Generalizes quandle constructions and defines a multiplication that results in an abelian group.
problem Tackles the construction and multiplication of quandle structures.
method Defines a composition of quandle structures and proves conditions for it to form a quandle, then shows the resulting group is abelian.
result Multiplication of quandle structures results in an abelian group.
Paper proves multiplicative weight updates can train neural networks without learning rate tuning.
problem Vanishing and exploding gradients in gradient descent for compositional functions.
method Proves descent lemma for compositional functions using multiplicative weight updates and derives Madam optimizer.
result Madam optimizer trains state-of-the-art neural networks without learning rate tuning.
MCP learns reusable skills for complex tasks by combining simple ones.
problem Learning complex tasks with many skills requires impractical amounts of data.
method Factorizes skills into primitives that can be combined multiplicatively.
result MCP can learn and reuse skills for novel tasks from pre-training.
In this paper, we explicitly construct the Calabi composition of multiple affine hyperspheres possibly including some points viewing as 0-dimensional hypersheres. Then we compute all the basic affine invariants of the composed affine hyperspheres, proving that the composed affine hypersphere is symmetric one if and onl…
Improved SVMs learn from few samples with composition and multiple scales.
problem Learning with small sample sizes.
method Transformation-invariant SVMs with composition and locality at multiple scales.
result Kernels based on maximum similarity are positive definite and yield superior accuracy.
Unified framework for aligning and composing diffusion models to satisfy multiple constraints.
problem Improving quality and compliance of generated samples from diffusion models.
method Constrained optimization framework that unifies alignment and composition of diffusion models.
result Proposed framework effectively satisfies multiple constraints in image generation.
New method estimates effects of multiple nutrients on blood glucose.
problem Estimating physiological response to multiple nutrient treatments.
method Convolution-based multi-output Gaussian process model.
result Improved prediction accuracy and better interpretation of individual nutrient effects.
We show that any multiplicative bijection between the algebras of differentiable functions, defined on differentiable manifolds of positive dimension, is an algebra isomorphism, given by composition with a unique diffeomorphism.
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.
JIMA uses multi-level preference data to recommend composite items.
problem Recommending composite items efficiently with multi-level preference information.
method Joint Interaction Modeling (JIMA) approach that integrates multi-level preference data and interactions.
result JIMA outperforms advanced baselines in offline and online settings.
System learns to combine multiple model components for personalized text generation.
problem Adapting and biasing language models for personal preferences.
method Combines model-defined components, learns activation and probability combination from unlabeled text.
result Directly generates text with personalized components from unlabeled data.
PEAK tests means of multiple data streams with sequential betting.
problem Testing means of multiple data streams with nonparametric methods.
method Sequential, nonparametric testing using a betting scheme.
result PEAK provides up to 85% reduction in samples for stopping.
New conditions for weighted composition operators in group homomorphisms.
problem Conditions for weighted composition operators in group homomorphisms.
method Range decreasing group homomorphisms.
result New insights into weighted composition operators and their algebraic structure.
Unified framework controls false discovery rate in bandit multiple testing.
problem Designing adaptive algorithms to identify true discoveries in multiple hypothesis testing.
method Unified modular framework using e-processes for FDR control in arbitrary settings.
result Unified framework ensures FDR control for dependent and simultaneous arm queries.
DGPs collapse to near-deterministic transformations, limiting their compositional structure discovery.
problem Limitations of variational inference in DGPs lead to suboptimal posterior approximations.
method Examine alternative variational inference schemes allowing for dependencies across different layers.
result Alternative variational inference schemes can better capture the compositional structure in DGPs.
Proposes a new model for clustering multiplex networks with compositional data.
problem Clustering multiplex networks with multiple types of relations and compositional data.
method Multiplex Dirichlet stochastic block model for compositional networks.
result Validated through simulation and applied to international export data.
This paper improves neural network explanations by quantifying and visualizing semantic compositions.
problem Improving neural network explanations for natural language processing tasks.
method Proposes a formal way to quantify word and phrase importance, introduces SCD and SOC algorithms.
result Our algorithms outperform prior methods in explaining neural network predictions.
