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.
Study meromorphic open-string vertex algebras and modules over Riemannian manifolds.
problem Characterize meromorphic open-string vertex algebras and their modules over Riemannian manifolds.
method Explicitly determine bases for meromorphic open-string vertex algebras and their modules, using parallel tensors and eigenfunctions of the Laplace-Beltrami operator.
result Every irreducible module of a specific type is completely reducible if every composition factor is generated by eigenfunctions of eigenvalue p(p−1)K for some p∈Z+. 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.
A new neural network captures and explains trajectory patterns.
problem Analyzing complex spatial trajectories in urban planning and neuroscience.
method Composite Signal Neural Networks (CompSNN) combining three interpretable ANN modules.
result CompSNN outperforms individual modules and visualizes useful signal parts.
RB-Modulation trains free diffusion models without external adapters.
problem Training-free personalization of diffusion models with style and content control.
method Stochastic optimal control with a style descriptor and cross-attention aggregation.
result Precise content and style extraction and control without external adapters.
The paper extends T-duality and Jacobi forms to Witten gerbe modules.
problem Extending T-duality and Jacobi forms to Witten gerbe modules.
method Constructing graded Hori maps and showing their isomorphisms on T-dual circle bundles, and constructing Witten gerbe modules.
result Graded twisted Chern characters of Witten gerbe modules are Jacobi forms under certain conditions.
We introduce a graphical calculus for computing morphism spaces between the categorified spin networks of Cooper and Krushkal. The calculus, phrased in terms of planar compositions of categorified Jones-Wenzl projectors and their duals, is then used to study the module structure of spin networks over the colored unknot…
Several formulas for computing coarse indices of twisted Dirac type operators are introduced. One type of such formulas is by composition product in E-theory. The other type is by module multiplications in K-theory, which also yields an index theoretic interpretation of the duality between Roe algebra and stable Hi…
Tree-AMP simplifies inference in complex tree-structured models.
problem Inference in high-dimensional tree-structured models.
method Approximate Message Passing algorithms for various machine learning tasks.
result Theoretical performance predictions and automated entropy estimation.
Study shows how transformers learn to combine simple tasks into complex ones.
problem Understanding how transformers learn to perform complex tasks not seen during training.
method Controlled setting involving variable assignment and modular addition; partitioned training data analysis.
result Small transformers can generalize to unseen combinations of variables and numbers.
The paper proves a global geometric formula for volume holonomy in gauge theory.
problem Describing higher parallel transport in classical principal bundle theory.
method Global geometric approach to parallel transport on surfaces and volumes.
result Global formula for volume holonomy and gauge invariance.
Modulating masks improve lifelong reinforcement learning.
problem Catastrophic forgetting and task interference in lifelong reinforcement learning.
method Adapted modulating masks for deep lifelong reinforcement learning (LRL) with PPO and IMPALA agents.
result Superior performance in both discrete and continuous RL tasks compared to LRL baselines.
We develop a model to predict effects of sequential interventions, clarifying their combined impact.
problem Uncertainty in generalizing behavioral predictions for combinations of interventions.
method Explicit model for composition of interventions, identifying their combined effect.
result Our compositional model aids prediction in sparse data conditions.
SympNets identify Hamiltonian systems from data using linear, activation, and gradient modules.
problem Identifying Hamiltonian systems from data.
method Composition of linear, activation, and gradient modules; universal approximation theorems.
result SympNets can approximate arbitrary symplectic maps and generalize well to various Hamiltonian systems.
Enhances DGPs with adaptive RKHS Fourier features for better non-stationary pattern modeling.
problem Capturing complex non-stationary patterns in non-linear dynamical systems.
method Integrates ODE-based RKHS Fourier features into DGPs using convolution operations for adaptive amplitude and phase modulation. Uses a doubly stochastic variational inference framework.
result Improved predictive performance across various regression tasks.
It is a well known result from Thistlethwaite that the Jones polynomial of a non-split alternating link is alternating. We find the right generalization of this result to the case of non-split alternating tangles. More specifically: the Jones polynomial of tangles is valued in a certain skein module, we describe an alt…
Representations in the auditory cortex might be based on mechanisms similar to the visual ventral stream; modules for building invariance to transformations and multiple layers for compositionality and selectivity. In this paper we propose the use of such computational modules for extracting invariant and discriminativ…
DEPTS learns to forecast periodic time series with improved accuracy.
problem Forecasting periodic time series is challenging due to complex dependencies and diverse periods.
method DEPTS uses a decoupled formulation with an expansion module and a periodicity module to handle these challenges.
result DEPTS significantly improves forecasting accuracy, reducing errors by up to 20%.
The paper extends Lie bracket to noncommutative geometry using differential operators.
problem Generalizing Lie bracket to noncommutative geometry.
method Antisymmetrizing compositions of vector fields and treating symbols of differential operators.
result Provided necessary and sufficient conditions for jet modules to represent differential operators.
In the present article, we combine some techniques in the harmonic analysis together with the geometric approach given by modules over sheaves of rings of twisted differential operators (D-modules), and reformulate the composition series and branching problems for objects in the Bernstein-Gelfand-Gelfand pa…
We study the behavior of Pin(2)-monopole Floer homology under connected sums. After constructing a (partially defined) A∞-module structure on the Pin(2)-monopole Floer chain complex of a three manifold (in the spirit of Baldwin and Bloom's monopole category), we identify up to …
Slot Attention extracts object-centric representations from images.
problem Learning distributed representations that don't capture natural scene composition.
method Slot Attention module interfaces with CNN outputs to produce task-dependent abstract slots.
result Slot Attention enables generalization to unseen compositions.
