Study reveals bad local maxima in Gaussian mixture models, affecting EM algorithm performance.
problem Bad local maxima in Gaussian mixture models' likelihood function.
method Analyzes population likelihood function and EM algorithm convergence.
result EM algorithm can converge to bad local maxima with high probability.
Gradient-based methods find saddle points, not critical points, in neural networks.
problem Gradient-based optimization methods converge to saddle points rather than critical points in deep neural networks.
method Critical point-finding methods used to analyze neural network losses.
result Gradient-based methods often converge to or pass through gradient-flat regions, where gradient norm has a stationary point.
Geometric study of linear neural networks identifies pure and spurious critical points.
problem Understanding the landscape of loss functions in linear neural networks.
method Geometric properties of functional spaces and parameterization analysis.
result Different phenomena cause the absence of bad local minima in linear networks, depending on the architecture and loss function.
New attacks reduce bad queries in black-box classifiers, improving effectiveness.
problem Evasion attacks often issue many bad queries, which are costly.
method Design new attacks that minimize bad queries while increasing non-bad queries.
result Reduces the number of bad queries by 1.5-7.3 times, improving attack effectiveness.
Proves deep learning has no poor local minima without unrealistic assumptions.
problem The difficulty of training deep neural networks.
method Mathematical proofs for deep linear and nonlinear neural networks.
result Deep neural networks have no poor local minima.
Deep networks avoid bad local minima with no bad valleys.
problem Finding sub-optimal local minima in deep neural networks.
method Analyzing over-parameterized networks with specific activation and loss functions.
result No bad local valleys, implying no sub-optimal strict local minima.
A simple modification improves GAN performance by discarding bad samples.
problem Improving GAN performance with minimal computational cost.
method Top-k update procedure: zero out gradient contributions from least realistic elements.
result Significant improvement in FID score for conditional generation on CIFAR-10.
Incorrect fixed point assertions in digital topology are discussed.
problem Incorrect or poorly stated fixed point assertions in digital topology.
method Discussion of problematic publications in digital metric spaces.
result Clarification of incorrect fixed point assertions.
Fixed point assertions in digital topology are often incorrect or poorly stated.
problem Fixed points in digital metric spaces
method Discussing publications with bad assertions
result Identifying and correcting errors in fixed point assertions
Incorrect fixed point assertions in digital topology are discussed.
problem Incorrect, incorrectly proven, or trivial fixed point assertions in digital topology.
method Continues earlier work on identifying and critiquing bad fixed point assertions.
result Clarifies the nature and extent of incorrect fixed point assertions in digital topology.
Proposes a new factor to improve BAB strategies by recognizing bad-beta assets.
problem Investors often misprice assets based on beta, ignoring bad-beta.
method Double-sorting on beta and bad-beta to create a new factor.
result The Betting Against Bad Beta factor improves BAB strategies.
Reviews recent findings on neural network landscapes.
problem Non-convexity of loss functions causing bad landscapes.
method Rigorous geometric analysis and empirical exploration.
result Wide neural nets may have sub-optimal local minima.
Early SGD hyperparameters affect deep neural network training, showing a break-even point.
problem Understanding how early SGD hyperparameters influence deep neural network training.
method Analysis of stochastic gradient descent (SGD) hyperparameters and their effects on the optimization trajectory.
result A break-even point exists where SGD implicitly regularizes the loss surface and improves gradient conditioning.
Removes all bad local minima without adding extra units.
problem Neural network loss landscapes have bad local minima.
method Converts all bad local minima to non-local minima at infinity using auxiliary parameters.
result Removes all bad local minima from any loss landscape.
The abstract constructs a set of bad 3-orbifolds and shows how any bad 3-orbifold can be transformed into a good one.
problem Characterizing and transforming bad 3-orbifolds into good ones.
method Explicit construction of bad 3-orbifolds and a method of cutting-and-capping to transform them.
result Any bad 3-orbifold can be transformed into a good 3-orbifold through a finite number of operations.
Gradient-flow helps find good minima in complex models.
problem Understanding why gradient-based algorithms work in non-convex optimization.
method Kac-Rice analysis and gradient-flow from statistical physics.
result Gradient-flow finds good global minima in the presence of many spurious local minima.
