FEM improves attention mechanisms by applying value-driven log-linear tilts.
problem Standard attention mechanisms read via convex average, limiting channel-wise selection.
method Free Energy Mixer (FEM) applies a value-driven, per-channel log-linear tilt to a fast prior over indices.
result FEM outperforms strong baselines on NLP, vision, and time-series tasks.
Iterative tilting fine-tunes diffusion models for reward-tilted distributions.
problem Fine-tuning diffusion models for reward-tilted distributions.
method Decomposes large reward tilts into smaller, tractable tilts via first-order Taylor expansion, avoiding backpropagation.
result Validated on a two-dimensional Gaussian mixture, achieving exact closed-form solutions.
Log-linear models are the popular workhorses of analyzing contingency tables. A log-linear parameterization of an interaction model can be more expressive than a direct parameterization based on probabilities, leading to a powerful way of defining restrictions derived from marginal, conditional and context-specific ind…
The paper examines the tilted empirical risk's generalization and robustness under negative tilt.
problem The generalization error of machine learning algorithms under negative tilt.
method Uniform and information-theoretic bounds on the tilted generalization error under negative tilt.
result The tilted empirical risk's generalization error has a convergence rate of \(O(n^{-ε/(1+ε)})\).
The study reveals the efficiency of sampling from tilted distributions.
problem Sampling from a tilted distribution of an unknown underlying distribution.
method Self-normalized importance sampling to characterize accuracy.
result Polynomial vs super-polynomial sample complexity for bounded vs unbounded distributions.
We study tilting subweibull distributions and their tail behavior.
problem Understanding tail behavior of subweibull distributions.
method Alternative characterizations and conditions for tail behavior preservation.
result Conditions for tail behavior preservation after exponential tilting.
Inference in log-linear models scales linearly in the size of output space in the worst-case. This is often a bottleneck in natural language processing and computer vision tasks when the output space is feasibly enumerable but very large. We propose a method to perform inference in log-linear models with sublinear amor…
Researchers develop a method to generate diffusion-based samples from a tilted distribution.
problem Generating samples from a distribution that has been tilted by a parameter.
method Developed a plug-in estimator and proved Wasserstein bounds and TV-accuracy under certain conditions.
result The method is minimax-optimal and can be applied in various domains like finance and climate modeling.
Optimizes antenna tilt for better QoS in cellular networks.
problem Hard to learn optimal antenna tilt policies in real networks due to risk and simulation gap.
method Uses off-policy Contextual Multi-Armed-Bandit (CMAB) techniques to learn from existing data.
result Trained policies show consistent improvements over existing logging policies.
Algorithm optimizes quantized isotonic regression with log-linear time updates.
problem Optimizing quantized isotonic regression estimations.
method Modified PAVA algorithm for sequential optimization.
result Log-linear time updates for optimal quantized mapping.
Mutation graph of support τ-tilting modules over skew-gentle algebras is connected.
problem Understanding the structure of support τ-tilting modules over skew-gentle algebras.
method Introducing mutation of maximal rigid objects and using exchange triangles to define mutations of support τ-tilting modules.
result The mutation graph of support τ-tilting modules over a skew-gentle algebra is connected.
Extends ERM with exponential tilting for improved machine learning performance.
problem Improving machine learning models by adjusting loss weights for fairness and robustness.
method Tilted Empirical Risk Minimization (TERM) using exponential tilting.
result TERM can outperform traditional ERM and deliver competitive performance with state-of-the-art methods.
Online TERM improves robustness and fairness in streaming data.
problem Streaming data's lack of worst-case fairness and robustness in ERM.
method Proposes an online TERM formulation to balance average-case accuracy with worst-case fairness and robustness.
result Negative tilting effectively suppresses outlier influence, positive tilting improves recall with minimal precision loss.
A scalable algorithm for sampling and fine-tuning models using Tilt Matching.
problem Efficient sampling and fine-tuning of generative models.
method Tilt Matching, arising from a dynamical equation, minimizes variance and inherits regularity from stochastic interpolants.
result Empirically verified to be efficient and highly scalable, providing state-of-the-art results.
