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Sorbonne Université

Academic institutioneurope · fr
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Research library753linked papers
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Selected work

Representative Papers

Measure-to-measure interpolation using Transformers

Nov 07, 2024arXiv.org

This paper investigates the expressive power of Transformers as arbitrary input-to-output measure mappings. Method: We reformulate Transformers from a measure-theoretic perspective, modeling them as differentiable maps on continuous measure spaces—departing from conventional discrete token-based interpretations. Leveraging continuity equations to describe particle dynamics, we design an attention mechanism incorporating spherical geometry constraints and optimal transport theory. Contribution/Results: We propose the first Transformer architecture provably capable of exact matching between arbitrary input–target measure pairs. Under the minimal assumption that a transport map exists between each pair, a single model achieves precise matching for N arbitrary measure pairs. We establish theoretical completeness by proving that Transformers serve as universal interpolators between measures and provide explicit parameter constructions. This work fundamentally characterizes the expressive capacity of Transformers for measure transformation tasks.

10 citations1 influentialRead paper

Embedded Graph Convolutional Networks for Real-Time Event Data Processing on SoC FPGAs

Jun 11, 2024arXiv.org

To address the challenges of high-throughput, ultra-low-latency, and energy-efficient real-time event processing for automotive embedded systems, this paper proposes a hardware-software co-optimization framework targeting SoC FPGAs. We present the first PointNet++ acceleration implementation on the Xilinx ZCU104 platform and introduce an event-aware asynchronous graph convolutional network (EFGCN) capable of online analysis of continuous event streams. Our approach integrates model pruning, quantization, and a customized pipelined accelerator architecture, achieving over 100× model size reduction. Experimental evaluation demonstrates a throughput of 13.3 MEPS and an end-to-end latency of 4.47 ms, with only 2.3% and 1.7% accuracy degradation on N-Caltech101 and N-Cars benchmarks, respectively. This work establishes the first hardware architecture for asynchronous GCNs, and we publicly release the complete software-hardware stack. Our framework provides an efficient, edge-deployable paradigm for event-driven intelligent perception.

6 citations1 influentialRead paper

LLM-ABBA: Understanding time series via symbolic approximation

Nov 27, 2024arXiv.org

This work addresses the challenge of effectively leveraging semantic information in time series for large language models (LLMs). To this end, we propose the first framework that deeply integrates adaptive Brownian bridge aggregation (ABBA) with LLMs. Methodologically: (1) we design an amplitude- and period-preserving ABBA symbolic representation to bridge temporal structure with LLM embedding spaces; (2) we introduce a fixed piecewise-linear chain reconstruction technique to significantly suppress cumulative quantization error; and (3) we combine fine-tuning, prompt engineering, and controllable symbolic–numerical inverse mapping to achieve semantic alignment. Our approach achieves state-of-the-art performance on UCR and three medical time-series classification benchmarks, as well as on the TSER regression benchmark—marking the first instance where an LLM surpasses prior methods on TSER. Moreover, its forecasting accuracy rivals that of advanced dedicated time-series models.

2 citations1 influentialRead paper

Learning a Neural Solver for Parametric PDE to Enhance Physics-Informed Methods

Oct 09, 2024International Conference on Learning Representations

Physics-informed neural networks (PINNs) face challenges—including ill-conditioned optimization, slow convergence, and poor generalization—when solving parametric partial differential equations (PDEs). This paper proposes a data-driven neural solver that parameterizes adaptive gradient descent as a neural network, jointly modeling distributions of PDE coefficients and initial/boundary conditions under physical constraints, while dynamically conditioning the optimizer to alleviate loss function ill-conditioning. To our knowledge, this is the first work to introduce neural solvers into parametric PDE settings, enabling end-to-end training via implicit differentiation and backpropagation. Experiments demonstrate a 2–5× speedup in training with enhanced convergence stability. At inference, the solver generalizes robustly to unseen parameter combinations, significantly reducing required iterations while maintaining high accuracy.

2 citationsRead paper

Online Stochastic Matching: A Polytope Perspective

Dec 29, 2021

This paper studies online stochastic matching under graph-theoretic compatibility constraints, where items of distinct classes arrive according to independent Poisson processes, compatibility is encoded by an undirected graph, and unmatched items are queued. Targeting the joint optimization of stability, matching delay, and long-run matching rate, we establish—for the first time—the fundamental connection between the existence of stable policies, the dimension of the convex polyhedron formed by nonnegative solutions to conservation equations, and the structural properties of the compatibility graph. We propose a novel policy design paradigm wherein performance bounds are characterized by the vertices of this polyhedron. Leveraging stochastic process modeling, graph theory, and convex analysis, we construct stable policies that either achieve or approximate these vertex bounds. These policies maximize the long-run matching rate while ensuring system stability and yield tight theoretical bounds on matching delay in terms of graph structure.

2 citationsRead paper
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