Logarithmic-time schedules boost large-scale language model training efficiency.
problem Improving performance and efficiency in large-scale language model training.
method Designing time-varying hyperparameters ( β 1 , β 2 , λ ) (β_1, β_2, λ) ( β 1 , β 2 , λ ) for AdamW, specifically logarithmic-time scheduling with damping mechanisms. result ADANA optimizer achieves up to 40% compute efficiency compared to tuned AdamW, with gains persisting as model scale increases.
Logarithmic improvements in eigenfunction restriction estimates on hyperbolic manifolds.
problem Logarithmic improvements of L 2 L^2 L 2 geodesic restriction estimates for eigenfunctions. method Adapting Chen and Sogge's approach, using explicit wave kernel formula, and detailed oscillatory integral estimates.
result Logarithmic improvement to ( log λ ) − 1 2 (\logλ)^{-\frac12} ( log λ ) − 2 1 in L 2 L^2 L 2 -restriction bounds. The study improves upper bounds on nodal sets using quantum ergodicity.
problem Improving upper bounds on the size of nodal sets of eigenfunctions.
method Application of small scale quantum ergodicity in nodal sets.
result Logarithmic improvements on nodal sets for negatively curved manifolds.
New bounds on minimax regret for sequential probability assignment using logarithmic loss.
problem Minimizing regret in sequential probability assignment against arbitrary experts.
method Using self-concordance property of logarithmic loss to derive tight bounds.
result Tight bounds on minimax regret for various expert classes.
Quantum computing speeds up training Gaussian processes exponentially.
problem Training Gaussian processes efficiently.
method Quantum algorithms for computing the logarithm of the determinant and matrix inversion.
result Exponential improvement in estimating the marginal likelihood of Gaussian processes.
The study improves Bochner inequality on Finsler manifolds to derive important inequalities.
problem Improving Bochner inequality on Finsler manifolds to derive new inequalities.
method Using improved Bochner inequality and its integrated form, the study derives a sharp Poincaré-Lichnerowicz inequality, a new proof for logarithmic Sobolev inequality, and an estimate of geodesic ball volumes.
result Derivation of new inequalities and estimates on Finsler manifolds.
New binary approach for multiclass classification scales logarithmically with classes.
problem Efficient multiclass classification for large number of classes.
method Proves a boosting theorem and translates it into an algorithm.
result Exponential speed improvements for large number of classes.
The paper improves estimates of eigenfunctions and nodal sets on manifolds with nonpositive sectional curvature.
problem Improving estimates of eigenfunctions and nodal sets on manifolds with nonpositive sectional curvature.
method Combining Toponogov's triangle comparison theorem and propagation of singularities arguments.
result Logarithmic improvements of eigenfunction and nodal set estimates.
This work improves policy evaluation and selection using logarithmic smoothing for pessimistic off-policy estimation.
problem Offline evaluation and selection of policies from past data.
method Develops novel concentration bounds and a logarithmically smoothed estimator (LS) for improved policy selection and learning.
result The logarithmically smoothed estimator (LS) provides tighter bounds and better policy selection and learning.
WaveletNet improves edge device efficiency with logarithmic convolution.
problem Efficiency and performance on edge devices for CNNs.
method Introduces WaveletNet architecture with wavelet convolution and depthwise fast wavelet transform.
result WaveletNet achieves superior and comparable performance to state-of-the-art models on CIFAR-10 and ImageNet.
New bounds for Bayesian bandits show prior improves performance.
problem Improving regret bounds for Bayesian bandits.
method Upper confidence bound algorithm with finite-time logarithmic regret bounds.
result Derives O ( c Δ log n ) O(c_Δ\log n) O ( c Δ log n ) and O ( c h log 2 n ) O(c_h \log^2 n) O ( c h log 2 n ) upper bounds for Bayesian bandits. The study improves bounds on the number of closed geodesics and logarithmic improvements in the Weyl law.
problem Estimating the number of closed geodesics and improving logarithmic bounds in the Weyl law.
method Study of non-degeneracy properties of nearly closed orbits for predominant sets of metrics.
result Logarithmic improvements in the Weyl law and exponential bounds on the number of closed geodesics.
For word-equations in groups, we find a logarithmic bound on non-solutions.
problem Finding the length of non-solutions to word-equations in groups.
method Analyzing finite-rank free groups and applying results to broader classes of groups.
result Logarithmic bound on non-solutions for word-equations in groups.
Paper analyzes and improves KL-regularized RL for LLMs with logarithmic regret.
problem Improving efficiency of RL fine-tuning for large language models.
method Optimism-based KL-regularized online contextual bandit algorithm with novel regret analysis.
result Achieves an O ( η log ( N R T ) ⋅ d R ) \mathcal{O}\big(η\log (N_{\mathcal R} T)\cdot d_{\mathcal R}\big) O ( η log ( N R T ) ⋅ d R ) logarithmic regret bound. Improved activation function NLReLU boosts neural network performance.
problem Performance issues with ReLU activation function.
method NLReLU uses parametric natural logarithmic transform to improve ReLU.
result NLReLU provides higher accuracy than ReLU in various neural networks.
