Study on when RLVR can learn compositional problems.
problem Understanding when RLVR can learn compositional problems.
method Theoretical analysis of task-advantage ratio to characterize learnability.
result Identified conditions for learnability of compositional problems.
Paper introduces a new learner for generalizing complex tasks.
problem Generalizing to new, complex tasks without prior experience.
method Compositional problem graph and compositional recursive learner.
result Compositional approach can generalize to more complex problems than non-compositional learners.
New method solves doubly-nonconvex composite optimization problems.
problem Solving composite optimization problems with both functions nonconvex.
method Stochastic gradient descent with quasiconvex penalty function.
result Convergence properties for doubly-nonconvex composite optimization.
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with segments of equal size, the composite dimension can be expressed as a function …
C-ADAM is a new adaptive solver for complex nested problems.
problem Solving compositional problems involving nested expected values.
method Adaptive solver for non-linear functional nesting of expected values.
result C-ADAM converges to a stationary point in O ( δ − 2.25 ) O(δ^{-2.25}) O ( δ − 2.25 ) . A new method for faster optimization of machine learning problems.
problem Minimization of composition of expected value functions.
method C-SAG, a novel extension of SAG for FS-CEVF problems.
result C-SAG achieves lower oracle query complexity per iteration than C-SVRG and converges faster.
Paper tackles gradient estimation for large-scale composition problems.
problem Optimization of large-scale composition problems with convex and non-convex structures.
method Stochastically Controlled Stochastic Gradient (SCSG) method for variance reduction.
result Query complexity improved for convex and non-convex problems.
Consider the stochastic composition optimization problem where the objective is a composition of two expected-value functions. We propose a new stochastic first-order method, namely the accelerated stochastic compositional proximal gradient (ASC-PG) method, which updates based on queries to the sampling oracle using tw…
Tree-SMU enables strong compositional generalization in neural networks.
problem Zero-shot generalization to novel compositions of concepts.
method Tree Stack Memory Units (Tree-SMU) with Stack Memory Units (SMU).
result Tree-SMU achieves strong empirical results on mathematical reasoning benchmarks.
Develops consistent approximations for composite optimization problems.
problem Significant errors in solutions due to approximations in optimization problems.
method Specifies conditions for well-behaved approximations in minimizers, stationary points, and level-sets for a broad class of composite problems.
result Framework of consistent approximations for composite problems, including stochastic, neural-network, and multi-objective optimization.
Improved subgradient method tackles ill-conditioned composite optimization problems.
problem Slow convergence of subgradient method for composite optimization problems.
method Preconditioned subgradient method with Levenberg-Marquardt approach.
result Linear convergence rate for composite optimization problems under mild conditions.
New method reduces complexity for nonconvex optimization problems.
problem Minimizing composite functions with random or finite sum inner mappings.
method Stochastic composite gradient method with incremental variance reduction.
result Achieves complexity similar to best first-order methods for expected-value and finite-sum nonconvex functions.
AdaGrad fails to adapt to Hölder-smoothness in composite optimization problems.
problem AdaGrad's convergence rate is suboptimal for composite objectives.
method Exhibited a simple one-dimensional convex problem to highlight AdaGrad's limitations.
result AdaGrad does not achieve the classical convergence rate for Hölder-smooth objectives.
New method solves complex optimization problems efficiently.
problem Optimizing complex functions with inner expectations in machine learning.
method Combines variance reduction methods with duality-free techniques.
result Proves linear convergence for convex and non-convex cases.
Framework for lifelong learning of compositional structures.
problem Learning to reuse self-contained chunks of knowledge for novel problems.
method Separates learning into combining existing components and adapting them.
result Framework handles trade-off between stability and flexibility.
Paper analyzes stability and generalization of SCO algorithms.
problem Understanding how SCO algorithms perform on unseen data.
method Algorithmic stability analysis in statistical learning theory.
result Derives dimension-independent excess risk bounds for SCGD and SCSC.
Unified algorithm for minimizing composite functions with flexible design.
problem Minimizing composite functions with specific structural properties.
method Unified accelerated algorithm for complementary composite minimization.
result Near-optimal algorithms for various optimization problems.
