Can the 2.25 Matrix Bound Work Over Every Field?
#matrixmultiplication #fieldtheory #rootsofunity #computationalcomplexity
#matrixmultiplication #fieldtheory #rootsofunity #computationalcomplexity
November 4, 2026 at 2:01 AM
Can the 2.25 Matrix Bound Work Over Every Field?
#matrixmultiplication #fieldtheory #rootsofunity #computationalcomplexity
#matrixmultiplication #fieldtheory #rootsofunity #computationalcomplexity
How One Shift Forces a Profile to Triple
The shifted-tripling inequality is a compact statement with a powerful consequence: P(a, 3h + a − 1) ≥ 3P(a, h).
#tensortheory #matrixmultiplication #computationalcomplexity #mathematics
The shifted-tripling inequality is a compact statement with a powerful consequence: P(a, 3h + a − 1) ≥ 3P(a, h).
#tensortheory #matrixmultiplication #computationalcomplexity #mathematics
November 2, 2026 at 10:01 PM
How One Shift Forces a Profile to Triple
The shifted-tripling inequality is a compact statement with a powerful consequence: P(a, 3h + a − 1) ≥ 3P(a, h).
#tensortheory #matrixmultiplication #computationalcomplexity #mathematics
The shifted-tripling inequality is a compact statement with a powerful consequence: P(a, 3h + a − 1) ≥ 3P(a, h).
#tensortheory #matrixmultiplication #computationalcomplexity #mathematics
GEG-IAMP achieves (1−ε)-approximation to maximum SK energy with O(N²/ε) work and polynomial dimension threshold, improving prior exponential bounds and providing first asymptotic FPRAS for this NP-hard optimization problem.
#Optimization #ComputationalComplexity #Research
#Optimization #ComputationalComplexity #Research
Polynomial-Time Approximation Algorithm for the Sherrington-Kirkpatrick Model
iq.fp2.dev
November 5, 2026 at 10:14 AM
GEG-IAMP achieves (1−ε)-approximation to maximum SK energy with O(N²/ε) work and polynomial dimension threshold, improving prior exponential bounds and providing first asymptotic FPRAS for this NP-hard optimization problem.
#Optimization #ComputationalComplexity #Research
#Optimization #ComputationalComplexity #Research
How t ≤ 3/4 Becomes ω(ℂ) ≤ 2.25
A bound on matrix multiplication can emerge from a parameter that does not initially look like matrix multiplication at all.
#matrixmultiplication #computationalcomplexity #tensormath #complexnumbers
A bound on matrix multiplication can emerge from a parameter that does not initially look like matrix multiplication at all.
#matrixmultiplication #computationalcomplexity #tensormath #complexnumbers
November 3, 2026 at 6:02 PM
How t ≤ 3/4 Becomes ω(ℂ) ≤ 2.25
A bound on matrix multiplication can emerge from a parameter that does not initially look like matrix multiplication at all.
#matrixmultiplication #computationalcomplexity #tensormath #complexnumbers
A bound on matrix multiplication can emerge from a parameter that does not initially look like matrix multiplication at all.
#matrixmultiplication #computationalcomplexity #tensormath #complexnumbers
Everything Comes Down to t ≤ 3/4
The decisive move is a squeeze on the diagonal of an abstract profile P(a,b).
#matrixmultiplication #computationalcomplexity #tensormath #mathvisualization
The decisive move is a squeeze on the diagonal of an abstract profile P(a,b).
#matrixmultiplication #computationalcomplexity #tensormath #mathvisualization
November 2, 2026 at 2:01 AM
Everything Comes Down to t ≤ 3/4
The decisive move is a squeeze on the diagonal of an abstract profile P(a,b).
#matrixmultiplication #computationalcomplexity #tensormath #mathvisualization
The decisive move is a squeeze on the diagonal of an abstract profile P(a,b).
#matrixmultiplication #computationalcomplexity #tensormath #mathvisualization
Matrix Multiplication Is a Tensor Problem
A single entry of XY comes from one row of X paired with one column of Y.
#matrixmultiplication #tensorrank #computationalcomplexity #mathematics
A single entry of XY comes from one row of X paired with one column of Y.
#matrixmultiplication #tensorrank #computationalcomplexity #mathematics
November 1, 2026 at 10:02 PM
Matrix Multiplication Is a Tensor Problem
A single entry of XY comes from one row of X paired with one column of Y.
