The Gumbel-max trick and its extensions simplify sampling from categorical distributions in machine learning.
problem Sampling from categorical distributions with unnormalized probabilities.
method Extensions of the Gumbel-max trick for various applications.
result Simplified and efficient methods for sampling and gradient estimation.
A new algorithm FastGM speeds up generating Gumbel-Max variables.
problem Efficiently generating multiple Gumbel-Max variables from high-dimensional vectors.
method FastGM reduces time complexity from O(kn+) to O(klnk+n+) by generating variables in descending order. result Significantly reduces computation time for generating k Gumbel-Max variables. Unified framework for gradient estimation in combinatorial spaces.
problem Scaling relaxed gradient estimators to large combinatorial distributions.
method Introducing stochastic softmax tricks within the perturbation model framework.
result Stochastic softmax tricks improve model performance and discover more latent structure.
The well-known Gumbel-Max trick for sampling from a categorical distribution can be extended to sample k elements without replacement. We show how to implicitly apply this 'Gumbel-Top-k' trick on a factorized distribution over sequences, allowing to draw exact samples without replacement using a Stochastic Beam Sea…
Many machine learning tasks require sampling a subset of items from a collection based on a parameterized distribution. The Gumbel-softmax trick can be used to sample a single item, and allows for low-variance reparameterized gradients with respect to the parameters of the underlying distribution. However, stochastic o…
Reparameterization of variational auto-encoders with continuous random variables is an effective method for reducing the variance of their gradient estimates. In the discrete case, one can perform reparametrization using the Gumbel-Max trick, but the resulting objective relies on an argmax operation and is non-dif…
Thompson sampling has impressive empirical performance for many multi-armed bandit problems. But current algorithms for Thompson sampling only work for the case of conjugate priors since these algorithms require to infer the posterior, which is often computationally intractable when the prior is not conjugate. In this …
Proposes a new method for estimating counterfactual treatment effects.
problem Uncertainty in identifying causal mechanisms from observational data.
method Introduces a parameterized family of causal mechanisms that generalize Gumbel-max, trained to minimize counterfactual effect variance.
result Trained mechanisms yield lower variance estimates of counterfactual treatment effects.
Study on estimating Gumbel--Max watermark proportions in edited documents.
problem Estimating the proportion of a document generated from a watermarked LLM.
method Comparison of full observation and pivotal reduction observation regimes; development of estimators and information-theoretic lower bounds.
result Full observation yields a substantially smaller sample complexity compared to pivotal reduction.
Estimates proportions of LLM-generated text in mixed documents.
problem Estimating the proportion of text generated by a pre-specified LLM in mixed documents.
method Developed estimators for two observation regimes: full observation and pivotal reduction, and established sample complexity bounds.
result Full observation estimators require fewer samples than pivotal reduction estimators.
LLM-as-a-service prices vary arbitrarily due to tokenization multiplicity.
problem Arbitrary price variation in LLM-as-a-service due to multiple tokenizations of the same output.
method Introduce canonical generation to restrict LLMs to unique tokenizations and develop an efficient sampling algorithm.
result Our sampling algorithm for canonical generation solves tokenization multiplicity and maintains comparable performance and runtime to standard sampling.
The paper develops a method for inferring second opinions from experts using counterfactual inference.
problem Designing efficient decision support systems for second opinions.
method Set invariant Gumbel-Max structural causal model for multiclass classification.
result The proposed model can infer second opinions more accurately than non-causal models.
Study of skateboard flips as continuous curves in SO(3) group.
problem Characterize skateboard flip tricks as continuous motions.
method Model flips as curves in SO(3), analyze lifts to S3, derive formulas. result There are only four distinct flip tricks up to continuous deformation.
A new method centers outliers in robust PCA without manual intervention.
problem Outliers in robust PCA require manual centering, complicating the analysis.
method Introduces a 'bias trick' to automatically center non-outliers.
result First optimal RPCA algorithm with automatic centering.
