Serge Youmbi

University of Derby, Computer Science, Graduate Student

Followers

Following

Public Views

Interests

Uploads

Papers by Serge Youmbi

Deriving Insights: Traditional Neural Networks using Haskell Grenade

Serge Youmbi, 2026

This research paper presents a comprehensive exploration of neural network implementation using G... more This research paper presents a comprehensive exploration of neural network implementation using Grenade, a dependently-typed neural network library for Haskell created by Huw Campbell. 1 Unlike mainstream frameworks such as TensorFlow and PyTorch, which rely on runtime tensor shape checking, Grenade leverages Haskell's advanced type system to encode network architectures at the type level, catching dimension mismatches at compile time rather than runtime. Through ten distinct financial machine learning examples-spanning feedforward networks, convolutional architectures, recurrent models, autoencoders, variational autoencoders, generative adversarial networks, attention mechanisms, graph neural networks, and ensemble systems-we demonstrate how functional programming paradigms offer unique advantages for neural network construction. These advantages include referential transparency ensuring reproducible training, immutable data structures preventing accidental state corruption, and compositional design enabling modular network assembly. Our empirical results across a portfolio of sixteen stocks reveal practical insights: the Long Short-Term Memory architecture achieved 57% directional accuracy in the ensemble system, attention mechanisms identified cross-sector dependencies with TSLA receiving 1.98 units of cumulative attention, and variational autoencoders optimally extracted risk factors at 150 training epochs before overfitting commenced.

Download

A Survey of Category Theory and Deep Learning

Serge Youmbi, 2025

This survey presents a comprehensive examination of the emerging intersection between category th... more This survey presents a comprehensive examination of the emerging intersection between category theory-the abstract mathematical study of structure, composition and deep learning, the driving force behind contemporary artificial intelligence. We trace the historical development of categorical approaches to machine learning, from early type-theoretic foundations through to modern frameworks for understanding neural network composition, automatic differentiation, and learned representations. The survey is organised around six thematic clusters: compositional foundations, differentiation and learning dynamics, geometric and equivariant structures, semantic and logical frameworks, probabilistic and information-theoretic perspectives, and implementation paradigms. Throughout, we emphasise the bidirectional nature of this relationship: category theory provides deep learning with rigorous compositional semantics and new architectural principles, whilst deep learning challenges category theory with novel mathematical structures demanding formalisation. We critically assess the maturity, tractability, and A Survey of Category Theory and Deep Learning 2 empirical validation of existing approaches, identify significant gaps in the literature, and outline promising directions for future research. This survey is intended to be accessible to practitioners with machine learning backgrounds whilst providing sufficient mathematical depth to serve as a reference for researchers working at this interdisciplinary frontier.

Download

Probabilistic Programming for Quantitative Finance: A Functional Approach Using Algebraic Effects

Serge Youmbi, 2026

This paper presents a comprehensive framework for expressing financial models as probabilistic pr... more This paper presents a comprehensive framework for expressing financial models as probabilistic programs using algebraic effects in Haskell. We demonstrate how the prob-fx library enables separation of model specification from inference execution, allowing identical models to be analysed using Metropolis-Hastings, importance sampling, or forward simulation without modification. Through ten detailed case studies spanning derivative pricing, credit risk modelling, portfolio allocation, interest rate dynamics, market regime detection, and multi-factor asset pricing, we demonstrate that probabilistic programs closely mirror mathematical formulations whilst maintaining computational efficiency. The functional approach yields referential transparency for reproducibility, compositionality for model building, and compile-time type safety for catching specification errors-addressing persistent challenges in financial software development.

Download

A Foundational Framework for Understanding Neural Computation through Category Theory and Operational Semantics

Serge Youmbi, 2026

This paper presents a comprehensive theoretical framework for understanding deep neural networks ... more This paper presents a comprehensive theoretical framework for understanding deep neural networks through the lens of categorical logic, drawing upon foundational work in categorical operational semantics for logic programming. We establish formal correspondences between the compositional structure of categories and the layered architecture of neural networks, demonstrating that functors provide a natural mathematical abstraction for neural network transformations whilst natural transformations capture the essence of learning and optimisation processes. 1 The framework introduces several novel contributions: first, we formalise neural network architectures as objects in a category NN where morphisms represent layerwise transformations preserving computational structure; second, we demonstrate that backpropagation emerges naturally from the contravariant nature of gradient computation, interpretable through the lens of categorical duality; third, we establish soundness and completeness results for neural inference systems analogous to those proven for first-order hereditarily Harrop (FOHH) logic programming. 2 Our categorical approach provides several practical benefits: it enables formal verification of neural network properties through type-theoretic methods, offers principled techniques for neural architecture design via universal constructions, and establishes a rigorous foundation for understanding attention mechanisms as instances of the Beck-Chevalley condition. We demonstrate these concepts through detailed diagrams and worked examples, making the mathematical machinery accessible to practitioners in artificial intelligence and machine learning.

