Proposes unbiased estimators for training mixture of experts models.
problem Efficiently training large-scale mixture of experts models on modern hardware.
method Two unbiased estimators based on principled stochastic assignment procedures.
result Both estimators are more effective and robust than biased alternatives.
The capacity of a neural network to absorb information is limited by its number of parameters. Conditional computation, where parts of the network are active on a per-example basis, has been proposed in theory as a way of dramatically increasing model capacity without a proportional increase in computation. In practice…
Theory of MoE Transformers' generalization and scaling.
problem Understanding the generalization and scaling of Mixture-of-Experts (MoE) Transformers.
method Developed a theory that separates active capacity from routing combinatorics, derived a sup-norm covering-number bound, and proved a constructive approximation theorem.
result Generalization and scaling laws for MoE Transformers, showing how active capacity and routing structure affect performance.
This study analyzes communication constraints in MoE architectures using information theory.
problem Communication constraints in Mixture-of-Experts (MoE) architectures.
method Developed a rate-distortion characterization of finite-rate gating in MoE architectures using information theory.
result Yielded capacity-aware limits for communication-constrained MoE systems.
A matching in a two-sided market often incurs an externality: a matched resource may become unavailable to the other side of the market, at least for a while. This is especially an issue in online platforms involving human experts as the expert resources are often scarce. The efficient utilization of experts in these p…
Paper connects MoE and self-attention, proposing active-attention.
problem Improving efficiency and performance of self-attention mechanisms.
method Established connection between MoE and self-attention, analyzed quadratic gating functions, proposed active-attention mechanism.
result Active-attention outperforms standard self-attention in various tasks.
A method to improve LLMs by automating the construction of a mixture of expert prompts.
problem Limitation of single instruction prompts in covering complex problem spaces.
method Divide the problem space into sub-regions, each governed by a specialized expert with both an instruction and demos. A two-phase process constructs these experts.
result Achieves an average win rate of 81% across major benchmarks.
Training convolutional networks (CNN's) that fit on a single GPU with minibatch stochastic gradient descent has become effective in practice. However, there is still no effective method for training large CNN's that do not fit in the memory of a few GPU cards, or for parallelizing CNN training. In this work we show tha…
New algorithm bounds regret in mediator feedback bandit problems.
problem Mediator feedback bandit game with policy sets.
method Adopting EXP4 algorithm, new regret bounds based on policy set capacity.
result Nearly-matching lower bounds for policy set families.
DSelect-k improves MoE models for multi-task learning with better performance and smoother training.
problem Smoothness and convergence issues in sparse gate selection for MoE models.
method Developed DSelect-k, a differentiable and sparse gate for MoE models.
result DSelect-k achieves statistically significant improvements in prediction and expert selection over Top-k.
STAR improves equivariant and invariant representation learning by routing projection heads.
problem Redundant feature learning in equivariant and invariant representation learning.
method Soft Task-Aware Routing (STAR) for projection heads specialization.
result Lower canonical correlations between invariant and equivariant embeddings.
Localized Multidirectional Correction improves non-refusal target-response behavior in foundation models.
problem Controlled post-training refusal suppression in routed MoE and hybrid-MoE foundation models.
method Introduce Localized Multidirectional Correction (LoMC), a support-gated intervention framework.
result Substantially improves non-refusal target-response behavior while maintaining general capability under a compact intervention footprint.
A new data-driven model forecasts electricity prices efficiently.
problem Forecasting electricity prices using traditional methods.
method Integrates data-driven and fundamental models, learns from historical data.
result Significantly improves forecasting accuracy compared to existing models.
In real-world machine learning applications, data subsets correspond to especially critical outcomes: vulnerable cyclist detections are safety-critical in an autonomous driving task, and "question" sentences might be important to a dialogue agent's language understanding for product purposes. While machine learning mod…
In an era of ubiquitous large-scale streaming data, the availability of data far exceeds the capacity of expert human analysts. In many settings, such data is either discarded or stored unprocessed in datacenters. This paper proposes a method of online data thinning, in which large-scale streaming datasets are winnowed…
Optimizes COVID-19 testing policy using a Multi-Armed Bandit approach.
problem Balancing discovery of positive cases with population surveillance.
method Risk scoring and random sampling based on Multi-Armed Bandit theory.
result Effective prioritization captures 65-92% of positive cases with varying testing capacity.