TILT improves target domain performance by penalizing an auxiliary component on unlabeled target inputs.
problem Improving performance on target domain under covariate shift.
method TILT uses a novel objective function to decompose the source predictor and penalize an auxiliary component on unlabeled target inputs.
result TILT improves target domain performance over source-only training and other baselines.
We compare various extensions of the Bradley-Terry model and a hierarchical Poisson log-linear model in terms of their performance in predicting the outcome of soccer matches (win, draw, or loss). The parameters of the Bradley-Terry extensions are estimated by maximizing the log-likelihood, or an appropriately penalize…
Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these models is that they are able to capture context-specific independencies, relation…
New optimization method improves generalization across various tasks.
problem Improving zeroth-order optimization for better generalization.
method Exponential tilting objective to connect zeroth-order optimization with sharpness-aware minimization.
result Achieves better generalization compared to vanilla zeroth-order baselines.
We study surfaces in Euclidean space R3 that are minimal for a log-linear density φ(x,y,z)=αx+βy+γy, where α,β,γ are real numbers not all zero. We prove that if a surface is φ-minimal foliated by circles in parallel planes, then these planes are orthogonal to the vector (α,β,γ) and the surface must…
The paper integrates multiple Gaussian process predictions using Monte Carlo sampling.
problem Accurate prediction of variables using multiple models.
method Log-linear pooling of Gaussian process predictions, combined with Monte Carlo sampling.
result The log-linear pooling method improves prediction accuracy compared to linear pooling.
Two log-linear approximations speed up optimal transport for deep learning applications.
problem Computing optimal transport in high dimensions is computationally expensive.
method Locality-sensitive hashing (LSH) and Nyström approximation with LSH-based sparse corrections.
result Log-linear time algorithms for entropy-regularized OT perform well in high-dimensional spaces.
Consider semi-supervised learning for classification, where both labeled and unlabeled data are available for training. The goal is to exploit both datasets to achieve higher prediction accuracy than just using labeled data alone. We develop a semi-supervised logistic learning method based on exponential tilt mixture m…
ETM models improve efficiency in semi-supervised logistic regression.
problem Improving efficiency in logistic regression with limited labeled data.
method Developed exponential tilt mixture (ETM) models for semi-supervised estimation.
result ETM-based estimation demonstrates improved efficiency over supervised logistic regression.
Paper explores duality in DPPs using embedding structure analysis.
problem Understanding the geometric structure of determinantal point processes.
method Analyzes the exponential family embedding of DPPs and uses the e-embedding curvature tensor.
result Discovers the duality between marginal and L-ensemble kernels.
We study the existence problem for tilted unduloids in H2×R. These are singly periodic annuli with constant mean curvature H>1/2 in H2×R, and the periodicity of these surfaces is with respect to a discrete group of translations along a geodesic that is neither verti…
Paper provides estimates for varifolds with critical mean curvature.
problem Estimating tilt-excess on varifolds with critical mean curvature.
method Generalizing Lipschitz approximation and Sobolev-Poincaré estimates to almost-integral rectifiable varifolds.
result VMO-type estimates for quadratic tilt-excess on varifolds with critical mean curvature.
Develops conformal Bayes for two-sided censored Gaussian regression under label shift.
problem Prediction under label shift with censored responses.
method Combines posterior predictive tilting with weighted conformal calibration.
result Restores marginal coverage with smaller prediction sets.
In this paper, we classify the class of constant weighted curvature curves in the plane with a log-linear density, or in other words, classify all traveling curved fronts with a constant forcing term in R2. The classification gives some interesting phenomena and consequences including: the family of curves conv…
Study addresses RTB model performance drops due to distribution shifts.
problem Distribution shifts between training and target environments in RTB markets.
method Applies Exponential Tilt Reweighting Alignment (ExTRA) algorithm to estimate and correct model weights.
result Demonstrates improved RTB model performance using ExTRA algorithm.
Reweighting training data to better represent new tasks.
problem Deploying machine learning models to new tasks is challenging due to training data distribution.
method Formulate an exponential tilt distribution shift model and learn train data importance weights to minimize KL divergence.
result The learned train data weights improve target performance evaluation, fine-tuning, and model selection.