The lattice cohomology of a plumbed 3--manifold M associated with a connected negative definite plumbing graph is an important tool in the study of topological properties of M, and in the comparison of the topological properties with analytic ones when M is realized as complex analytic singularity link. By defini…
We classify generalized distance-squared mappings of Rn+1 into R2n+1 (n≥1) having generic central points. Moreover, we show that there does not exist a universal bad set Σ⊂(Rn+1)2n+1 in the case of this dimension-pair.
Algorithm checks local optimality and escapes saddles in ReLU networks.
problem Checking local optimality and escaping saddles in ReLU networks with nondifferentiable points.
method Polyhedral geometry to reduce complexity, exploiting convex and nonconvex QPs.
result Algorithm efficiently solves local optimality and saddle point issues in ReLU networks.
Unified-GAN improves SSL with both good and bad samples.
problem Improve semi-supervised learning performance with limited labeled data.
method Unified-GAN combines adversarial training with good and bad samples.
result Unified-GAN achieves state-of-the-art performance and robustness to varying labeled data.
This paper compares EM and GD in two-component mixture models, finding EM escapes bad local optima more reliably.
problem Understanding the convergence of EM and GD in mixture models, especially in regions where one component is missing.
method Analyzing regions called one-cluster regions in two-component mixture models of Gaussians and Bernoullis, comparing the propensity of EM and GD to converge to these regions.
result EM escapes one-cluster regions exponentially fast, while GD escapes them linearly fast, indicating EM is less likely to converge to bad local optima.
Depth alone does not create bad local minima without nonlinearity.
problem Understanding the role of depth and nonlinearity in creating local minima in deep learning models.
method Analyzing the properties of non-convex loss surfaces in deep linear neural networks and proving the absence of bad local minima without nonlinearity.
result Depth alone does not create bad local minima in deep linear neural networks.
RMCSE improves voltage estimation in low-observability distribution systems.
problem Insufficient measurements in distribution system state estimation.
method Combines matrix completion and power system model, minimizes rank and residual with different weights.
result Robust voltage estimation in low-observability systems without bad data detection.
This paper allows unbounded learning rates in gradient descent for better convergence.
problem Proving convergence of gradient descent with unbounded learning rates.
method Introducing a function h(t) to control the learning rates and proving convergence under Armijo's condition.
result Convergence of the sequence {x_n} is proven under specific conditions on the cost function f.
The paper shows deep neural networks have no bad local minima and no diverging paths to infinity.
problem The risk of diverging to infinity in deep neural networks.
method Mathematical analysis of regularizers and loss functions.
result For a large class of over-parameterized deep neural networks, the loss function has no bad local minima and no decreasing paths to infinity.
Study finds stocks with common firm fears earn lower returns.
problem Identifying and quantifying firm-level investor fears.
method Analysis of equity options to identify common firm-level fears and their impact on stock returns.
result Stocks with exposure to common bad fears earn lower returns and require higher compensation.
This paper introduces a gradient analysis framework to improve language model performance by rewarding good examples and penalizing bad ones.
problem Improving language model output quality by penalizing bad examples.
method Gradient analysis of loss functions to reward good examples and penalize bad ones.
result ExMATE is superior to MLE and combining DPO with ExMATE enhances performance.
Improves VAT method for semi-supervised learning with simpler techniques.
problem Improving semi-supervised learning performance with robust classifiers.
method Adopts Bad GAN approach to generate bad samples and employs adversarial training.
result Achieves competitive performance with fewer computations.
New proof shows knot Floer thickness limits bad domains in diagrams.
problem Understanding knot thickness and dealternating number.
method Modified Stipsicz-Szabo approach using Kauffman states.
result Knot Floer thickness is a lower bound on dealternating number.
Adding one neuron fixes neural network's bad local minima.
problem Non-convexity of loss function leading to many bad local minima in neural networks.
method Adding one special neuron with a skip connection to the output or one per layer.
result Every local minimum becomes a global minimum after adding one neuron.
Study shows how bad and good volatility spread differently in forex markets.
problem Understanding how volatility spreads asymmetrically in forex markets.
method High-frequency, intra-day data of major currencies from 2007-2015.
result Negative spillovers are linked to sovereign debt crisis, positive to subprime and monetary policies.
Wide CNNs with shared weights and max pooling have linearly independent features and can achieve zero training error.
problem Understanding the optimization landscape and expressiveness of deep CNNs.
method Analysis of loss landscape and expressiveness of practical deep CNNs with shared weights and max pooling layers.
result Wide CNNs can achieve zero training error and have a well-behaved loss surface with almost no bad local minima.