CMT efficiently manages memory by inserting and querying memories in logarithmic time.
problem Managing large memory stores efficiently for quick access and updates.
method Designing a Contextual Memory Tree (CMT) that inserts and retrieves memories in logarithmic time.
result CMT improves classification algorithms and image-captioning tasks, demonstrating better computational efficiency.
Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.
problem Queue peak laws in stochastic networks with geometric thresholds.
method Self-normalization mechanism
result Logarithmic scaling of queue peaks after geometric thresholds.
Greedy pruning reduces neural networks by a logarithmic number of tickets, improving accuracy.
problem Pruning large neural networks to reduce size while maintaining accuracy.
method Greedy optimization-based pruning method with exponential decay guarantee.
result The discrepancy between pruned and original networks decays exponentially with network size.
Sharp estimates for diffusion and Ricci flow on surfaces.
problem Improving estimates for diffusion and flow equations.
method Proving sharp local L^1 - L^∞ smoothing estimates.
result Sharp decay estimates for logarithmic fast diffusion equation and Ricci flow on surfaces.
Paper shows FB and FC are equally hard up to logarithmic factors.
problem Comparing fixed budget and fixed confidence approaches in best-arm identification.
method Proposes FC2FB, a meta algorithm converting FC to FB.
result FC sample complexity is an upper bound for FB sample complexity up to logarithmic factors.
New algorithm for sequential off-policy learning improves performance over batch methods.
problem Training policies from logged interaction data in a sequential setting.
method Combines Logarithmic Smoothing with online PAC-Bayesian tools.
result Improves performance and accelerates convergence in sequential off-policy learning.
The paper proves the concavity of p p p -entropy power and applies it to functional inequalities.
problem Proving concavity of p p p -entropy power on Riemannian manifolds. method Analyzing the p p p -heat equation on closed Riemannian manifolds with nonnegative Ricci curvature. result New proofs and improvements of L p L^p L p -Euclidean Nash and Logarithmic Sobolev inequalities. In this paper, we introduce the notions of logarithmic Poisson structure and logarithmic principal Poisson structure; we prove that the latter induces a representation by logarithmic derivation of the module of logarithmic Kahler differentials; therefore, it induces a differential complex from which we derive the notio…
Paper analyzes and improves adaptive gradient methods for optimization.
problem Improving optimization methods for deep neural networks.
method Analyzes and proposes variants of RMSProp and Adagrad for online convex optimization.
result Proposes SC-Adagrad and SC-RMSProp with logarithmic regret bounds for strongly convex functions.
Improved SVRG for quadratic functions achieves better performance and running times.
problem Minimizing quadratic functions with a specific type of Hessian matrix.
method Variant of SVRG algorithm for quadratic functions with improved analysis.
result Improved performance and running times for quadratic functions compared to state-of-the-art methods.
Quantum ergodic eigenfunctions improve inner radius bounds of nodal domains.
problem Improving bounds on inner radius of nodal domains for quantum ergodic eigenfunctions.
method Using recent results on eigenfunction equidistribution on small balls and modified growth estimates.
result Logarithmic and polynomial improvements on inner radius for various manifolds.
Oracle-efficient algorithms reduce combinatorial semi-bandit regret to logarithmic time.
problem Scalability issue in combinatorial semi-bandit problems due to high combinatorial optimization costs.
method Oracle-efficient frameworks that minimize oracle queries while maintaining tight regret guarantees.
result Achieved i l d e O ( T ) ilde{O}(\sqrt{T}) i l d e O ( T ) regret with O ( log log T ) O(\log\log T) O ( log log T ) oracle queries for worst-case linear rewards. Optimizes quantile and semi-adversarial regret with novel root-logarithmic regularizers.
problem Minimizes regret in adversarial and semi-adversarial online learning.
method FTRL with root-logarithmic regularizers for quantile and semi-adversarial settings.
result Achieves minimax optimal regret bounds in both paradigms.
New method solves ∂ ˉ \bar{\partial} ∂ ˉ -equations for logarithmic forms on Kahler manifolds.
problem Solving ∂ ˉ \bar{\partial} ∂ ˉ -equations for logarithmic forms on Kahler manifolds. method Using harmonic integral theory for currents on Kahler manifolds.
result Constructs the extension for logarithmic ( n , q ) (n,q) ( n , q ) -forms on the central fiber. Develops a new option pricing model under G-expectation framework.
problem Modeling uncertainty in financial markets and robust valuation under model uncertainty.
method G-expectation framework, logarithmic transformation, finite difference schemes.
result Unified risk-neutral valuation approach yielding G-Black-Scholes equation.
Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.
problem Gap between upper and lower bounds on sample complexity for fat-shattering dimension.
method Provided an improved uniform convergence bound.
result Closed the gap between existing upper and lower bounds on sample complexity.
Study rigidity by logarithmic capacity and related functions.
problem Rigidity phenomena in kernel functions and capacities.
method Exploration of Bergman kernel, logarithmic capacity, Green's function, and Euclidean distance/volume.
result Established rigidity theorems by logarithmic capacity.