Transformers learn to make decisions in new contexts from offline data.
problem Understanding when and how transformers can perform in-context reinforcement learning.
method Theoretical framework analyzing supervised pretraining for ICRL, including algorithm distillation and decision-pretrained transformers.
result Transformers can efficiently approximate optimal reinforcement learning algorithms for various environments.
Multi-expert L2D underfits more severely, requiring new methods.
problem Underfitting in multi-expert L2D settings.
method PiCCE (Pick the Confident and Correct Expert), a surrogate-based method.
result PiCCE effectively reduces multi-expert L2D to a single-expert-like problem, resolving underfitting.
New method improves traffic forecasting models by adapting to spatial shifts.
problem Improving traffic forecasting models' ability to handle spatial shifts over years.
method Proposes a novel Mixture of Experts (MoE) framework for spatiotemporal models.
result Significant improvement in performance for handling spatial distribution shifts.
We study various capacities on compact Kähler manifolds which generalize the Bedford-Taylor Monge-Ampère capacity. We then use these capacities to study the existence and the regularity of solutions of complex Monge-Ampère equations.
Solves a discrete logarithmic Minkowski problem for electrostatic p-capacity.
problem Characterize measures generated by electrostatic p-capacity.
method Solves the discrete logarithmic Minkowski problem for 1 < p < n.
result Solves the discrete logarithmic Minkowski problem for measures in general position.
TENP prunes experts and neurons in Mixture-of-Experts models for efficient deployment.
problem Efficient deployment of large language models constrained by static parameter footprint.
method Structured Trapezoidal ExpertNeuron Pruning (TENP) identifies and retains important experts and neurons.
result DeepSeek model achieves 10% better performance on code generation tasks with 40% expert sparsity.
CapOptix uses options theory to price capacity in electricity markets.
problem Traditional capacity market designs fail to account for risk and price shocks.
method Interprets capacity commitments as reliability options and uses Markov Regime Switching Process.
result CapOptix provides more accurate pricing of capacity premia compared to existing mechanisms.
A method to select important experts for Gaussian processes to balance computational efficiency and uncertainty quantification.
problem Balancing computational efficiency and uncertainty quantification in Gaussian processes for big data.
method Using graphical models to select important experts and aggregate their predictions while ensuring uncertainty quantification.
result Substantially reduces computational cost of aggregating dependent experts while ensuring calibrated uncertainty quantification.
In this article, we propose the notion of the general p-affine capacity and prove some basic properties for the general p-affine capacity, such as affine invariance and monotonicity. The newly proposed general p-affine capacity is compared with several classical geometric quantities, e.g., the volume, the p-var…
While symplectic manifolds have no local invariants, they do admit many global numerical invariants. Prominent among them are the so-called symplectic capacities. Different capacities are defined in different ways, and so relations between capacities often lead to surprising relations between different aspects of sympl…
Study excess capacity in neural networks using Rademacher complexity.
problem Understanding how much capacity deep networks have beyond what's needed for classification.
method Unified Rademacher complexity bounds for function composition and convolutional layers, considering Lipschitz constants and initialization norms.
result There is substantial excess capacity per task, and capacity can be kept similar across different tasks.
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.
Study binary perceptrons' capacity using random duality theory.
problem Characterize the capacity of binary perceptrons with general thresholds.
method Utilized fully lifted random duality theory (fl RDT) to characterize the capacity.
result Characterizations match replica symmetry breaking predictions and uncover the capacity for zero-threshold scenario.
Study capacity constraints in continual learning with a simple model.
problem Understanding optimal resource allocation for agents with limited memory and compute resources.
method Analyzes a capacity-constrained linear-quadratic-Gaussian (LQG) sequential prediction problem and demonstrates optimal capacity allocation strategies.
result Derives a solution to the capacity-constrained LQG sequential prediction problem and shows how to optimally allocate capacity across sub-problems in the steady state.
We consider the problem of contextual bandits with stochastic experts, which is a variation of the traditional stochastic contextual bandit with experts problem. In our problem setting, we assume access to a class of stochastic experts, where each expert is a conditional distribution over the arms given a context. We p…
New complete panel dataset for LMICs helps analyze innovation and development.
problem Lack of complete data for empirical analyses in LMICs.
method Predictive Mean Matching multiple imputation technique.
result Created a large dataset of 47 variables for 82 LMICs from 2005-2019.