FeDualEx tackles saddle point optimization in federated learning with composite objectives.
problem Saddle point optimization with constraints and non-smooth regularization in federated learning.
method Federated Dual Extrapolation (FeDualEx) algorithm for saddle point optimization and composite objectives.
result FeDualEx effectively solves saddle point optimization problems with composite objectives in federated learning.
Paper proposes iLPA for solving DC composite optimization problems, with applications to matrix completion with outliers.
problem Solving nonconvex and nonsmooth DC composite optimization problems.
method Inexact linearized proximal algorithm (iLPA) for DC composite optimization problems.
result The iLPA achieves local R-linear convergence rate under the Kurdyka-Łöjasiewicz property.
Model predicts composite structures assembly quality with input uncertainty.
problem Accurate prediction of dimensional deviations and residual stress in composite structures assembly.
method Neural Network Gaussian Process considering input uncertainty.
result NNGPIU model outperforms other methods for nonsmooth, nonlinear responses.
New algorithm reduces complexity for optimizing complex machine learning tasks.
problem Optimizing complex machine learning objectives like reinforcement learning and portfolio management.
method Developed SARAH-Compositional algorithm using Stochastic Recursive Gradient Descent.
result Achieved optimal IFO complexity bounds for stochastic compositional optimization.
New MCMC method for generating composition ratios.
problem Combining and selecting knowledge to create new compositions.
method Proposes a new MCMC algorithm with specific constraints.
result Shows the effectiveness of combining MCMC with supervised learning.
Extends knockoff filter for composite null hypotheses in variable selection.
problem Handling composite null hypotheses in variable selection.
method Developed two methods for composite inference with knockoffs: S-OLS and FRPP.
result Proposed heuristic variants of S-OLS outperforming BH procedure for composite nulls.
RICH models scenes as hierarchical tree to learn and generate complex compositions.
problem Learning compositional structures between parts and objects in natural scenes.
method RICH uses a latent scene graph to organize entities into a tree structure and employs a top-down inference approach.
result RICH learns and generates complex scene hierarchies from unlabeled data.
Routing networks tackle challenges in modular and compositional computation.
problem Challenges in learning and training compositional models with module parameters and their composition.
method Routing networks as a general approach to address these challenges, examining the interplay of algorithmic decisions.
result Empirical analysis of routing networks reveals the interplay of challenges and design decisions.
This paper advances FL algorithms for composite optimization and statistical recovery.
problem Federated learning optimization and statistical recovery in composite settings.
method Proposes Fast Federated Dual Averaging for strongly convex and smooth loss, and Multi-stage Federated Dual Averaging for restricted strongly convex and smooth loss.
result Establishes state-of-the-art iteration and communication complexity, and high probability complexity bound with linear speedup.
Study challenges neural models in compositional learning tasks.
problem Challenges in neural models for compositional and relational learning.
method Introduced ConceptWorld environment for generating images from compositional concepts, tested various neural architectures.
result Neural models struggle with longer compositional chains and substitutivity tests.
Adapts Altman's model to compositional data for bankruptcy prediction.
problem Predicting business default using standard financial ratios has issues.
method Uses compositional data methodology with log-ratios and machine learning.
result Compositional methods improve predictive performance, especially random forests.
New method for optimizing complex composite functions with reduced variance.
problem Optimizing multi-level composite functions with nested random and smooth mappings.
method Normalized proximal approximate gradient (NPAG) method with nested stochastic variance reduction.
result Total sample complexity of O ( ε − 3 ) O(ε^{-3}) O ( ε − 3 ) in expectation and O ( N + N ε − 2 ) O(N+\sqrt{N}ε^{-2}) O ( N + N ε − 2 ) in finite-sum cases. This paper introduces compositional data analysis for financial ratios, improving industry-level analysis.
problem Statistical issues with standard financial ratios at industry level.
method Compositional data analysis techniques for financial ratios.
result Improved analysis of financial ratios using compositional data methods.
