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Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…

First-order automatic differentiation is a ubiquitous tool across statistics, machine learning, and computer science. Higher-order implementations of automatic differentiation, however, have yet to realize the same utility. In this paper I…

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms…

The application of operator overloading algorithmic differentiation (AD) to computer programs in order to compute the derivative is quite common. But, the replacement of the underlying computational floating point type with the specialized…

This paper presents a new functionality of the Automatic Differentiation (AD) tool Tapenade. Tapenade generates adjoint codes which are widely used for optimization or inverse problems. Unfortunately, for large applications the adjoint code…

Higher-dimensional automata (HDA) are a model of concurrency that models simultaneous execution of events using higher dimensional cells. HDA recognize languages of pomsets, a generalization of finite words whose letters are partially…

Reinforcement learning (RL) for large language model reasoning is frequently hindered by signal loss, a phenomenon where standard uniform sampling with small group sizes fails to uncover informative learning signals for difficult prompts.…

We derive algorithms for higher order derivative computation of the rectangular $QR$ and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and reverse mode of algorithmic differentiation (AD) using…

First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some…

Combinatory Homomorphic Automatic Differentiation (CHAD) was originally formulated as a semantics-driven source-to-source transformation for reverse-mode AD of total (terminating) functional programs. In this work, we extend CHAD to…

The rapid advancement of large-language models (LLMs) has driven extensive research into parameter compression after training has been completed, yet compression during the training phase remains largely unexplored. In this work, we…

Simulation-based optimization using agent-based models is typically carried out under the assumption that the gradient describing the sensitivity of the simulation output to the input cannot be evaluated directly. To still apply…

This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assuming that the linear span of the dictionary is dense, as in…

We show that deterministic collapsible pushdown automata of second order can recognize a language that is not recognizable by any deterministic higher-order pushdown automaton (without collapse) of any order. This implies that there exists…

Finite-turn pushdown automata (PDA) are investigated concerning their descriptional complexity. It is known that they accept exactly the class of ultralinear context-free languages. Furthermore, the increase in size when converting…

Conditional inference on arbitrary subsets of variables is a core problem in probabilistic inference with important applications such as masked language modeling and image inpainting. In recent years, the family of Any-Order Autoregressive…

Dynamic programming (DP) is a fundamental method in operations research, but formulating DP models has traditionally required expert knowledge of both the problem context and DP techniques. Large Language Models (LLMs) offer the potential…

Off-policy learning ability is an important feature of reinforcement learning (RL) for practical applications. However, even one of the most elementary RL algorithms, temporal-difference (TD) learning, is known to suffer form divergence…

Dual numbers are a well-established tool for computing derivatives and constitute the basis of forward-mode automatic differentiation. While the theoretical framework for computing derivatives of arbitrary order is well understood,…

Sentence compression is an important problem in natural language processing with wide applications in text summarization, search engine and human-AI interaction system etc. In this paper, we design a hybrid extractive sentence compression…