We describe Bayesian Layers, a module designed for fast experimentation with neural network uncertainty. It extends neural network libraries with drop-in replacements for common layers. This enables composition via a unified abstraction over deterministic and stochastic functions and allows for scalability via the unde…
BacHMMachine harmonizes Baroque chorales using theory-driven principles and Hidden Markov Models.
problem Algorithmic harmonization of Baroque chorales.
method Theory-driven approach guided by music composition principles, combined with data-driven learning of key and chord transitions.
result BacHMMachine generates musically coherent harmonizations with reduced computational burden and greater interpretability.
We give an explicit handy (and cocycle-free) description of the groupoid of weak maps between two crossed-modules in terms of certain digrams of groups which we we call a {\em butterflies}. We define composition of butterflies and this way find a bicategory that is naturally biequivalent to the 2-category of pointed ho…
We introduce Compositional Imitation Learning and Execution (CompILE): a framework for learning reusable, variable-length segments of hierarchically-structured behavior from demonstration data. CompILE uses a novel unsupervised, fully-differentiable sequence segmentation module to learn latent encodings of sequential d…
Music relies heavily on repetition to build structure and meaning. Self-reference occurs on multiple timescales, from motifs to phrases to reusing of entire sections of music, such as in pieces with ABA structure. The Transformer (Vaswani et al., 2017), a sequence model based on self-attention, has achieved compelling …
We start a systematic analysis of links up to 5-move equivalence. Our motivation is to develop tools which later can be used to study skein modules based on the skein relation being deformation of a 5-move (in an analogous way as the Kauffman skein module is a deformation of a 2-move, i.e. a crossing change). Our main …
We construct the first combinatorial 1-cocycle with values in the Z[x,x−1]-module of isotopy classes of singular long knots in 3-space with a signed planar double point, and which represents a non trivial cohomology class in the topological moduli space of long knots. It can be interpreted as an invaria…
MoDeGPT compresses large language models without accuracy loss, saving 98% compute costs.
problem Compression of large language models for resource-constrained devices.
method Structured compression framework using modular decomposition and matrix pair reduction.
result MoDeGPT achieves 90-95% zero-shot performance with 25-30% compression rates.
Study of modular representations in homology of congruence subgroups.
problem Understanding modular representations in homology of congruence subgroups.
method Analysis of sequences of modular representations of symplectic and special linear groups over finite fields.
result Established periodic representation stability in the sense of Church--Farb.
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 …
New geometric approach for analyzing compositional data like gut microbiomes.
problem Analyzing non-negative compositional data with relative values only.
method Reinterpret compositional data as quotient topology of a sphere, using spherical harmonics and reflection group actions.
result Construction of Reproducing Kernel Hilbert Space (RKHS) for compositional data.
Study on deep neural networks using branching processes and Mehler's formula.
problem Understanding the mathematical role of activation functions in compositional neural networks.
method Connection between compositional kernels and branching processes via Mehler's formula; new random features algorithm.
result Explicit formulas for eigenvalues of compositional kernels quantify complexity.
This paper models how features influence event triggers in high-dimensional networks.
problem Estimating context-dependent networks in high-dimensional marked point processes.
method Leveraging compositional time series and regularization methods, the paper considers autoregressive multinomial and logistic-normal models for network estimation.
result The logistic-normal model leads to a convex negative log-likelihood objective and captures dependence across categories.
We establish conditions for compositional generalization in machine learning.
problem Achieving compositional generalization in machine learning models.
method We reformulate compositionality as a property of the data-generating process and derive mild conditions on the training distribution and model architecture.
result Our theoretical framework enables compositional generalization under mild conditions.
This paper proves hyperbolicity of virtual knot compositions.
problem Proving hyperbolicity of virtual knot compositions.
method Exploring the composition of hyperbolic virtual knots.
result Strong lower bounds on the volume of compositions.
Develops methods for causal inference in compositional data using instrumental variables.
problem Interpreting summary statistics like diversity indices as causal effects in compositional data.
method Statistical data transformations and regression techniques tailored for compositional data.
result Advantages and limitations of the proposed methods demonstrated on synthetic and real microbiome data.
In classical field theory, the composite fibred manifolds Y -> Z -> X provides the adequate mathematical formulation of gauge models with broken symmetries, e.g., the gauge gravitation theory. This work is devoted to connections on composite fibred manifolds. In particular, we get the horizontal splitting of the vertic…
The p-index improves investment performance for NYSE stocks but not for SSE stocks.
problem Improving investment performance for stocks using the p-index.
method Comparing different p-ratio strategies and empirical efficient frontiers for SSE and NYSE stocks.
result The p-index enhances investment performance for NYSE stocks but not for SSE stocks.
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.
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.
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.
SCL discovers compositional structures in analogical reasoning tasks.
problem Discovering compositional structures in analogical reasoning tasks like Raven's Progressive Matrices.
method Proposes Scattering Compositional Learner (SCL) that composes neural networks in sequence.
result Achieves state-of-the-art performance on RPM datasets with significant improvements.
Composite neural network improves PM2.5 prediction.
problem Improving PM2.5 prediction accuracy.
method Composite neural network framework with pre-trained models.
result Composite neural network outperforms individual models and new components added.
New filters match advanced composition for adaptive privacy, with practical constants.
problem Limitations of existing adaptive composition methods.
method Constructed new filters and odometers that match advanced composition rates, including constants.
result Achieved fully adaptive privacy with practical filters and odometers.
Paper develops momentum schemes with variance reduction for non-convex composition optimization.
problem Lack of convergence guarantee and efficient momentum design in existing algorithms.
method Develops various momentum schemes with SPIDER-based variance reduction.
result Achieves near-optimal sample complexity and linear convergence rate.