Greedy coordinate descent achieves linear convergence for non-smooth composite problems.
problem Optimization of non-smooth composite problems.
method Greedy selection of subgradients for optimization.
result Linear convergence rates independent of problem dimension n n n . New algorithm framework solves stochastic composite nonconvex optimization problems efficiently.
problem Solving stochastic composite nonconvex optimization problems.
method ProxSARAH framework using SARAH estimator with proximal gradient and averaging steps.
result Achieves best-known complexity bounds with constant and adaptive step-sizes.
Paper solves robust convex problems with heavy-tailed noise.
problem Solving convex compositional problems with heavy-tailed noise.
method Sub-Gaussian confidence bounds under weak heavy-tailed noise assumptions, using boosting strategy.
result Achieves nearly optimal high probability convergence result.
The paper develops variance-reduced methods to solve complex optimization problems.
problem Non-convex composition optimization with many inner functions.
method Variance-reduced techniques applied to SGD and SVRG.
result Significant improvement in query complexity for large inner function numbers.
Paper analyzes word embedding composition using tensor decomposition.
problem Given vector representations of two words, compute a vector for the entire phrase.
method Generative model with low rank Tucker decomposition of word embedding correlations.
result Word embeddings and a core tensor can be derived from the Tucker decomposition.
New samplers improve compositional generation with diffusion models.
problem Improving compositional generation with diffusion models.
method Score-based interpretation, energy-based parameterization, Metropolis-corrected samplers.
result New samplers enable successful compositional generation across various tasks.
New sparse GP model learns compositional kernels efficiently.
problem Learning accurate Gaussian Process models with complex kernel structures.
method MultiSVGP model with Horseshoe prior for kernel selection.
result Our model provides better fit and faster computation for large-scale data.
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., problems of the form $\min_x \mathbf{E}_v [f_v\big(\mathbf{E}_…
Here we study non-convex composite optimization: first, a finite-sum of smooth but non-convex functions, and second, a general function that admits a simple proximal mapping. Most research on stochastic methods for composite optimization assumes convexity or strong convexity of each function. In this paper, we extend t…
System composes polyphonic music using LSTM and RL.
problem Complex polyphonic music composition.
method Divided music into monophonic streams, trained LSTM to generate sequences, used RL to find pleasant compositions.
result System generates intricate melodies, chords, and contrapuntal sequences.
PICLE uses probabilistic models to efficiently evaluate and compose modules for continual learning.
problem Challenging search space of module compositions in continual learning.
method Probabilistic framework to cheaply compute module compositions' fitness.
result First modular CL algorithm to achieve perceptual, few-shot, and latent transfer.
Generative model learns to compose images of objects from different distributions.
problem Capturing complex interactions between objects in scenes.
method Composition-by-Decomposition (CoDe) network.
result Model generates realistic composite images capturing interactions between input objects.
New algorithm solves composite optimization problems with unknown expectations.
problem Solving composite optimization problems with unknown statistical expectations.
method Proposes a new stochastic primal-dual algorithm for composite optimization problems with unknown statistical expectations.
result Converges to a saddle point of the Lagrangian function.
Unified tractability conditions for various compositional inference queries.
problem Analyzing tractability of probabilistic and causal inference queries.
method Algebraic perspective on circuits, focusing on semiring operators.
result Unified sufficient conditions for tractable composition of operators.
We consider in this paper a class of composite optimization problems whose objective function is given by the summation of a general smooth and nonsmooth component, together with a relatively simple nonsmooth term. We present a new class of first-order methods, namely the gradient sliding algorithms, which can skip the…
Adaptive sampling method solves constrained and composite optimization problems.
problem Solving constrained optimization problems with stochastic objectives and deterministic constraints.
method Proximal gradient method with adaptive sampling to improve gradient approximation quality.
result Convergence results established for both strongly convex and general convex objectives.
New sampling methods for constrained and composite distributions.
problem Sampling from log-concave distributions with constraints and composite structures.
method Proximal sampler applied to lifted convex sets with separation and subgradient oracles.
result Practical and unbiased samplers for constrained and composite distributions.
In many applications one may acquire a composition of several signals that may be corrupted by noise, and it is a challenging problem to reliably separate the components from one another without sacrificing significant details. Adding to the challenge, in a compressive sensing framework, one is given only an undersampl…