follow a power-law distribution. Interestingly, we find that the nucleation rate $R_{Hom}$ decays exponentially with the network size $N$, and accordingly the critical nucleus size increases linearly with $N$, implying that homogeneous nucleation is not relevant in the thermodynamic limit. These observations are robust to the change of $\gamma$ and also present in random networks. In addition, we have also studied the dynamics of heterogeneous nucleation, wherein $w$ impurities are initially added, either to randomly selected nodes or to targeted ones with largest degrees. We find that targeted impurities can enhance the nucleation rate $R_{Het}$ much more sharply than random ones. Moreover, $\ln (R_{Het}/R_{Hom})$ scales as $w^{\gamma-2/\gamma-1}$ and $w$ for targeted and random impurities, respectively. A simple mean field analysis is also present to qualitatively illustrate above simulation results.Comment: 7 pages, 5 figure

Exploring Lightweight Hierarchical Vision Transformers for Efficient Visual Tracking

Transformer-based visual trackers have demonstrated significant progress owing to their superior modeling capabilities. However, existing trackers are hampered by low speed, limiting their applicability on devices with limited computational power. To alleviate this problem, we propose HiT, a new family of efficient tracking models that can run at high speed on different devices while retaining high performance. The central idea of HiT is the Bridge Module, which bridges the gap between modern lightweight transformers and the tracking framework. The Bridge Module incorporates the high-level information of deep features into the shallow large-resolution features. In this way, it produces better features for the tracking head. We also propose a novel dual-image position encoding technique that simultaneously encodes the position information of both the search region and template images. The HiT model achieves promising speed with competitive performance. For instance, it runs at 61 frames per second (fps) on the Nvidia Jetson AGX edge device. Furthermore, HiT attains 64.6% AUC on the LaSOT benchmark, surpassing all previous efficient trackers.Comment: This paper was accepted by ICCV202

SeqTrack: Sequence to Sequence Learning for Visual Object Tracking

In this paper, we present a new sequence-to-sequence learning framework for visual tracking, dubbed SeqTrack. It casts visual tracking as a sequence generation problem, which predicts object bounding boxes in an autoregressive fashion. This is different from prior Siamese trackers and transformer trackers, which rely on designing complicated head networks, such as classification and regression heads. SeqTrack only adopts a simple encoder-decoder transformer architecture. The encoder extracts visual features with a bidirectional transformer, while the decoder generates a sequence of bounding box values autoregressively with a causal transformer. The loss function is a plain cross-entropy. Such a sequence learning paradigm not only simplifies tracking framework, but also achieves competitive performance on benchmarks. For instance, SeqTrack gets 72.5% AUC on LaSOT, establishing a new state-of-the-art performance. Code and models are available at here.Comment: CVPR2023 pape

The g-irradiation-induced chemical change from b-FeOOH to

Abstract The reactions of g-irradiation on 5 nm b-FeOOH in the presence of isopropanol and water have been investigated. In the initial stage of the g-irradiation, b-FeOOH turned into a-FeOOH. With the g-irradiation continued, a-FeOOH was slowly reduced to Fe 3 O 4 . After the g-irradiation with a dose of 64.3 kGy, all the bFeOOH and a-FeOOH disappeared and the product was a single phase of Fe 3 O 4 , which had an average particle size of 54 nm. The process of this reaction is discussed. The g-irradiation of b-FeOOH should be a new method of preparing magnetite.