Upper bounds for Lagrangian capacities of Liouville domains
problem Lagrangian capacity of Liouville domains
method Using S1-equivariant techniques result Extremal Lagrangian torus on the boundary of ellipsoid
Improved time series forecasting with expert loss integration.
problem Enhancing time series forecasting accuracy and efficiency.
method Adaptive Mixture-of-Experts framework with expert-specific loss integration and online learning.
result Significantly improved forecasting accuracy and computational efficiency.
Memory capacity of DAM scales exponentially with feature separation, unaffected by correlations.
problem Understanding how feature correlations impact DAM's capacity.
method Developed an empirical framework to analyze DAM's capacity under varying feature correlations and pattern separations.
result Memory capacity scales exponentially with feature separation, unaffected by correlations.
Proves local maximizers for higher Ekeland-Hofer capacities in 4D star-shaped domains.
problem Finding local maximizers for higher Ekeland-Hofer capacities in specific domains.
method Analogous to 4D local Viterbo conjecture, proving maximizers for rational ellipsoids.
result Local maximizers of the k-th Ekeland-Hofer capacities are symplectomorphic to rational ellipsoids.
Develops a theory for mth order p-affine capacity for convex bodies containing the origin.
problem Defines and studies the mth order p-affine capacity for convex bodies containing the origin.
method Provides equivalent definitions, proves properties, and establishes inequalities.
result Establishes inequalities comparing to other geometric measures.
Derives an empirical capacity model for self-attention neural networks.
problem Theoretical capacity of large transformer models is not fully utilized by current optimization algorithms.
method Analyzes memory capacity of transformers using synthetic training data and common training algorithms.
result Derives an empirical capacity model (ECM) for a generic transformer.
HS-MoE selects sparse experts using adaptive priors and data-adaptive gating.
problem Sparse expert selection in mixture-of-experts architectures.
method Combines horseshoe prior with input-dependent gating for data-adaptive sparsity.
result Data-adaptive sparsity in expert usage.
Improves online learning algorithms for functional models with capacity assumptions.
problem Convergence rates of online stochastic gradient descent algorithms for functional linear models.
method Characterizations of slope function regularity, kernel space capacity, and sampling process covariance operator.
result Capacity assumptions can alleviate saturation of convergence rates as function regularity increases.
We introduce the concept of pseudo symplectic capacities which is a mild generalization of that of symplectic capacities. As a generalization of the Hofer-Zehnder capacity we construct a Hofer-Zehnder type pseudo symplectic capacity and estimate it in terms of Gromov-Witten invariants. The (pseudo) symplectic capacitie…
LLMs learn to recommend models and hyperparameters from dataset metadata.
problem Model and hyperparameter selection in machine learning is challenging and resource-intensive.
method Converted datasets into metadata and prompted LLMs to recommend models and hyperparameters.
result LLMs can recommend competitive models and hyperparameters without search.
Study relates symplectic homology capacity to periodic orbits in Liouville domains.
problem Relating symplectic homology capacity to periodic orbits in Liouville domains.
method Uses positive symplectic homology and Hofer-Zehnder capacity to establish bounds and existence of periodic points.
result Non-zero positive symplectic homology implies finite upper bound for Hofer-Zehnder capacity relative to skeleton and Hamiltonian diffeomorphisms.
NAMEx merges experts using Nash bargaining for improved performance.
problem Sparse Mixture of Experts merging strategies lack a principled weighting mechanism.
method Reinterpreting expert merging through game theory, introducing Nash Merging and complex momentum.
result NAMEx consistently outperforms competing methods across various tasks and system sizes.
Learning capacity measures model complexity, correlating with test loss and sample size.
problem Understanding model complexity and its relation to test performance.
method Formal correspondence between thermodynamics and inference; learning capacity as a measure of effective dimensionality.
result Learning capacity correlates with test loss and is a small fraction of model parameters.
Study compares Monge-Ampère capacities on Kähler manifolds.
problem Comparing Monge-Ampère capacities on compact Kähler manifolds.
method Proved all capacities comparable, used Xia's integration by parts formula.
result All Monge-Ampère capacities are comparable.
Generalizes memory and forecasting capacities for nonlinear recurrent networks with dependent inputs.
problem Understanding memory and forecasting capabilities in networks with dependent inputs.
method Formulated bounds for memory and forecasting capacities in terms of network size and input properties.
result Proved that memory capacity for linear recurrent networks with independent inputs is given by the rank of the controllability matrix.
This paper is devoted to a geometric-measure-theoretic study of the brand new affine BV-capacity which is essentially different from the classic BV-capacity in dimension greater than one.