arXiv subjects

Gaetan Hains

Publications and source records attributed to Gaetan Hains.

6 recordsLinked to original sources

arXiv2026

MoA-Structured Decode Attention DNF Derivation, KV-Cache Accumulation, GQA/MQA, and OpenACC Kernel

We derive four memory-optimal inference artifacts for transformer attention using the Mathematics of Arrays (MoA), each following directly from the forward-pass Denotational Normal Form (DNF) of with the query-row index fixed to the current decode step. The artifacts are: (1)~a single-query decode DNF in which the $\psi$-reduction eliminates the $K^\top$ buffer algebraically, achieving $(d_k + nd_k+ nd_v+ d_v)\times4\,{B}$ Dynamic Random Access Memory (DRAM) traffic result numerically verified to $\|{err}\|_\leq2\times10^{-7}$; (2)~a C/OpenACC Graphics Processing Unit (GPU) kernel with Operational Normal Form (ONF) stride arithmetic and hardware-coalesced memory access, verified to $\|\mathrm{err}\|_\infty=0$ (exact IEEE-754 floating-point arithmetic); (3)~a multi-step KV-cache with $O(d_k+d_v)$ per-step append via MoA concatenation $\#$; and (4)~Grouped-Query Attention (GQA) and Multi-Query Attention (MQA) derived via $\psi$-selection, achieving a proven $\frac {h_q} { h_{kv} }$ reduction in KV traffic. All programs are verified against PyTorch scaled_dot_product_attention.

cs.LG↗

arXiv2026

Attention at the Theoretical Minimum: A Mathematics of Arrays Framework for Memory-Optimal Transformer Kernels

The attention mechanism is the dominant computational bottleneck in modern transformer-based AI. Its standard implementation incurs quadratic memory traffic in the sequence length~$n$, and DRAM accesses cost 100--1000$\times$ more energy than arithmetic operations on contemporary hardware, so any analysis focused solely on FLOP counts fundamentally mischaracterises the bottleneck. We present a Mathematics of Arrays (MoA) reformulation of scaled dot-product attention and its numerically stable softmax, deriving a Denotational Normal Form (DNF) that eliminates all intermediate arrays -- including the implicit transposed-key buffer and every softmax temporary -- by algebraic construction rather than empirical tuning. The DNF achieves $O(n_{dk} + n{_{dv}})$ data movement versus $O(n^2 + n_{dk} + n_{dv})$ for the standard implementation, where $n$ is the sequence length, $dk$ is the key dimensionality and $dv$ the value dimensionality, and is verified numerically against PyTorch at full double-precision floating-point on concrete inputs. Unlike hardware-specific accelerators or empirical tiling schemes such as FlashAttention, MoA simultaneously provides array fusion, shape-transformation correctness, and predictive cost models from a single algebraic framework. Memory minimality is a theorem established before any code is written. A predictive performance model projects $2$--$100\times$ speedup and $2$--$50\times$ energy reduction, with the advantage widening at exascale. The derivation establishes a formally verified pipeline from Python specification through (ONF) Operational Normal Form, and dimension-lifted hardware mapping, providing performance-portable AI kernels of direct relevance to DARPA edge-deployment and DOE exascale priorities.

cs.LG↗

arXiv2023

Data Extraction, Transformation, and Loading Process Automation for Algorithmic Trading Machine Learning Modelling and Performance Optimization

A data warehouse efficiently prepares data for effective and fast data analysis and modelling using machine learning algorithms. This paper discusses existing solutions for the Data Extraction, Transformation, and Loading (ETL) process and automation for algorithmic trading algorithms. Integrating the Data Warehouses and, in the future, the Data Lakes with the Machine Learning Algorithms gives enormous opportunities in research when performance and data processing time become critical non-functional requirements.

cs.DC↗

arXiv2023

Short-Term Stock Price Forecasting using exogenous variables and Machine Learning Algorithms

Creating accurate predictions in the stock market has always been a significant challenge in finance. With the rise of machine learning as the next level in the forecasting area, this research paper compares four machine learning models and their accuracy in forecasting three well-known stocks traded in the NYSE in the short term from March 2020 to May 2022. We deploy, develop, and tune XGBoost, Random Forest, Multi-layer Perceptron, and Support Vector Regression models. We report the models that produce the highest accuracies from our evaluation metrics: RMSE, MAPE, MTT, and MPE. Using a training data set of 240 trading days, we find that XGBoost gives the highest accuracy despite running longer (up to 10 seconds). Results from this study may improve by further tuning the individual parameters or introducing more exogenous variables.

q-fin.TR↗

arXiv2020

Machine Learning Prediction of Gamer's Private Networks

The Gamer's Private Network (GPN) is a client/server technology created by WTFast for making the network performance of online games faster and more reliable. GPN s use middle-mile servers and proprietary algorithms to better connect online video-game players to their game's servers across a wide-area network. Online games are a massive entertainment market and network latency is a key aspect of a player's competitive edge. This market means many different approaches to network architecture are implemented by different competing companies and that those architectures are constantly evolving. Ensuring the optimal connection between a client of WTFast and the online game they wish to play is thus an incredibly difficult problem to automate. Using machine learning, we analyzed historical network data from GPN connections to explore the feasibility of network latency prediction which is a key part of optimization. Our next step will be to collect live data (including client/server load, packet and port information and specific game state information) from GPN Minecraft servers and bots. We will use this information in a Reinforcement Learning model along with predictions about latency to alter the clients' and servers' configurations for optimal network performance. These investigations and experiments will improve the quality of service and reliability of GPN systems.

cs.DC↗

arXiv2019

State-of-the-Art on Query & Transaction Processing Acceleration

The vast amount of processing power and memory bandwidth provided by modern Graphics Processing Units (GPUs) make them a platform for data-intensive applications. The database community identified GPUs as effective co-processors for data processing. In the past years, there were many approaches to make use of GPUs at different levels of a database system. In this Internal Technical Report, based on the [1] and some other research papers, we identify possible research areas at LIP6 for GPU-accelerated database management systems. We describe some key properties, typical challenges of GPU-aware database architectures, and identify major open challenges.

cs.DC↗