math notes

These are the most bountiful types of notes that I have. These are (some) atomized notes from (math) courses I have taken while using my obsidian vault. Some of my full Lecture Notes are also available for perusal.

Post Maturity Last Edited Created
Baire Category Theorem 🌲 2025-06-05 2025-06-05
bijective bounded linear operators have bounded linear inverses 🌲 2025-06-05 2025-06-05
closed subspaces of banach spaces are banach 🌲 2025-06-05 2025-06-05
convergent graph sequence 🌲 2025-06-05 2025-03-24
equivalence relation 🌲 2025-06-05 2025-06-05
fully random graphs converge to the graphon in probability 🌲 2025-06-05 2025-03-26
graphon shift operator 🌲 2025-06-05 2025-03-31
graphon 🪴 2025-06-05 2025-03-24
open mapping theorem 🌲 2025-06-05 2025-06-05
quotient of a vector space 🌲 2025-06-05 2025-06-05
the cartesian product of banach spaces is banach 🌲 2025-06-05 2025-06-05
uniform boundedness theorem 🌲 2025-06-05 2025-06-05
ways to sample graphs from graphons 2025-06-05 2025-03-26
closed graph theorem 🌲 2025-06-05 2025-06-05
partial order 🌲 2025-06-05 2025-06-05
upper bound 🌲 2025-06-05 2025-06-05
maximal element 🌲 2025-06-05 2025-06-05
chain 🌲 2025-06-05 2025-06-05
Hamel basis 🌲 2025-06-05 2025-06-05
Zorn's lemma 🌲 2025-06-05 2025-06-05
cut distance 🪴 2025-06-04 2025-03-24
lipschitz graph convolutions of graph signals converge to lipschitz graphon filters 🌲 2025-06-03 2025-04-15
fixed coefficients yield the same spectral response for both graphon and graph convolutions 🌲 2025-06-02 2025-04-09
spectral representation of graphon convolutions 🌲 2025-06-02 2025-04-09
Banach space 🌲 2025-05-30 2025-05-27
Graph Isomorphism Network 🌲 2025-05-30 2025-03-03
bounded linear operator space is banach 🌲 2025-05-30 2025-05-30
c band cardinality 🌲 2025-05-30 2025-04-22
continuous map 🌲 2025-05-30 2025-05-29
convergence bound for graph convolutions 🌲 2025-05-30 2025-04-22
eigenfunction 🌲 2025-05-30 2025-03-31
graph homomorphism 🌲 2025-05-30 2025-03-03
graph motif 🪴 2025-05-30 2025-03-24
graphon fourier transform 🌲 2025-05-30 2025-04-02
graphon shift operators are self-adjoint 🌲 2025-05-30 2025-03-31
graphon signal 🪴 2025-05-30 2025-03-26
template graph 🌲 2025-05-30 2025-03-26
we can write a graphon in the basis of its shift operator 🌲 2025-05-30 2025-04-01
absolutely summable series have Cauchy partial sums 🌲 2025-05-29 2025-05-29
banach spaces have all absolutely summable series are summable 🌲 2025-05-29 2025-05-29
complete metric spaces have banach continuous bounded function spaces 🌲 2025-05-29 2025-05-27
continuous bounded function space 🌲 2025-05-29 2025-05-27
finite vector space 🌲 2025-05-29 2025-05-27
infinity norm for continuous bounded function space 🌲 2025-05-29 2025-05-27
l-p vector space 🌲 2025-05-29 2025-05-27
semi-norm 🌲 2025-05-29 2025-05-27
summable series 🌲 2025-05-29 2025-05-29
weighted graph (sample) 🌲 2025-05-28 2025-03-26
distance 🌲 2025-05-27 2025-03-24
Chebyshev Polynomial 🌲 2025-05-13 2025-02-17
Convergence in the cut norm implies convergence in L2 🌲 2025-05-13 2025-03-26