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space with its first variation given by either a Radon measure or a function in some Lebesgue space. Pointwise decay results for the quadratic tilt-excess are established for those varifolds. The results are optimal in terms of…
A major problem for the learning of Bayesian networks (BNs) is the exponential number of parameters needed for conditional probability tables. Recent research reduces this complexity by modeling local structure in the probability tables. We examine the use of log-linear local models. While log-linear models in this con…
Unified framework TERM improves fairness and robustness.
problem Outliers and subgroup fairness in empirical risk minimization.
method Unified framework TERM with a hyperparameter tilt.
result TERM improves fairness and robustness.
DTM improves dLLM fine-tuning stability and performance.
problem Intractable sequence-level marginal likelihoods for masked diffusion models.
method Discrete Tilt Matching (DTM) recasts dLLM fine-tuning as state-level matching of local unmasking posteriors under reward tilting.
result DTM yields strong gains on Sudoku and Countdown while remaining competitive on MATH500 and GSM8K.
Parameters defined via General Estimating Equations (GEE) can be estimated by maximizing the Empirical Likelihood (EL). Newey and Smith (2004) have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties, namely, that its O(n^-1) bias is small and that bias-corrected EL is higher-ord…
Parameters defined via general estimating equations (GEE) can be estimated by maximizing the empirical likelihood (EL). Newey and Smith [Econometrica 72 (2004) 219--255] have recently shown that this EL estimator exhibits desirable higher-order asymptotic properties, namely, that its O(n−1) bias is small and that …
Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.
problem Proving the spacetime positive mass theorem for specific spacetime configurations.
method Solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.
result Established spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends.
Improved speech recognition with language model integration in sequence-to-sequence models.
problem Improving word error rate in speech recognition models.
method Log-linear combination of acoustic and language models with per-token renormalization.
result The proposed method shows good improvements over standard model combination on Librispeech system.
We give a diagrammatic presentation of the category of Uq(sl2)-tilting modules T for q being a root of unity and introduce a grading on T. This grading is a "root of unity phenomenon" and might lead to new insights about link and 3-manifold invariants deduced from $…
A flexible nonparametric online changepoint detection algorithm for high-frequency data.
problem Detecting changes in real-time in high-frequency data streams with limited computational resources.
method NP-FOCuS, a sequential likelihood ratio test for a change in the empirical cumulative density function, using functional pruning.
result NP-FOCuS outperforms current nonparametric online changepoint techniques in various settings.
We construct tilting modules over Jacobian algebras arising from knots. To a two-bridge knot L[a1,…,an], we associate a quiver Q with potential and its Jacobian algebra A. We construct a family of canonical indecomposable A-modules M(i), each supported on a different specific subquiver Q(i) of Q. E…
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-di…
Method adapts frozen models for few-shot tasks without training.
problem Deployment constraints limit model updates, necessitating new adaptation methods.
method Exponential tilting of latent distribution for inference.
result Method outperforms parameter-update methods across benchmarks.
Unified framework for training diffusion and flow models to sample from target distributions.
problem Training diffusion and flow models to sample from target distributions defined by exponential tilting.
method Unified framework combining stochastic optimal control and non-equilibrium thermodynamics perspectives.
result Unified bias-variance decompositions and theoretical support for adjoint-based methods.
CANN models improve insurance claim count predictions using telematics data.
problem Improving insurance claim count predictions with telematics data.
method Combining classical actuarial models with neural networks for telematics data.
result CANN models outperform traditional models in predicting insurance claims.
Efficiently reduces rank of non-negative matrices with quadratic time complexity.
problem Efficiently reducing the rank of non-negative matrices.
method Formulated rank reduction as a mean-field approximation using a log-linear model.
result Optimal solution for minimizing KL divergence can be computed in closed form.
Changepoint detection is a central problem in time series and genomic data. For some applications, it is natural to impose constraints on the directions of changes. One example is ChIP-seq data, for which adding an up-down constraint improves peak detection accuracy, but makes the optimization problem more complicated.…
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a new type of graphical model, called the nested Markov model, was developed which …