#matrixmultiplication #tensorrank #computationalcomplexity #mathematics
A single entry of XY comes from one row of X paired with one column of Y.
#matrixmultiplication #tensorrank #computationalcomplexity #mathematics
No, OpenAI Didn’t Make Your GPU Faster
A lower matrix-multiplication exponent is not a software update.
#matrixmultiplication #computationalcomplexity #algorithms #mathematics
A lower matrix-multiplication exponent is not a software update.
#matrixmultiplication #computationalcomplexity #algorithms #mathematics
October 31, 2026 at 6:01 PM
No, OpenAI Didn’t Make Your GPU Faster
A lower matrix-multiplication exponent is not a software update.
#matrixmultiplication #computationalcomplexity #algorithms #mathematics
A lower matrix-multiplication exponent is not a software update.
#matrixmultiplication #computationalcomplexity #algorithms #mathematics
Why Polynomial Multiplication Appears in the 2.25 Proof
The surprising move in this proof architecture is to feed tensor characters polynomial multiplication tensors—not ordinary matrix tensors.
#matrixtensors #polynomialmultiplication #computationalcomplexity #mathematics
The surprising move in this proof architecture is to feed tensor characters polynomial multiplication tensors—not ordinary matrix tensors.
#matrixtensors #polynomialmultiplication #computationalcomplexity #mathematics
November 1, 2026 at 6:01 PM
Why Polynomial Multiplication Appears in the 2.25 Proof
The surprising move in this proof architecture is to feed tensor characters polynomial multiplication tensors—not ordinary matrix tensors.
#matrixtensors #polynomialmultiplication #computationalcomplexity #mathematics
The surprising move in this proof architecture is to feed tensor characters polynomial multiplication tensors—not ordinary matrix tensors.
#matrixtensors #polynomialmultiplication #computationalcomplexity #mathematics
Why 2.25 Is a Huge Jump From 2.371177
A change from 2.371177 to 2.25 looks like only 0.121177. For matrix multiplication, it is not a small change: these numbers are exponents.
#matrixmultiplication #computationalcomplexity #algorithms #math
A change from 2.371177 to 2.25 looks like only 0.121177. For matrix multiplication, it is not a small change: these numbers are exponents.
#matrixmultiplication #computationalcomplexity #algorithms #math
October 31, 2026 at 2:01 PM
Why 2.25 Is a Huge Jump From 2.371177
A change from 2.371177 to 2.25 looks like only 0.121177. For matrix multiplication, it is not a small change: these numbers are exponents.
#matrixmultiplication #computationalcomplexity #algorithms #math
A change from 2.371177 to 2.25 looks like only 0.121177. For matrix multiplication, it is not a small change: these numbers are exponents.
#matrixmultiplication #computationalcomplexity #algorithms #math
Why 7 Multiplications Beat 8
The standard 2×2 block method looks locked into eight multiplications: each of the four output blocks needs two block products. Strassen’s 1969 insight was to rearrange the algebra.
#matrixmultiplication #strassenalgorithm #computationalcomplexity #math
The standard 2×2 block method looks locked into eight multiplications: each of the four output blocks needs two block products. Strassen’s 1969 insight was to rearrange the algebra.
#matrixmultiplication #strassenalgorithm #computationalcomplexity #math
November 1, 2026 at 2:01 AM
Why 7 Multiplications Beat 8
The standard 2×2 block method looks locked into eight multiplications: each of the four output blocks needs two block products. Strassen’s 1969 insight was to rearrange the algebra.
#matrixmultiplication #strassenalgorithm #computationalcomplexity #math
The standard 2×2 block method looks locked into eight multiplications: each of the four output blocks needs two block products. Strassen’s 1969 insight was to rearrange the algebra.
#matrixmultiplication #strassenalgorithm #computationalcomplexity #math
Resolves fundamental gap in quantum complexity: determining homology of weighted clique complexes is QMA₁-hard with inverse-polynomial spectral gaps. Uses topological gadget encodings and filtered-Hodge theory for complete hardness proof.
#QuantumComplexity #ComputationalComplexity #Research
#QuantumComplexity #ComputationalComplexity #Research
Complete Proof of QMA₁-Hardness for Weighted Gapped Clique Homology
arxiv.org
October 13, 2026 at 1:56 PM
Resolves fundamental gap in quantum complexity: determining homology of weighted clique complexes is QMA₁-hard with inverse-polynomial spectral gaps. Uses topological gadget encodings and filtered-Hodge theory for complete hardness proof.