NICE learns a representation to avoid bad controls in causal inference.
problem Avoiding bad controls in causal inference from observational data.
method Uses invariant risk minimization (IRM) to learn a representation of covariates that avoids bad controls.
result NICE outperforms adjusting for all covariates in cases with unknown collider variables and bad controls.
We show that every bad orbifold vector bundle can be realized as the restriction of a good orbifold vector bundle to a suborbifold of the base space. We give an explicit construction of this result in which the Chen-Ruan orbifold cohomology of the two base spaces are isomorphic (as additive groups). This construction i…
This paper reverses a construction by merging boundary critical points into an interior one.
problem Pushing interior critical points to the boundary and splitting them into two boundary points.
method Specific assumptions allow merging two boundary critical points into one interior critical point.
result Merging two boundary critical points into a single interior critical point.
The minimal number of critical points is studied for smooth functions on closed manifolds.
problem Determining the minimal number of critical points for smooth functions on closed manifolds.
method Investigates cylindrical ball neighborhoods and exotic critical points, proving the conjecture for certain types of critical points.
result The minimal number of critical points is the same for smooth functions without exotic critical points on closed manifolds of dimension at least 6.
The study examines how investor protection and past information affect stock returns and interest rates.
problem Empirical regularities related to investor protection and past information in asset pricing models.
method Developed a dynamic asset pricing model with a controlling shareholder and good/bad memory in budget dynamics.
result Good/bad memory of investors on historical market information affects stock returns and interest rates, strengthening investor protection in high ownership concentration.
Paper compares dimensionality reduction methods for affect classification.
problem Difficulty in obtaining labeled training samples for affect classification.
method Five dimensionality reduction approaches are compared.
result No single approach universally outperforms others in affect classification.
Hard to approximate critical points for simple nonconvex functions.
problem Approximating critical points of nonconvex functions.
method Proving hardness results for polynomial-time approximation of critical points.
result Proving that approximating critical points is intractable for simple nonconvex functions.
The study confirms a conjecture about critical points of smooth functions.
problem Understanding isolated critical points of smooth functions.
method Investigated cone-like, reasonable, and Rothe H hypothesis critical points.
result The conjecture holds true for certain critical points.
Graph attacks can be successful with just a few bad nodes.
problem Adversarial attacks on graph neural networks.
method Identifying and exploiting anchor nodes to compromise graph models.
result A few bad nodes can significantly degrade graph model performance.
Trees represent critical points, linking function topology.
problem Understanding the topology of functions with isolated critical points.
method Corresponding trees to critical points, proving equivalence if trees are isomorphic.
result Constructed a complete topological invariant for functions on 3-manifolds.
V-BAD is a first black-box video attack framework that successfully fools deep video recognition models.
problem Vulnerability of video recognition models to black-box adversarial attacks.
method Tentative perturbations transferred from image models and partition-based rectifications for patches of tentative perturbations.
result V-BAD can craft both untargeted and targeted attacks with high success rates using a manageable number of queries.
Enhanced tracking control for AUVs with improved policy gradient method.
problem Trajectory tracking problem for underactuated AUVs with unknown dynamics and constrained inputs.
method Hybrid actors-critics architecture with multiple actors and critics, Pseudo Q-learning, and deterministic policy gradient.
result High-level tracking control accuracy and stable learning of AUVs.
The paper classifies functions with isolated critical points on a compact surface and develops a criterion for their global equivalence.
problem Classifying functions with isolated critical points on the boundary of a compact surface.
method Topological classification in a neighborhood of critical points, construction of chord diagrams, and development of a criterion for global equivalence.
result A criterion for global topological equivalence of functions with three critical points on a compact surface.
Optimization can learn Johnson-Lindenstrauss embeddings without randomization.
problem Achieving compact data representations with theoretical guarantees.
method A novel optimization-based approach over the space of random solution samplers.
result The method avoids bad stationary points and converges to a deterministic solution.
ResNets with depth and nonlinearity avoid bad local minima.
problem Avoiding bad local minima in deep learning models.
method Proving depth and nonlinearity in ResNets create no bad local minima.
result ResNets with depth and nonlinearity have values no worse than global minimum and can improve further.
Asymmetries in volatility spillovers are highly relevant to risk valuation and portfolio diversification strategies in financial markets. Yet, the large literature studying information transmission mechanisms ignores the fact that bad and good volatility may spill over at different magnitudes. This paper fills this gap…