Related papers: Encodings of Turing machines in Linear Logic

We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…

We present three different functional interpretations of intuitionistic linear logic ILL and show how these correspond to well-known functional interpretations of intuitionistic logic IL via embeddings of IL into ILL. The main difference…

In this paper an algorithm is designed which generates in-equivalent Boolean functions of any number of variables from the four Boolean functions of single variable. The grammar for such set of Boolean function is provided. The Turing…

Deep Learning architectures, and in particular Transformers, are conventionally viewed as a composition of layers. These layers are actually often obtained as the sum of two contributions: a residual path that copies the input and the…

Because of the pervasive usage of Neural Networks in human sensitive applications, their interpretability is becoming an increasingly important topic in machine learning. In this work we introduce a simple way to interpret the output…

Speculative decoding is a technique that uses multiple language models to accelerate infer- ence. Previous works have used an experi- mental approach to optimize the throughput of the inference pipeline, which involves LLM training and can…

This paper presents an approach to model an unknown Ladder Logic based Programmable Logic Controller (PLC) program consisting of Boolean logic and counters using Process Mining techniques. First, we tap the inputs and outputs of a PLC to…

We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching…

To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that understands a rich shared code. A semantic embedding is a form of…

Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…

To mitigate the high inference latency stemming from autoregressive decoding in Large Language Models (LLMs), Speculative Decoding has emerged as a novel decoding paradigm for LLM inference. In each decoding step, this method first drafts…

We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…

We treat interpolation for various logics.

Modular exponentiation is crucial to number theory and cryptography, yet remains largely unexplored from a mechanistic interpretability standpoint. We train a 4-layer encoder-decoder Transformer model to perform this operation and…

With the recent success of embeddings in natural language processing, research has been conducted into applying similar methods to code analysis. Most works attempt to process the code directly or use a syntactic tree representation,…

Machine learning techniques have been shown to be effective to recognize different phases of matter and produce phase diagrams in the parameter space interested, while they usually require prior labeled data to perform well. Here, we…

Large language models (LLMs) exhibit failure modes on seemingly trivial tasks. We propose a formalisation of LLM interaction using a deterministic multi-tape Turing machine, where each tape represents a distinct component: input characters,…

Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such…

Predicting a label correctly does not necessarily require representing the operation that produces it. Transformer representations are known to carry label-level information, but whether they encode semantic operations producing those…

We propose trace logic, an instance of many-sorted first-order logic, to automate the partial correctness verification of programs containing loops. Trace logic generalizes semantics of program locations and captures loop semantics by…