Related papers: On Coinductive Equivalences for Higher-Order Proba…
We study how large language models (LLMs) reason about memorized knowledge through simple binary relations such as equality ($=$), inequality ($<$), and inclusion ($\subset$). Unlike in-context reasoning, the axioms (e.g., $a < b, b < c$)…
Many machine learning applications require the ability to learn from and reason about noisy multi-relational data. To address this, several effective representations have been developed that provide both a language for expressing the…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
We present a novel technique for learning semantic representations, which extends the distributional hypothesis to multilingual data and joint-space embeddings. Our models leverage parallel data and learn to strongly align the embeddings of…
Recent zero-shot evaluations have highlighted important limitations in the abilities of language models (LMs) to perform meaning extraction. However, it is now well known that LMs can demonstrate radical improvements in the presence of…
The call-by-value lambda calculus can be endowed with permutation rules, arising from linear logic proof-nets, having the advantage of unblocking some redexes that otherwise get stuck during the reduction. We show that such an extension…
An important approach for efficient inference in probabilistic graphical models exploits symmetries among objects in the domain. Symmetric variables (states) are collapsed into meta-variables (meta-states) and inference algorithms are run…
We define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of…
Large Language Models (LLMs) have demonstrated impressive in-context learning (ICL) capabilities from few-shot demonstration exemplars. While recent learning-based demonstration selection methods have proven beneficial to ICL by choosing…
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the…
Enabling preserving bisimilarity is a refinement of strong bisimilarity that preserves safety as well as liveness properties. To define it properly, labelled transition systems needed to be upgraded with a successor relation, capturing…
Experimental evidence indicates that simple models outperform complex deep networks on many unsupervised similarity tasks. We provide a simple yet rigorous explanation for this behaviour by introducing the concept of an optimal…
We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution…
We present a neural network architecture based on bidirectional LSTMs to compute representations of words in the sentential contexts. These context-sensitive word representations are suitable for, e.g., distinguishing different word senses…
We introduce context augmentation, a data-augmentation approach that uses large language models (LLMs) to generate contexts around observed strings as a means of facilitating valid frequentist inference. These generated contexts serve to…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…
Levy-Longo Trees and Bohm Trees are the best known tree structures on the {\lambda}-calculus. We give general conditions under which an encoding of the {\lambda}-calculus into the {\pi}-calculus is sound and complete with respect to such…
Recognizing semantically similar sentences or paragraphs across languages is beneficial for many tasks, ranging from cross-lingual information retrieval and plagiarism detection to machine translation. Recently proposed methods for…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…