LabFab
Exploring math, physics, machine learning, and finance insights.
Tag trend following
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Tag market volatility
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Tag convexity
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Tag portfolio protection
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Tag tail risk
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Tag risk parity
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Tag options alternatives
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Tag hedge funds
Last week I came across a fascinating research paper, “Tail Protection for Long Investors: Trend Convexity at Work” by researchers from Capital Fund Management. As someone who’s weathered multiple market...
Tag momentum
Gradient descent is the workhorse of modern machine learning, but vanilla gradient descent often struggles with challenges like saddle points, ravines, and local minima. Momentum-based methods address these limitations through...
Tag gradient descent
Gradient descent is the workhorse of modern machine learning, but vanilla gradient descent often struggles with challenges like saddle points, ravines, and local minima. Momentum-based methods address these limitations through...
Tag convergence analysis
Gradient descent is the workhorse of modern machine learning, but vanilla gradient descent often struggles with challenges like saddle points, ravines, and local minima. Momentum-based methods address these limitations through...
Tag optimization theory
Gradient descent is the workhorse of modern machine learning, but vanilla gradient descent often struggles with challenges like saddle points, ravines, and local minima. Momentum-based methods address these limitations through...
Tag neural networks
Graph Neural Networks (GNNs) represent a fundamental paradigm shift in deep learning, extending the remarkable success of neural networks from Euclidean domains like images and sequences to the irregular, non-Euclidean...
Gradient descent is the workhorse of modern machine learning, but vanilla gradient descent often struggles with challenges like saddle points, ravines, and local minima. Momentum-based methods address these limitations through...
Tag saddle points
Gradient descent is the workhorse of modern machine learning, but vanilla gradient descent often struggles with challenges like saddle points, ravines, and local minima. Momentum-based methods address these limitations through...
Tag ravines
Gradient descent is the workhorse of modern machine learning, but vanilla gradient descent often struggles with challenges like saddle points, ravines, and local minima. Momentum-based methods address these limitations through...
Tag dynamical systems
Gradient descent is the workhorse of modern machine learning, but vanilla gradient descent often struggles with challenges like saddle points, ravines, and local minima. Momentum-based methods address these limitations through...
Tag quantum gravity
Imagine zooming into the fabric of spacetime itself, magnifying it by a factor of $10^{35}$—from human scales down to the Planck length of approximately $1.6 \times 10^{-35}$ meters. What would...
Tag loop quantum gravity
Imagine zooming into the fabric of spacetime itself, magnifying it by a factor of $10^{35}$—from human scales down to the Planck length of approximately $1.6 \times 10^{-35}$ meters. What would...
Tag spin networks
Imagine zooming into the fabric of spacetime itself, magnifying it by a factor of $10^{35}$—from human scales down to the Planck length of approximately $1.6 \times 10^{-35}$ meters. What would...
Tag spacetime
Imagine zooming into the fabric of spacetime itself, magnifying it by a factor of $10^{35}$—from human scales down to the Planck length of approximately $1.6 \times 10^{-35}$ meters. What would...
Tag general relativity
Imagine zooming into the fabric of spacetime itself, magnifying it by a factor of $10^{35}$—from human scales down to the Planck length of approximately $1.6 \times 10^{-35}$ meters. What would...
Tag quantum mechanics
Richard Feynman’s path integral formulation stands as one of the most elegant and profound reformulations of quantum mechanics ever conceived. Unlike the traditional Schrödinger equation approach, path integrals offer an...
Imagine zooming into the fabric of spacetime itself, magnifying it by a factor of $10^{35}$—from human scales down to the Planck length of approximately $1.6 \times 10^{-35}$ meters. What would...
Tag feynman path integral
Richard Feynman’s path integral formulation stands as one of the most elegant and profound reformulations of quantum mechanics ever conceived. Unlike the traditional Schrödinger equation approach, path integrals offer an...
Tag functional integration
Richard Feynman’s path integral formulation stands as one of the most elegant and profound reformulations of quantum mechanics ever conceived. Unlike the traditional Schrödinger equation approach, path integrals offer an...
Tag quantum field theory
The concept of a connection stands as one of the most beautiful unifications in mathematical physics, bridging the abstract world of differential geometry with the concrete phenomena of gauge fields...
Richard Feynman’s path integral formulation stands as one of the most elegant and profound reformulations of quantum mechanics ever conceived. Unlike the traditional Schrödinger equation approach, path integrals offer an...
Tag statistical mechanics
Richard Feynman’s path integral formulation stands as one of the most elegant and profound reformulations of quantum mechanics ever conceived. Unlike the traditional Schrödinger equation approach, path integrals offer an...
Tag monte carlo methods
Richard Feynman’s path integral formulation stands as one of the most elegant and profound reformulations of quantum mechanics ever conceived. Unlike the traditional Schrödinger equation approach, path integrals offer an...