#QuantumComplexity #ComputationalComplexity #Research
#QuantumComplexity #ComputationalComplexity #Research
Vor 15 Jahren: Der Tod von Dennis Ritchie hinterlässt immer noch Spuren.
„How did Dennis Ritchie Produce his PhD Thesis?“ versucht das typographische Rätsel seiner Doktorarbeit zu lösen. Eine faszinierende Entdeckungsreise in die Zeit der Kugelkopf-Schreibmaschinen vor dem „Desktop Publishing“.
„How did Dennis Ritchie Produce his PhD Thesis?“ versucht das typographische Rätsel seiner Doktorarbeit zu lösen. Eine faszinierende Entdeckungsreise in die Zeit der Kugelkopf-Schreibmaschinen vor dem „Desktop Publishing“.
October 12, 2026 at 6:59 AM
Vor 15 Jahren: Der Tod von Dennis Ritchie hinterlässt immer noch Spuren.
„How did Dennis Ritchie Produce his PhD Thesis?“ versucht das typographische Rätsel seiner Doktorarbeit zu lösen. Eine faszinierende Entdeckungsreise in die Zeit der Kugelkopf-Schreibmaschinen vor dem „Desktop Publishing“.
„How did Dennis Ritchie Produce his PhD Thesis?“ versucht das typographische Rätsel seiner Doktorarbeit zu lösen. Eine faszinierende Entdeckungsreise in die Zeit der Kugelkopf-Schreibmaschinen vor dem „Desktop Publishing“.
As #AI Closed In on ‘Unique Games’ Proof, Researchers Raced to Beat the Machines
#ComputationalComplexity #Technology
#ComputationalComplexity #Technology
As AI Closed In on ‘Unique Games’ Proof, Researchers Raced to Beat the Machines | Quanta Magazine
In the shadow of a rumored AI proof of one of the biggest problems in their field, three computer scientists rushed to publish their own milestone result.
www.quantamagazine.org
October 9, 2026 at 5:53 PM
As #AI Closed In on ‘Unique Games’ Proof, Researchers Raced to Beat the Machines
#ComputationalComplexity #Technology
#ComputationalComplexity #Technology
As #AI Closed In on ‘Unique Games’ Proof, Researchers Raced to Beat the Machines
#ComputationalComplexity #Technology
#ComputationalComplexity #Technology
As AI Closed In on ‘Unique Games’ Proof, Researchers Raced to Beat the Machines | Quanta Magazine
In the shadow of a rumored AI proof of one of the biggest problems in their field, three computer scientists rushed to publish their own milestone result.
www.quantamagazine.org
October 9, 2026 at 5:53 PM
As #AI Closed In on ‘Unique Games’ Proof, Researchers Raced to Beat the Machines
#ComputationalComplexity #Technology
#ComputationalComplexity #Technology
AIによる「Unique Games Conjecture」証明の波紋：人間と機械の競争が理論計算機科学にもたらす変革
AIの数学・計算量理論への進出と、人間研究者による直前のマイルストーン達成の攻防を解説。
#TheoreticalComputerScience #AI #GraphTheory #AutomatedReasoning #ComputationalComplexity
AIの数学・計算量理論への進出と、人間研究者による直前のマイルストーン達成の攻防を解説。
#TheoreticalComputerScience #AI #GraphTheory #AutomatedReasoning #ComputationalComplexity
AIによる「Unique Games Conjecture」証明の波紋：人間と機械の競争が理論計算機科学にもたらす変革
AIの数学・計算量理論への進出と、人間研究者による直前のマイルストーン達成の攻防を解説。
ai.warp-studio.com
October 8, 2026 at 2:26 AM
AIによる「Unique Games Conjecture」証明の波紋：人間と機械の競争が理論計算機科学にもたらす変革
AIの数学・計算量理論への進出と、人間研究者による直前のマイルストーン達成の攻防を解説。
#TheoreticalComputerScience #AI #GraphTheory #AutomatedReasoning #ComputationalComplexity
AIの数学・計算量理論への進出と、人間研究者による直前のマイルストーン達成の攻防を解説。
#TheoreticalComputerScience #AI #GraphTheory #AutomatedReasoning #ComputationalComplexity
A quantum oracle exists where NP is hard on average but quantum cryptographic primitives (EFI pairs, OWPuzzs) provably don't exist—establishing that quantum cryptography isn't fundamental to computational hardness.