Davis-Kahan Theorem 🌲 2025-05-13 2025-04-09
GCN layers can be written as graph convolutions 🌲 2025-05-13 2025-02-20
GINs are maximally powerful for anonymous input graphs 🪴 2025-05-13 2025-03-03
GNNs inherit stability from their layers 🌲 2025-05-13 2025-03-12
GNNs perform better than their constituent filters 🌲 2025-05-13 2025-03-12
Graph Neural Networks 🌲 2025-05-13 2025-02-05
Lipschitz continuous 🌲 2025-05-13 2025-03-05
Lipschitz filters are stable to additive perturbations 🌲 2025-05-13 2025-03-10
MPNNs can be expressed as graph convolutions 🌲 2025-05-13 2025-02-18
We can verify whether graphs without node features and different laplacian eigenvalues are not isomorphic 🌲 2025-05-13 2025-02-21
Weisfeiler-Leman Graph Isomorphism Test 🌲 2025-05-13 2025-02-21
aggregation readout layer 🌲 2025-05-13 2025-02-21
almost exact recovery is impossible when the signal to noise ratio is less than the threshold 🌲 2025-05-13 2025-02-10
analytic function 🪴 2025-05-13 2025-02-03
approximation of heaviside functions using convolutional graph filters 🌲 2025-05-13 2025-02-04
balanced stochastic block model 🌲 2025-05-13 2025-02-10
bandlimited convergent graph signals converge in the fourier domain 🌲 2025-05-13 2025-04-09
bandlimited graphon signal 🌲 2025-05-13 2025-04-09
c eigenvalue margin 🌲 2025-05-13 2025-04-22
chebyshev equioscillation theorem 🌲 2025-05-13 2025-02-20
chebyshev polynomials are orthogonal 🌲 2025-05-13 2025-02-20
color refinement algorithm 🌲 2025-05-13 2025-02-21
compressed sparse row representation 🌲 2025-05-13 2025-02-12
computational graph 🌲 2025-05-13 2025-03-03
conditions for finding a convolutional graph filter 🌲 2025-05-13 2025-01-29
contextual stochastic block model 🌲 2025-05-13 2025-02-12
convergence in L-p implies convergence in cut norm 🌲 2025-05-13 2025-03-26
convolutional filter bank 🌲 2025-05-13 2025-02-05
convolutional graph filters are local 🌲 2025-05-13 2025-01-29
convolutional graph filters are permutation equivariant 🌲 2025-05-13 2025-01-29
convolutional graph filters are shift equivariant 🌲 2025-05-13 2025-01-29
coordinate representation 🌲 2025-05-13 2025-02-12
cut norm 🪴 2025-05-13 2025-03-24
cycle homomorphism density is given by the trace of the adjacency matrix 🌲 2025-05-13 2025-03-04
discriminability of a graph filter 🪴 2025-05-13 2025-03-10
eigenvalues of the induced graphon converge pointwise to the eigenvalues of the limit 🌲 2025-05-13 2025-04-02
eigenvector misalignment 🌲 2025-05-13 2025-03-10
feature-aware spectral embeddings 🌲 2025-05-13 2025-02-12
filter permutation invariance 🌲 2025-05-13 2025-03-10
fully connected readout layer 🌲 2025-05-13 2025-02-19
fully random graph 🌲 2025-05-13 2025-03-26
graph SAGE 🌲 2025-05-13 2025-02-20
graph attention model 🌲 2025-05-13 2025-02-19
graph automorphism 🌲 2025-05-13 2025-03-05
graph convolution 🌲 2025-05-13 2025-01-29
graph convolutional network 🌲 2025-05-13 2025-02-20
graph convolutions are stable to perturbations in the data and coefficients 🌲 2025-05-13 2025-03-05
graph edit distance 🌲 2025-05-13 2025-03-24
graph isomorphism is not solvable in polynomial time 🪴 2025-05-13 2025-03-02