RHPO improves data-efficiency for hierarchical reinforcement learning.
problem High data requirements for general reinforcement learning algorithms in robotics.
method RHPO employs compositional inductive biases and task sharing mechanisms.
result RHPO enables stable and fast learning for complex domains with positive transfer.
Generative Adversarial Networks (GANs) can produce images of remarkable complexity and realism but are generally structured to sample from a single latent source ignoring the explicit spatial interaction between multiple entities that could be present in a scene. Capturing such complex interactions between different ob…
New framework infers multiple classes per image for one-shot learning.
problem Inferring multiple classes per image in one-shot learning.
method Compositional embedding framework with joint training of embedding and composition/query functions.
result Compositional embedding models outperform existing methods on various datasets.
Edgeworth Accountant calculates privacy loss under differential privacy compositions efficiently.
problem Efficiently computing overall privacy loss under composition of private algorithms.
method Analytical approach using f f f -differential privacy framework and Edgeworth expansion. result Non-asymptotic ( ε , δ ) (ε, δ) ( ε , δ ) -differential privacy bounds with reduced computational cost. Paper combines geometry and time-series analysis for spatiotemporal data.
problem Multivariate time-series data from multiple sensors.
method Combines manifold learning, Riemannian geometry, and spectral analysis.
result Proposes Riemannian multi-resolution analysis (RMRA) for dynamic mode extraction.
Describes explaining neurons in deep representations using compositional logical concepts.
problem Interpreting neuron behavior in deep neural networks.
method Identifying compositional logical concepts that closely approximate neuron behavior.
result Compositional explanations provide insights into model performance and allow for adversarial example creation.
Unified theory for neural scaling laws in hierarchically compositional data.
problem Understanding neural scaling laws in hierarchically compositional data.
method Probabilistic context-free grammars and power-law distributed production rules.
result Unified learning curve behavior for classification and next-token prediction tasks.
New algorithm samples efficiently from complex composite potentials.
problem Sampling from densities with smooth and non-smooth components.
method Metropolis-Hastings framework with proximal-based proposal.
result Mixes to target density in O ( d log ( d / ε ) ) O(d \log (d/\varepsilon)) O ( d log ( d / ε )) iterations. Improved Q-learning for robot control with faster data-efficiency.
problem Poor data-efficiency and stochasticity in deep Q-learning.
method Composite Q-learning: Decomposes Q-function into short- and long-term predictions.
result Significant learning speedup and improved data-efficiency in robot tasks.
With the proliferation of mobile devices and the internet of things, developing principled solutions for privacy in time series applications has become increasingly important. While differential privacy is the gold standard for database privacy, many time series applications require a different kind of guarantee, and a…
Paper simplifies DP composition for adaptive privacy budgets, enabling better privacy and accuracy in deep learning.
problem Tension between efficiency and flexibility in DP composition theorems.
method Rényi Differential Privacy (RDP) for adaptive privacy budgets, proving simpler composition theorem with smaller constants.
result Practical DP composition for adaptive privacy budgets, enabling better privacy and accuracy in deep learning.
Agents compose pre-trained policies for complex tasks, improving zero-shot performance.
problem Challenges in long-horizon predictions and estimating visitation distributions induced by policy sequences.
method Learn predictive jumpy world models of multi-step dynamics, enhancing predictions with a consistency objective.
result Compositional planning with jumpy world models yields, on average, a 200% relative improvement over primitive actions on long-horizon tasks.
There is tremendous interest in precision medicine as a means to improve patient outcomes by tailoring treatment to individual characteristics. An individualized treatment rule formalizes precision medicine as a map from patient information to a recommended treatment. A treatment rule is defined to be optimal if it max…
Bayesian model predicts evolving guest origin markets in tourism.
problem Forecasting the changing composition of guest origin markets in tourism.
method Developed and applied Bayesian Dirichlet autoregressive moving average (BDARMA) models to Airbnb booking data.
result BDARMA models achieve lower forecast error and competitive performance in guest origin market shares.
Bayesian models predict evolving guest origin markets in tourism.
problem Forecasting the changing composition of guest origin markets in tourism.
method Developed and applied Bayesian Dirichlet autoregressive moving average (BDARMA) models to Airbnb booking data.
result BDARMA models outperform standard benchmarks in forecasting guest origin market shares.