Nash's theorem proved with Günther's trick
problem Proving Nash's smooth embedding theorem
method Using Günther's trick
result Nash's theorem proved
Explains Conway's tangle trick and its mathematical origins.
problem Understanding the relationship between braids and elliptic curves.
method Discusses the tangle trick, its mathematical underpinnings, and historical context.
result Establishes the connection between braids and elliptic curves.
We prove all knots can be transformed into a trefoil using special diagrams.
problem Transforming any knot into a trefoil using magic tricks.
method Introducing knotholder diagrams to encode transformations.
result All knots can be transformed into a trefoil.
Geometric trick simplifies link homotopy and concordance.
problem Homotopy and concordance of links in homology spheres.
method Relative Whitney trick to remove double points.
result Links in homology spheres can be simplified to topologically slice links.
Tricks improve retail product image classification accuracy.
problem Retail Product Image Classification
method Various tricks including a new LCA layer, Instagram-pretrained Convnet, and Maximum Entropy loss.
result Increased accuracy of fine-tuned convnets by a large margin.
A new gradient estimator for categorical distributions reduces bias and variance.
problem Intractability of gradients for categorical distributions in discrete latent variable models.
method CatLog-Derivative trick and IndeCateR gradient estimator.
result IndeCateR reduces bias and variance of gradients for categorical distributions.
Establishes necessary and sufficient conditions for smooth triviality of Lie subalgebras and Lie ideals, and proves Moser's trick for foliations.
problem Smooth triviality of Lie subalgebras and Lie ideals
method Establishing necessary and sufficient conditions and proving Moser's trick for foliations
result Direct proof of Moser's trick for foliations
Triple-point Whitney trick classifies ornaments of 3-manifolds.
problem Classifying ornaments of 3-manifolds in high dimensions.
method Triple-point Whitney trick applied to orientable manifolds.
result Classification of ornaments by the μ-invariant.
Alexander trick applied to homology spheres for manifold homeomorphisms.
problem Group of homeomorphisms of contractible manifolds.
method Strong uniqueness statement for one-sided h-cobordisms.
result Group of homeomorphisms is contractible for d≥6. Embolic volume of compact manifolds is defined in terms of Berger's embolic inequality. In this paper, we show a result of relating embolic volume to the first Betti number. The proof relies on Gromov's covering argument appeared in systolic geometry. Berger called this method covering trick. We exploit and present mor…
Expands Bredon's trick for applications in geometry and topology.
problem Local-to-global extension principles in geometric and topological contexts.
method Novel applications and frameworks for stratified pseudomanifolds, Ricci flow, and persistent homology.
result Establishes Bredon's trick as a unifying framework.
Paper generalizes reparameterization trick for broader applicability.
problem Limited applicability of reparameterization trick to specific distributions.
method Introduces a generalized transformation-based gradient method.
result Proposed model combines advantages of control variates and generalized reparameterization.
Bredon's trick helps extend local properties to global topological spaces.
problem Extending local properties to global topological spaces.
method Bredon's trick for local properties to global spaces.
result Bredon's trick allows for natural alternative demonstrations of classic results.
We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability distributions not directly amenable to the reparameterizati…
We introduce a family of pairwise stochastic gradient estimators for gradients of expectations, which are related to the log-derivative trick, but involve pairwise interactions between samples. The simplest example of our new estimator, dubbed the fundamental trick estimator, is shown to arise from either a) introducin…
The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each time solving for the most likely configuration. We derive an entire family of r…
An online reinforcement learning algorithm is anytime if it does not need to know in advance the horizon T of the experiment. A well-known technique to obtain an anytime algorithm from any non-anytime algorithm is the "Doubling Trick". In the context of adversarial or stochastic multi-armed bandits, the performance of …
Inference in popular nonparametric Bayesian models typically relies on sampling or other approximations. This paper presents a general methodology for constructing novel tractable nonparametric Bayesian methods by applying the kernel trick to inference in a parametric Bayesian model. For example, Gaussian process regre…
New trick builds hyperbolic manifolds from compact ones, proving some don't virtually fiber.
problem Proving some hyperbolic manifolds don't virtually fiber.
method Hyperbolic reflection group trick, embedding theory, manifold topology.
result Constructed Gromov hyperbolic 7-manifolds that don't virtually fiber over a circle.
Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables. However, non-differentiability of the discrete units prohibits using the reparameterization trick, essential for lo…
Link framings can only change when a 3-manifold has a non-separating sphere.
problem Understanding how framings of links can change in 3-manifolds.
method Using McCullough's work on mapping class groups and the Dirac trick.
result Link framings can only change in specific 3-manifolds with a non-separating sphere.
New method for simplifying knots with specific properties.
problem Understanding knots with a specific unknotting number.
method Derive and apply the Montesinos trick for proper rational tangle replacement.
result Prove that knots with proper rational unknotting number one are prime and classify certain types.
We introduce an off-policy evaluation procedure for highlighting episodes where applying a reinforcement learned (RL) policy is likely to have produced a substantially different outcome than the observed policy. In particular, we introduce a class of structural causal models (SCMs) for generating counterfactual traject…
We discuss replica analytic continuation using several simple models in order to prove mathematically the validity of replica analysis, which is used in a wide range of fields related to large scale complex systems. While replica analysis consists of two analytical techniques, the replica trick (or replica analytic con…
Paper develops a weighted linearization approach for vector fields.
problem Linearizability of vector fields under weighted conditions.
method Formal Moser trick applied to power series, addressing weighted non-resonance condition.
result Formal Moser trick works over any field of characteristic zero.
Tricks adversarial attacks to target specific classes, improving classifier accuracy.
problem Recent adversarial defense approaches have failed to protect classifiers from untargeted attacks.
method Target Training defense tricks untargeted attacks into targeted attacks on designated classes, then derives the real class.
result 86.2% accuracy for CW-L2 (confidence=0) in CIFAR10, outperforming unsecured classifiers.
This paper solves a complex differential relation using a novel 'avoidance trick'.
problem Classifying tangent distributions satisfying non-involutivity conditions.
method Convex integration with an 'avoidance trick'.
result First example of a differential relation that is ample in some directions but not all.
A new network model combines features of DCBM, LSM, and β-model, using a cancellation trick for parameter estimation.
problem Challenging parameter fitting in network models.
method Introducing a cancellation trick to resolve parameter fitting issues in the logit-DCBM.
result R-SCORE significantly improves community detection over existing methods.
The reparameterization trick is widely used in variational inference as it yields more accurate estimates of the gradient of the variational objective than alternative approaches such as the score function method. Although there is overwhelming empirical evidence in the literature showing its success, there is relative…
Low-variance gradient estimation is crucial for learning directed graphical models parameterized by neural networks, where the reparameterization trick is widely used for those with continuous variables. While this technique gives low-variance gradient estimates, it has not been directly applicable to discrete variable…
Proves existence of planar curves with specific curvature.
problem Existence of planar closed curves with prescribed curvature.
method Variational methods, adding a parameter, monotonicity trick.
result Existence of planar closed curves with prescribed curvature for some curvature functions.
The article confirms two quasi-alternating surgeries for 9 asymmetric L-space knots.
problem Understanding quasi-alternating surgeries on asymmetric L-space knots.
method Using the Montesinos trick to confirm known surgeries.
result Confirmation of two quasi-alternating surgeries for each of 9 asymmetric L-space knots.
Improved diffusion bridge sampling with rKL-LD loss.
problem Improving sampling from unnormalized distributions using diffusion bridges.
method Employing the rKL-LD loss instead of the Log Variance (LV) loss for diffusion bridges.
result rKL-LD consistently outperforms LV loss in diffusion bridges.
We stabilize the Kumaraswamy distribution for efficient sampling and differentiation.
problem Numerical instabilities in the Kumaraswamy distribution's inverse CDF and log-pdf.
method Identified and resolved numerical issues, introduced a stabilized KS distribution.
result Stabilized Kumaraswamy distribution supports efficient sampling and differentiation.