graph isomorphism 🌲 2025-05-13 2025-02-21
graph perceptron 🌲 2025-05-13 2025-02-05
graph sequence converges if and only if the induced graphon sequence converges 🌲 2025-05-13 2025-03-26
graph shift operator 🌲 2025-05-13 2025-01-22
graph signal processing problem 🌲 2025-05-13 2025-02-04
graph signals 🌲 2025-05-13 2025-01-22
graph-level problem 🌲 2025-05-13 2025-02-04
graph 🌲 2025-05-13 2025-01-22
graphon convolution 🌲 2025-05-13 2025-04-09
graphon shift operator eigenvalues 🌲 2025-05-13 2025-04-01
heaviside functions 🪴 2025-05-13 2025-02-04
homomorphism density 🌲 2025-05-13 2025-03-04
hypothesis class 🪴 2025-05-13 2025-02-04
induced graphon signal 🌲 2025-05-13 2025-03-26
induced graphon 🪴 2025-05-13 2025-03-24
inductive learning 🫘 2025-05-13 2025-02-04
information theoretic threshold 🌲 2025-05-13 2025-02-12
integral Lipschitz filter 🌲 2025-05-13 2025-03-10
integral lipschitz filters are stable to dilations 🌲 2025-05-13 2025-03-10
inverse graph fourier transform 🌲 2025-05-13 2025-01-29
kernel cut metric 🪴 2025-05-13 2025-03-24
kernel cut norm 🌲 2025-05-13 2025-03-24
leaky ReLU 🌲 2025-05-13 2025-02-19
linear graph filter 🌲 2025-05-13 2025-01-29
message passing neural network 🌲 2025-05-13 2025-02-18
multi-layer graph perceptron 🌲 2025-05-13 2025-02-05
node-level task 🌲 2025-05-13 2025-02-04
operator distance modulo permutations 🌲 2025-05-13 2025-03-05
quasi-symmetry 🌲 2025-05-13 2025-03-05
random graphs in a gin are good for graph isomorphism 🌲 2025-05-13 2025-03-04
readout layer 🌲 2025-05-13 2025-02-19
relative perturbation edge changes are tied to node degree 🌲 2025-05-13 2025-03-10
relative perturbations 🌲 2025-05-13 2025-03-10
signal to noise ratio 🫘 2025-05-13 2025-02-10
sometimes spectral algorithms fail 🌲 2025-05-13 2025-02-12
spectral clustering 🫘 2025-05-13 2025-02-10
spectral embedding 🌲 2025-05-13 2025-02-12
spectral graph filter 🌲 2025-05-13 2025-02-04
spectral representation of a convolutional graph filter 🌲 2025-05-13 2025-01-29
stability and size tradeoff for realistic sparsity pattern considerations setting 🪴 2025-05-13 2025-03-10
stability-discriminability tradeoff for Lipschitz filters 🌲 2025-05-13 2025-03-10
stable graph filter 🌲 2025-05-13 2025-03-10
statistical risk minimization problem 🌲 2025-05-13 2025-02-04
stochastic block model 🌲 2025-05-13 2025-02-10
template graphs converge to the graphon 🌲 2025-05-13 2025-03-26
the spectral graph filter operates on a signal pointwise 🌲 2025-05-13 2025-01-29
the spectral representation of a graph filter is independent from the graph 🌲 2025-05-13 2025-01-29
we can represent any analytic function with convolutional graph filters 🌲 2025-05-13 2025-02-04
we can use GNNs to solve feature-aware semi-supervised learning problems 🌲 2025-05-13 2025-02-12
weighted sampled graphs converge to the graphon in probability 🌲 2025-05-13 2025-03-26
Hilbert-Schmidt integral operator 🌱 2025-04-15 2025-03-31
equivariant 🌲 2025-04-15 2025-01-30
singular value decomposition 🌲 2025-04-15 2024-10-11
invariant 🌲 2025-03-26 2025-01-30