#QuantumCryptography #ComputationalComplexity #Research
#QuantumCryptography #ComputationalComplexity #Research
Quantum Pessiland: Hardness Without Quantum Cryptography
arxiv.org
September 1, 2026 at 1:47 AM
A quantum oracle exists where NP is hard on average but quantum cryptographic primitives (EFI pairs, OWPuzzs) provably don't exist—establishing that quantum cryptography isn't fundamental to computational hardness.
#QuantumCryptography #ComputationalComplexity #Research
#QuantumCryptography #ComputationalComplexity #Research
en.wikipedia.org/wiki/Promise...
"
In #ComputationalComplexity theory, a #PromiseProblem is a generalization of a #DecisionProblem where the input is promised to belong to a particular subset of #AllPossibleInputs.
"
In #ComputationalComplexity theory, a #PromiseProblem is a generalization of a #DecisionProblem where the input is promised to belong to a particular subset of #AllPossibleInputs.
Promise problem - Wikipedia
en.wikipedia.org
August 29, 2026 at 4:24 AM
en.wikipedia.org/wiki/Promise...
"
In #ComputationalComplexity theory, a #PromiseProblem is a generalization of a #DecisionProblem where the input is promised to belong to a particular subset of #AllPossibleInputs.
"
In #ComputationalComplexity theory, a #PromiseProblem is a generalization of a #DecisionProblem where the input is promised to belong to a particular subset of #AllPossibleInputs.
I was lead down that #RabbitHole by:
en.wikipedia.org/wiki/BQP
"
In #ComputationalComplexity theory, #BoundedError #QuantumPolynomialTime ( #BQP) is the class of #DecisionProblems solvable by a #QuantumComputer in #PolynomialTime, with an #ErrorProbability of at most 1/3 for all instances.
en.wikipedia.org/wiki/BQP
"
In #ComputationalComplexity theory, #BoundedError #QuantumPolynomialTime ( #BQP) is the class of #DecisionProblems solvable by a #QuantumComputer in #PolynomialTime, with an #ErrorProbability of at most 1/3 for all instances.
BQP - Wikipedia
en.wikipedia.org
August 29, 2026 at 4:27 AM
I was lead down that #RabbitHole by:
en.wikipedia.org/wiki/BQP
"
In #ComputationalComplexity theory, #BoundedError #QuantumPolynomialTime ( #BQP) is the class of #DecisionProblems solvable by a #QuantumComputer in #PolynomialTime, with an #ErrorProbability of at most 1/3 for all instances.
en.wikipedia.org/wiki/BQP
"
In #ComputationalComplexity theory, #BoundedError #QuantumPolynomialTime ( #BQP) is the class of #DecisionProblems solvable by a #QuantumComputer in #PolynomialTime, with an #ErrorProbability of at most 1/3 for all instances.
🔥 Advancing Matrix Multiplication Complexity: A New Bound via AlphaEvolve
https://pneumetron.com/news/ai_research/advancing-matrix-multiplication-complexity-alphaevolve-c9d82d
#matrixmultiplication #computationalcomplexity #alphaevolve #optimization
https://pneumetron.com/news/ai_research/advancing-matrix-multiplication-complexity-alphaevolve-c9d82d
#matrixmultiplication #computationalcomplexity #alphaevolve #optimization
August 26, 2026 at 6:38 AM
🔥 Advancing Matrix Multiplication Complexity: A New Bound via AlphaEvolve
https://pneumetron.com/news/ai_research/advancing-matrix-multiplication-complexity-alphaevolve-c9d82d
#matrixmultiplication #computationalcomplexity #alphaevolve #optimization
https://pneumetron.com/news/ai_research/advancing-matrix-multiplication-complexity-alphaevolve-c9d82d
#matrixmultiplication #computationalcomplexity #alphaevolve #optimization
Quantum algorithm achieves polynomial log(q)-complexity approximation of torus points over finite fields, while proof shows the problem becomes #P-hard with unrestricted support parameters—revealing fundamental tradeoffs in quantum advantage.
#QuantumAlgorithms #ComputationalComplexity #Research
#QuantumAlgorithms #ComputationalComplexity #Research
Quantum Algorithms for Torus Point-Count Approximation Over Finite Fields
arxiv.org
August 26, 2026 at 5:38 AM
Quantum algorithm achieves polynomial log(q)-complexity approximation of torus points over finite fields, while proof shows the problem becomes #P-hard with unrestricted support parameters—revealing fundamental tradeoffs in quantum advantage.
