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A proper understanding of the striking generalization abilities of deep neural networks presents an enduring puzzle. Recently, there has been a growing body of numerically-grounded theoretical work that has contributed important insights to…
This paper defines antifragility for dynamical systems as convexity of a newly introduced "logarithmic rate". It shows how to compute this rate for positive linear systems, and it interprets antifragility in terms of pulsed alternations of…
Data-driven sequential decision has found a wide range of applications in modern operations management, such as dynamic pricing, inventory control, and assortment optimization. Most existing research on data-driven sequential decision…
Nature suggests that exploiting the elasticities and natural dynamics of robotic systems could increase their locomotion efficiency. Prior work on elastic snake robots supports this hypothesis, but has not fully exploited the nonlinear…
Biological and artificial learners are inherently exposed to a stream of data and experience throughout their lifetimes and must constantly adapt to, learn from, or selectively ignore the ongoing input. Recent findings reveal that, even…
Softmax function is widely used in artificial neural networks for multiclass classification, multilabel classification, attention mechanisms, etc. However, its efficacy is often questioned in literature. The log-softmax loss has been shown…
We obtain sharp bounds on the performance of Empirical Risk Minimization performed in a convex class and with respect to the squared loss, without assuming that class members and the target are bounded functions or have rapidly decaying…
Dynamics simulation with frictional contacts is important for a wide range of applications, from cloth simulation to object manipulation. Recent methods using smoothed lagged friction forces have enabled robust and differentiable simulation…
In this paper, we present a novel Newton-based extremum seeking controller for the solution of multivariable model-free optimization problems in static maps. Unlike existing asymptotic and fixed-time results in the literature, we present a…
A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase…
Dynamic logit models are popular tools in economics to measure state dependence. This paper introduces a new method to derive moment restrictions in a large class of such models with strictly exogenous regressors and fixed effects. We…
A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…
Decision-makers abhor uncertainty, and it is certainly true that the less there is of it the better. However, recognizing that uncertainty is part of the equation, particularly for deciding on environmental policy, is a prerequisite for…
Stochastic systems have a control-theoretic interpretation in which noise plays the role of control. In the weak-noise limit, relevant at low temperatures or in large populations, this leads to a precise mathematical mapping: the most…
In this paper, calculus of variation methods are generalized to find min-max optimal solution of uncertain dynamical systems with uncertain or certain cost. First, a new form of Euler-Lagrange conditions for uncertain systems is presented.…
Possibilistic logic, an extension of first-order logic, deals with uncertainty that can be estimated in terms of possibility and necessity measures. Syntactically, this means that a first-order formula is equipped with a possibility degree…
Deep neural networks exhibit periodic loss spikes during unregularized long-term training, a phenomenon known as the "Slingshot Mechanism." Existing work usually attributes this to intrinsic optimization dynamics, but its triggering…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
This paper studies the class of logarithmically completely monotonic (LCM) functions. These functions play an important role in characterising externally positive linear systems which find applications in important control problems such as…
Large reasoning models achieve strong performance on complex tasks by generating extended chains of thought, but they often "overthink": continuing to reason long after they have enough information to answer correctly. This wastes…