arXiv subjects

Jens E. Pedersen

Publications and source records attributed to Jens E. Pedersen.

6 recordsLinked to original sources

arXiv2026

Frame bounds and bandwidth tiling for time-causal bandpass wavelets

Wavelets and frames that provide strong guarantees for signal representations are a cornerstone in signal processing theory, but have long been restricted to non-causal settings. Recent work extended wavelet analysis to time-causal systems that operate on streaming signals, with exact reconstruction and time-recursive implementations. However, the frame guarantees that make such representations reliable under noise and quantization are uncharacterized. We derive closed-form frame bounds and conditioning on band-limited domains, peak frequencies, constant-Q bandwidth tiling, and spectral decay rates for time-causal bandpass wavelets. Our work provides design rules for the scale ratio and channel count, which we validate numerically against discrete implementations of the causal wavelets in terms of recursive filters.

eess.SP↗

arXiv2024

Neuromorphic Programming: Emerging Directions for Brain-Inspired Hardware

The value of brain-inspired neuromorphic computers critically depends on our ability to program them for relevant tasks. Currently, neuromorphic hardware often relies on machine learning methods adapted from deep learning. However, neuromorphic computers have potential far beyond deep learning if we can only harness their energy efficiency and full computational power. Neuromorphic programming will necessarily be different from conventional programming, requiring a paradigm shift in how we think about programming. This paper presents a conceptual analysis of programming within the context of neuromorphic computing, challenging conventional paradigms and proposing a framework that aligns more closely with the physical intricacies of these systems. Our analysis revolves around five characteristics that are fundamental to neuromorphic programming and provides a basis for comparison to contemporary programming methods and languages. By studying past approaches, we contribute a framework that advocates for underutilized techniques and calls for richer abstractions to effectively instrument the new hardware class.

cs.NE↗

arXiv2024

Neuromorphic Intermediate Representation: A Unified Instruction Set for Interoperable Brain-Inspired Computing

Spiking neural networks and neuromorphic hardware platforms that simulate neuronal dynamics are getting wide attention and are being applied to many relevant problems using Machine Learning. Despite a well-established mathematical foundation for neural dynamics, there exists numerous software and hardware solutions and stacks whose variability makes it difficult to reproduce findings. Here, we establish a common reference frame for computations in digital neuromorphic systems, titled Neuromorphic Intermediate Representation (NIR). NIR defines a set of computational and composable model primitives as hybrid systems combining continuous-time dynamics and discrete events. By abstracting away assumptions around discretization and hardware constraints, NIR faithfully captures the computational model, while bridging differences between the evaluated implementation and the underlying mathematical formalism. NIR supports an unprecedented number of neuromorphic systems, which we demonstrate by reproducing three spiking neural network models of different complexity across 7 neuromorphic simulators and 4 digital hardware platforms. NIR decouples the development of neuromorphic hardware and software, enabling interoperability between platforms and improving accessibility to multiple neuromorphic technologies. We believe that NIR is a key next step in brain-inspired hardware-software co-evolution, enabling research towards the implementation of energy efficient computational principles of nervous systems. NIR is available at neuroir.org

cs.NE↗

arXiv2024

Q-S5: Towards Quantized State Space Models

In the quest for next-generation sequence modeling architectures, State Space Models (SSMs) have emerged as a potent alternative to transformers, particularly for their computational efficiency and suitability for dynamical systems. This paper investigates the effect of quantization on the S5 model to understand its impact on model performance and to facilitate its deployment to edge and resource-constrained platforms. Using quantization-aware training (QAT) and post-training quantization (PTQ), we systematically evaluate the quantization sensitivity of SSMs across different tasks like dynamical systems modeling, Sequential MNIST (sMNIST) and most of the Long Range Arena (LRA). We present fully quantized S5 models whose test accuracy drops less than 1% on sMNIST and most of the LRA. We find that performance on most tasks degrades significantly for recurrent weights below 8-bit precision, but that other components can be compressed further without significant loss of performance. Our results further show that PTQ only performs well on language-based LRA tasks whereas all others require QAT. Our investigation provides necessary insights for the continued development of efficient and hardware-optimized SSMs.

cs.LG↗

arXiv2023

Subspace tracking for independent phase noise source separation in frequency combs

Advanced digital signal processing techniques in combination with ultra-wideband balanced coherent detection have enabled a new generation of ultra-high speed fiber-optic communication systems, by moving most of the processing functionalities into digital domain. In this paper, we demonstrate how digital signal processing techniques, in combination with ultra-wideband balanced coherent detection can enable optical frequency comb noise characterization techniques with novel functionalities. We propose a measurement method based on subspace tracking, in combination with multi-heterodyne coherent detection, for independent phase noise sources identification, separation and measurement. Our proposed measurement technique offers several benefits. First, it enables the separation of the total phase noise associated with a particular comb-line or -lines into multiple independent phase noise terms associated with different noise sources. Second, it facilitates the determination of the scaling of each independent phase noise term with comb-line number. Our measurement technique can be used to: identify the most dominant source of phase noise; gain a better understanding of the physics behind the phase noise accumulation process; and confirm, already existing, and enable better phase noise models. In general, our measurement technique provides new insights into noise behavior of optical frequency combs.

physics.optics↗

arXiv2021

Approaching the optimum phase measurement in the presence of amplifier noise

In fundamental papers from 1962 [1, 2], Heffener and Haus showed that it is not possible to construct a linear noiseless amplifier. The implies that the amplifier intrinsic noise sources induce random perturbations on the phase of the incoming optical signal which translates into spectral broadening. To achieve the minimum (quantum noise limited) induced phase fluctuation, and the corresponding minimum spectral broadening, an optimum phase measurement method is needed. We demonstrate that a measurement method based on the heterodyne detection and the extended Kalman filtering approaches an optimum phase measurement in the presence of amplifier noise. A penalty of 5 dB (numerical) and 15 dB (experimental) compared to the quantum limited spectral broadening is achieved. For comparison, the conventional phase measurement method's penalty exceeds 30 dB for the measurements. Our results reveal new scientific insights by demonstrating that the impact of amplifier noise can be significantly reduced by using the proposed phase measurement method. An impact is envisioned for the phase-based optical sensing system, as optical amplification could increase sensing distance with the minimum impact on the phase.

physics.optics↗