#QuantumAlgorithms #ComputationalComplexity #Research
#QuantumAlgorithms #ComputationalComplexity #Research
We establish fundamental computational barriers to efficient decoding of topological quantum codes, proving that minimum-weight decoding cannot be approximated better than Ω(N^1/14) without solving NP-hard problems.
#QuantumErrorCorrection #ComputationalComplexity #Research
#QuantumErrorCorrection #ComputationalComplexity #Research
Hardness of Approximation for Minimum-Weight Decoding of Topological Quantum Codes
arxiv.org
August 19, 2026 at 7:14 AM
We establish fundamental computational barriers to efficient decoding of topological quantum codes, proving that minimum-weight decoding cannot be approximated better than Ω(N^1/14) without solving NP-hard problems.
#QuantumErrorCorrection #ComputationalComplexity #Research
#QuantumErrorCorrection #ComputationalComplexity #Research
Hybrid CS Theory Seminar today (2026-07-13)
Excited to have Jack Stade (U. Copenhagen) presenting "The Boundary-Boundary Art-Gallery Problem is in NP" (which won Best Student Paper at STOC this year)
www.colorado.edu/cs-theory/th...
#MathSky #TCSSky #algorithms #geometry #ComputationalComplexity
Excited to have Jack Stade (U. Copenhagen) presenting "The Boundary-Boundary Art-Gallery Problem is in NP" (which won Best Student Paper at STOC this year)
www.colorado.edu/cs-theory/th...
#MathSky #TCSSky #algorithms #geometry #ComputationalComplexity
July 13, 2026 at 3:51 PM
Hybrid CS Theory Seminar today (2026-07-13)
Excited to have Jack Stade (U. Copenhagen) presenting "The Boundary-Boundary Art-Gallery Problem is in NP" (which won Best Student Paper at STOC this year)
www.colorado.edu/cs-theory/th...
#MathSky #TCSSky #algorithms #geometry #ComputationalComplexity
Excited to have Jack Stade (U. Copenhagen) presenting "The Boundary-Boundary Art-Gallery Problem is in NP" (which won Best Student Paper at STOC this year)
www.colorado.edu/cs-theory/th...
#MathSky #TCSSky #algorithms #geometry #ComputationalComplexity
Hybrid CS Theory Seminar today 2025-03-14
We're excited to have Spencer Peters from Cornell presenting "Recursive Lattice Reduction"
spencerpeters.io
www.colorado.edu/cs-theory/th...
#MathSky #Algorithms #ComputationalComplexity
We're excited to have Spencer Peters from Cornell presenting "Recursive Lattice Reduction"
spencerpeters.io
www.colorado.edu/cs-theory/th...
#MathSky #Algorithms #ComputationalComplexity
Home - Spencer Peters
spencerpeters.io
March 14, 2025 at 4:02 PM
Hybrid CS Theory Seminar today 2025-03-14
We're excited to have Spencer Peters from Cornell presenting "Recursive Lattice Reduction"
spencerpeters.io
www.colorado.edu/cs-theory/th...
#MathSky #Algorithms #ComputationalComplexity
We're excited to have Spencer Peters from Cornell presenting "Recursive Lattice Reduction"
spencerpeters.io
www.colorado.edu/cs-theory/th...
#MathSky #Algorithms #ComputationalComplexity
Happy Birthday, Richard E. Stearns! Stearns received the 1993 #ACMTuringAward with Juris Hartmanis in recognition of their seminal paper which established the foundations for the field of computational complexity theory. youtu.be/Z-Ek0CCThZQ?...
#ComputerScience #computationalcomplexity
#ComputerScience #computationalcomplexity
July 5, 2026 at 12:02 PM
Happy Birthday, Richard E. Stearns! Stearns received the 1993 #ACMTuringAward with Juris Hartmanis in recognition of their seminal paper which established the foundations for the field of computational complexity theory. youtu.be/Z-Ek0CCThZQ?...
#ComputerScience #computationalcomplexity
#ComputerScience #computationalcomplexity
Well played.
https://link.springer.com/chapter/10.1007/978-3-642-13122-6_15
#uno #cardgames #ComputationalComplexity #funwithalgorithms #algorithms #algorithmics #games #ai #computerscience #professorlife
https://link.springer.com/chapter/10.1007/978-3-642-13122-6_15
#uno #cardgames #ComputationalComplexity #funwithalgorithms #algorithms #algorithmics #games #ai #computerscience #professorlife
February 18, 2026 at 3:05 PM