The paper explores fairness in multi-component recommender systems.
problem How to ensure fairness in recommender systems composed of multiple models.
method Study of fairness ranking metrics, theoretical analysis, and empirical evaluation.
result Fairness in recommendation systems can be achieved by improving individual components.
Generative model synthesizes complex data structures with composite and nested types.
problem Synthesizing complex data structures with composite and nested types.
method Generic framework using causal transformers for struct and list generation.
result Consistently outperforms state-of-the-art models on standard and complex hierarchical datasets.
Networks have been a general tool for representing, analyzing, and modeling relational data arising in several domains. One of the most important aspect of network analysis is community detection or network clustering. Until recently, the major focus have been on discovering community structure in single (i.e., monople…
New model identifies microbial subcommunities robustly, accounting for cross-sample heterogeneity.
problem Inference in LDA is sensitive to the number of subcommunities and often creates artificial ones.
method Incorporates logistic-tree normal (LTN) model into LDA to account for cross-sample heterogeneity.
result Restores robustness of inference and identifies meaningful subcommunities.
BoTier optimizes experiments by balancing multiple objectives hierarchically.
problem Balancing multiple competing objectives in scientific experiments.
method Composite objective that flexibly represents a hierarchy of preferences over outcomes and parameters.
result Demonstrates robust applicability across various use cases and seamless integration.
ML predicts alloy properties considering chemistry, processing, and data transformations.
problem Designing and predicting alloy properties in high-dimensional design space.
method Physics-informed machine learning with engineered features from chemistry and heat treatment.
result ML models accurately predict alloy properties, including hysteresis in shape memory alloys.
In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of 2 k + 1 2k+1 2 k + 1 nodes, where each node is either a summation, a multiplication, or the application of one of the q q q basis functions to one of the p p p covariates. We show that in order to recover a labeled bi…
Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in E E E -theory. The other type is by module multiplications in K K K -theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Hi…
We establish an interesting connection between Morin singularities and stable homotopy groups of spheres. We apply this connection to computations of cobordism groups of certain singular maps. The differentials of the spectral sequence computing these cobordism groups are given by the composition multiplication in the …
The paper analyzes the error accumulation in a compositional score-based algorithm for SBI.
problem How to effectively combine multiple observations to improve parameter inference.
method Study of the GAUSS algorithm's compositional score and its mean squared error.
result Established an upper bound on the mean squared error of the compositional score.
UCB-TQL learns from multiple tasks with shared dynamics and adapts to task-specific variations.
problem Transfer reinforcement learning with composite MDPs where tasks share core dynamics but have sparse differences.
method UCB-TQL, a novel transfer RL algorithm for composite MDPs.
result Achieved a regret bound of i l d e O ( e H 5 N ) ilde{O}(\sqrt{eH^5N}) i l d e O ( e H 5 N ) that scales independently of the ambient dimension. Enhances image captioning with novel context combination methods.
problem Improving machine learning for image captioning with structured learning and meaningful interpretation.
method Combines Feature Distribution Composition (FDC), Multiple Role Representation Crossover (MRRC) attention layers, and language decoder.
result Significantly improved image captioning performance (35.3%) and established new standards.
We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the multiplicative linear functionals from the special algebra of Colombeau generaliz…
We present the multiplicative recurrent neural network as a general model for compositional meaning in language, and evaluate it on the task of fine-grained sentiment analysis. We establish a connection to the previously investigated matrix-space models for compositionality, and show they are special cases of the multi…
This paper studies the problem of Generalized Zero-shot Learning (G-ZSL), whose goal is to classify instances belonging to both seen and unseen classes at the test time. We propose a novel space decomposition method to solve G-ZSL. Some previous models with space decomposition operations only calibrate the confident pr…
Algorithm counts intersections of normal curves efficiently.
problem Efficiently solving word problems in mapping class groups of punctured surfaces.
method Fast algorithm for counting intersections of normal curves on triangulated surfaces.
result Efficient solution of the word problem for mapping class groups of punctured surfaces.