Enhanced Dantzig selector reduces recovery error in high dimensions.
problem Improving recovery accuracy in ultra-high dimensional settings.
method Constrained Dantzig selector with sequential linear programming.
result Achieves convergence rates within a logarithmic factor of the sample size of oracle rates.
Modified Bakry-Émery criterion inequality for Tsallis entropy monotonicity.
problem Establishing improved logarithmic Sobolev inequalities and monotonicity of Tsallis entropy.
method Proving a one-parameter family of weighted Bakry-Émery Γ 2 Γ_2 Γ 2 criterion inequalities and a modified inequality. result Yields a family of sharp Sobolev inequalities and monotonicity of Tsallis entropy.
New rule reduces exploration regret to logarithmic, improving bad episode handling.
problem Improving exploration regret in average reward MDPs.
method Replacing Doubling Trick with Vanishing Multiplicative rule in EVI-based algorithms.
result Regret is logarithmic under the new rule, significantly better than linear.
Study excess logarithmic residues for foliations to bound invariant hypersurfaces and test log canonicity.
problem Bounding invariant hypersurfaces and testing log canonicity of singularities.
method Introduce excess logarithmic residues, prove residue formula, derive Poincaré-type bound, and use them to recover log discrepancies.
result Componentwise logarithmic residues of a lifted foliation along the exceptional divisor recover log discrepancies of singularities.
Logarithmic connections on principal bundles over normal varieties are studied.
problem Existence and properties of logarithmic connections on principal bundles over normal varieties.
method Introducing logarithmic connections, showing equivalence to covariant derivatives, and proving existence conditions.
result Existence of logarithmic connections on principal bundles over normal varieties is equivalent to certain conditions on the associated vector bundles and adjoint bundles.
Study real logarithms of semi-simple matrices, focusing on differential structure.
problem Understanding the differential structure of real logarithms of semi-simple matrices.
method Examines the differential structure of real logarithms of semi-simple matrices under specific matrix types.
result Characterizes the differential structure of real logarithms of semi-simple matrices.
Introduces logarithmic Cartan geometry on complex manifolds with singularities.
problem Holomorphic Cartan geometry with singularities.
method Definition and study of logarithmic Cartan geometry on complex manifolds with polar part supported on a normal crossing divisor.
result Push-forward of a Cartan geometry constructed using a finite Galois ramified covering is a logarithmic Cartan geometry.
PPO-B improves sampling efficiency by using a logarithmic barrier method.
problem Low sampling efficiency in PPO due to exterior penalty method.
method Introducing a surrogate objective with interior penalty method.
result PPO-B outperforms PPO in terms of sampling efficiency.
Method identifies low-dimensional structure in high-dimensional probability measures.
problem Identifying low-dimensional structure in high-dimensional probability measures.
method Extends prior work on minimizing majorizations of the Kullback-Leibler divergence to identify optimal approximations within a specific class of measures.
result Connection between dimensional logarithmic Sobolev inequality and approximations with the ansatz.
Local logarithmic Brunn-Minkowski holds for zonoids.
problem Logarithmic Brunn-Minkowski conjecture for zonoids
method Bochner method variant
result Local form of conjecture proven for zonoids
Study Kähler-Einstein potentials on stable varieties near singularities
problem Asymptotic behavior of Kähler-Einstein potentials on stable varieties near singularities
method Using iterated logarithmic functions and refined lower bounds
result Improved estimates for Kähler-Einstein potentials
New framework for logarithmically divergent integrals on manifolds with corners.
problem Logarithmically divergent integrals on manifolds with corners.
method Introduces new geometric framework and morphisms in logarithmic geometry.
result Functorial characterization of regularized integration.
Improved GNN simulation of WL test with exponentially lower complexity.
problem Improving the complexity of simulating the Weisfeiler-Lehman test with GNNs.
method Exponentially lower complexity simulation of WL test using GNNs with polylogarithmic parameters and O(log n) bits feature vectors.
result Near-optimal construction with logarithmic lower bounds for feature vector length and neural network size.
Improved sampling for high-dimensional posteriors with underdamped Langevin.
problem Scalability issues in high-dimensional problems with approximate Thompson sampling.
method Underdamped Langevin Monte Carlo for accelerated posterior concentration.
result Logarithmic regret improvement from i l d e O ( d ) \mathcal{ ilde O}(d) i l d e O ( d ) to i l d e O ( d ) \mathcal{ ilde O}(\sqrt{d}) i l d e O ( d ) . Directly proves logarithmic systolic growth for all hyperbolic surfaces.
problem Proving logarithmic systolic growth for all hyperbolic surfaces.
method Using original Brooks/Buser-Sarnak surfaces through a direct approach.
result Directly proves logarithmic systolic growth for all hyperbolic surfaces.
Logarithmic separation profile in hyperbolic groups shows hierarchical structure.
problem Understanding hierarchical structure in hyperbolic groups with logarithmic separation.
method Proving groups with logarithmic separation split over cyclic groups and providing counterexamples.
result Not all groups with hierarchical structure have logarithmic separation profile.