Tag gauge theory
The concept of a connection stands as one of the most beautiful unifications in mathematical physics, bridging the abstract world of differential geometry with the concrete phenomena of gauge fields...
Tag yang-mills
The concept of a connection stands as one of the most beautiful unifications in mathematical physics, bridging the abstract world of differential geometry with the concrete phenomena of gauge fields...
Tag standard model
The concept of a connection stands as one of the most beautiful unifications in mathematical physics, bridging the abstract world of differential geometry with the concrete phenomena of gauge fields...
Tag differential geometry
The concept of a connection stands as one of the most beautiful unifications in mathematical physics, bridging the abstract world of differential geometry with the concrete phenomena of gauge fields...
Tag fiber bundles
The concept of a connection stands as one of the most beautiful unifications in mathematical physics, bridging the abstract world of differential geometry with the concrete phenomena of gauge fields...
Tag connections
The concept of a connection stands as one of the most beautiful unifications in mathematical physics, bridging the abstract world of differential geometry with the concrete phenomena of gauge fields...
Tag graph neural networks
Graph Neural Networks (GNNs) represent a fundamental paradigm shift in deep learning, extending the remarkable success of neural networks from Euclidean domains like images and sequences to the irregular, non-Euclidean...
Tag message passing
Graph Neural Networks (GNNs) represent a fundamental paradigm shift in deep learning, extending the remarkable success of neural networks from Euclidean domains like images and sequences to the irregular, non-Euclidean...
Tag graph convolution
Graph Neural Networks (GNNs) represent a fundamental paradigm shift in deep learning, extending the remarkable success of neural networks from Euclidean domains like images and sequences to the irregular, non-Euclidean...
Tag attention mechanisms
Graph Neural Networks (GNNs) represent a fundamental paradigm shift in deep learning, extending the remarkable success of neural networks from Euclidean domains like images and sequences to the irregular, non-Euclidean...
Tag molecular modeling
Graph Neural Networks (GNNs) represent a fundamental paradigm shift in deep learning, extending the remarkable success of neural networks from Euclidean domains like images and sequences to the irregular, non-Euclidean...
Tag knowledge graphs
Graph Neural Networks (GNNs) represent a fundamental paradigm shift in deep learning, extending the remarkable success of neural networks from Euclidean domains like images and sequences to the irregular, non-Euclidean...
Tag geometric deep learning
Graph Neural Networks (GNNs) represent a fundamental paradigm shift in deep learning, extending the remarkable success of neural networks from Euclidean domains like images and sequences to the irregular, non-Euclidean...
Tag large language models
Large Language Models present us with a fascinating paradox. They can write poetry that moves us to tears, engage in sophisticated philosophical discussions, and even generate code that solves complex...
Tag mathematical proof
Large Language Models present us with a fascinating paradox. They can write poetry that moves us to tears, engage in sophisticated philosophical discussions, and even generate code that solves complex...
Tag langlands program
Large Language Models present us with a fascinating paradox. They can write poetry that moves us to tears, engage in sophisticated philosophical discussions, and even generate code that solves complex...
Tag AI reasoning
Large Language Models present us with a fascinating paradox. They can write poetry that moves us to tears, engage in sophisticated philosophical discussions, and even generate code that solves complex...
Tag mathematical intelligence
Large Language Models present us with a fascinating paradox. They can write poetry that moves us to tears, engage in sophisticated philosophical discussions, and even generate code that solves complex...
Tag proof theory
Large Language Models present us with a fascinating paradox. They can write poetry that moves us to tears, engage in sophisticated philosophical discussions, and even generate code that solves complex...
Tag computational mathematics
Large Language Models present us with a fascinating paradox. They can write poetry that moves us to tears, engage in sophisticated philosophical discussions, and even generate code that solves complex...
Tag logical reasoning
Large Language Models present us with a fascinating paradox. They can write poetry that moves us to tears, engage in sophisticated philosophical discussions, and even generate code that solves complex...
Tag symplectic manifolds
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag Hamiltonian mechanics
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag Poisson brackets
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag Lagrangian submanifolds
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag moment maps
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag Kähler geometry
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag Darboux theorem
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag classical mechanics
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag phase space
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag geometric quantization
Picture this: every time you throw a ball, swing a pendulum, or watch planets orbit the sun, you’re witnessing one of mathematics’ most elegant and profound geometric structures at work....
Tag mirror symmetry
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag Calabi-Yau manifolds
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag homological mirror symmetry
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag Gromov-Witten invariants
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag derived categories
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag SYZ conjecture
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag torus fibrations
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag punctured invariants
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag tropical geometry
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag K3 surfaces
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag enumerative geometry
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
Tag quantum cohomology
Mirror symmetry is one of the most beautiful ideas in modern mathematics. It says that for many geometric shapes (specifically, Calabi-Yau varieties), there exists a “mirror partner” - a completely...