Download

Deep Neural Networks An Interactive Exploration Through State Machine-Orchestrated Visualisations Input Hidden Hidden Output

Serge Youmbi, 2026

Deep neural networks have revolutionised artificial intelligence, yet their internal mechanisms o... more Deep neural networks have revolutionised artificial intelligence, yet their internal mechanisms often remain opaque to practitioners and researchers alike. This research paper presents a comprehensive exploration of traditional deep learning architectures through the lens of interactive visualisation, demonstrating how finite state machines can orchestrate complex visual representations of neural network dynamics. We examine nine fundamental architectures-feedforward networks, vanilla recurrent neural networks, Long Short-Term Memory networks, Gated Recurrent Units, Transformer attention mechanisms, autoencoders, variational autoencoders, generative adversarial networks, and graph neural networks-providing intuitive explanations of their mathematical foundations alongside detailed descriptions of accompanying interactive visualisations built using XState and D3.js. Each visualisation employs state machine patterns to manage UI complexity, temporal navigation, and real-time rendering, offering researchers and practitioners unprecedented insight into the dynamic behaviour of these models during inference. By bridging theoretical understanding with interactive exploration, this work contributes both to the pedagogical resources available for deep learning education and to the broader goal of neural network interpretability.

Download

Deep Neural Networks: An Implementation in Haskell Using Recursion Schemes A Categorical Approach to Neural Network Composition and Training Catamorphism Forward Propagation Anamorphism Backward Propagation

Serge Youmbi, 2026

This paper presents a novel approach to implementing deep neural networks in Haskell using recurs... more This paper presents a novel approach to implementing deep neural networks in Haskell using recursion schemes from category theory. We demonstrate that neural network architectures can be elegantly expressed as free monads over layer functors, enabling forward propagation to be implemented as a catamorphism (generalised fold) and backward propagation as an anamorphism (generalised unfold). The complete training process emerges naturally as a metamorphism-the composition of these dual operations. Our implementation, called Catana 1 , supports multiple network architectures including dense networks, convolutional neural networks (CNNs), recurrent neural networks (RNNs), Long Short-Term Memory networks (LSTMs), and Transformers with self-attention mechanisms. We provide comprehensive examples including financial time series forecasting, demonstrating that this categorical approach yields implementations that are not only mathematically rigorous but also practical for real-world applications. The paper includes detailed explanations, intuitive diagrams, and complete code listings, making it accessible to researchers and practitioners interested in the intersection of functional programming, category theory, and machine learning.

Download

Multi-LLM Orchestration Patterns for Supply Chain Systems

Modern supply chains operate across vast, interconnected networks that demand intelligent coordin... more Modern supply chains operate across vast, interconnected networks that demand intelligent coordination of logistics, inventory, and distribution. Building on foundational principles from operations research—such as Simchi-Levi’s “Operations Rules” for balancing efficiency and resilience—this work explores how multi-LLM orchestration can extend these frameworks. By dynamically selecting and coordinating large language models based on task complexity, urgency, and precision, it introduces a principled architecture for applying advanced AI to supply chain optimisation.

Download

Multi Agent AI Systems for Financial Portfolio Management and Option Pricing

Multi Agent AI Systems for Financial Portfolio Management and Option Pricing, 2025

In advanced multi-agent frameworks, the deployment of domain-specific LLM-powered agents—each ful... more In advanced multi-agent frameworks, the deployment of domain-specific LLM-powered agents—each fulfilling unique functions such as fundamental analysis, sentiment interpretation, technical assessment, and trading with tailored risk profiles—creates a robust ecosystem for financial strategy formulation. Through systematic deliberation and cooperative decision-making, these agents collectively enhance trading efficacy, yielding marked improvements in cumulative returns, risk-adjusted performance (Sharpe ratio), and drawdown resilience relative to conventional benchmark approaches. The approach exemplifies how distributed expertise can redefine precision and adaptability in algorithmic trading.

Download

Algebraic Effects and Delimited Continuations for Multi-Agent AI Systems in Financial Portfolio Management and Options Pricing

Algebraic Effects and Delimited Continuations for Multi-Agent AI Systems in Financial Portfolio Management and Options Pricing, 2025

This document presents an architectural framework for building multi-agent AI systems in the fina... more This document presents an architectural framework for building multi-agent AI systems in the financial domain using Kyo’s algebraic effect system. Kyo, developed by Flavio Brasil at Nubank, introduces a novel approach to effect handling through first-class delimited continuations
that can be resumed zero, one, or multiple times (Brasil 2023, 2025). Unlike traditional approaches that rely on callback chains, promise combinators, or actor-based message passing, Kyo’s continuation-based semantics enable sophisticated control flow patterns essential for financial applications: speculative execution for latency-sensitive pricing,
transactional rollback for failed multi-leg trades, fan-out aggregation for consensus pricing, and checkpoint/resume for long-running optimisation loops. This architecture addresses critical production concerns including type-safe effect tracking, composable error handling, and formal reasoning about system behaviour—essential for regulatory compliance and risk management in institutional finance.

Download

Conceptualising Trigraphs: A Generalisation of Milner's Bigraphs

We explore a conceptual generalisation of Robin Milner's Bigraphs, known for forming a symmetric ... more We explore a conceptual generalisation of Robin Milner's Bigraphs, known for forming a symmetric partial monoidal category, into a novel concept termed "Trigraphs." We discuss the foundational aspects of Bigraphs, propose potential interpretations for a third structural component in Trigraphs, and consider how the categorical operations might be extended.

Download

Serge Youmbi

Uploads

Papers by Serge Youmbi

Log In