This paper proposes a preconditioning layer for stable weight conditioning in LLM training.

The polynomial-time low-degree conjecture, which predicts that low-degree indistinguishability, a uniform null distribution, permutation invariance, and independent resampling imply polynomial-time ha…

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

The authors introduce a quantum empirical operator and use it to prove a universal achievability result for composite quantum hypothesis testing.

This paper presents two algorithms using the Newton-Raphson method to calculate the floor of y**(1/m) for natural integer numbers y > 2 and m > 1, which can be used to determine if y is an integer pow…

This paper constructs strictly convex quadratic problems and initial points for which the long Barzilai--Borwein method does not converge root-superlinearly.

The paper develops an explicit multi-linear polynomial form for binary polynomial optimization problems after eliminating a subset of variables, allowing for characterization of new special classes wi…

The paper introduces Multifidelity Proper Orthogonal Decomposition (MFPOD), a method that significantly reduces the computational cost of dimension reduction by intelligently combining data from cheap…

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

This paper shows that finding the minimum geodetic set in chordal graphs is fixed parameter tractable, implying a polynomial-time algorithm for k-trees. It also proves that the problem is NP-hard on i…

The paper introduces a non-intrusive variant of index-aware learning for solving differential-algebraic equations (DAEs), ensuring that learned solutions maintain physical consistency like Kirchhoff's…

This paper unconditionally proves the Orthogonal Vectors and Monotone Orthogonal Vectors conjectures in concrete computational models, and provides stronger lower bounds for Boolean formulas and branc…

The paper studies the resources required to batch verify Boolean functions and provides lower bounds on the witness-query tradeoff based on approximate degree.

The paper uses majorization theory to analyze lattice reduction, showing that local swaps smooth the Gram-Schmidt profile and deriving variational and telescoping identities for the worst-case profile…

This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.

This paper derives the gradient of the Wolkowicz-Styan upper bound on the maximum eigenvalue of the cross-entropy loss Hessian in three-layer NNs to characterize directions leading to flat minima and…

The paper establishes conditions for QUBO formulations of combinatorial optimization problems that guarantee valid binary and feasible local minimizers using gradient-based methods.

The paper proposes FOAM, an adaptive damping method that stabilizes the Shampoo optimization algorithm by dynamically controlling damping and eigendecomposition frequency, thereby reducing staleness-i…