Oscillator-based Ising machines, in which the phases of coupled self-sustaining oscillators evolve toward decreasing an Ising Hamiltonian, are commonly interpreted as physical realizations of the Ising model. This interpretation, however, requires the phase dynamics generated by the physical oscillator network to match a prescribed Ising dynamics. Here we show that this correspondence is generally not guaranteed. For arbitrary self-sustaining oscillators under weak coupling, we derive the physical phase interaction from the harmonic overlap between the injected waveform and the perturbation projection vector (also referred to as impulse sensitivity function). We find that uncompensated harmonic phase mismatches between these two quantities generate even components in the physical coupling function, causing a network with the correct coupling topology to implement a non-Ising dynamics. We further show that delayed coupling provides a universal phase-compensation mechanism. For a fixed delay, we derive a condition on the delay under which the even components is minimized in the sense of L2-norm, and oscillator examples confirm that the predicted delay substantially suppresses the even components and brings the realized coupling function closer to the prescribed odd interaction. We then show that a periodically modulated delay can, under suitable moment conditions, eliminate the even components in the phase dynamics. These results establish a general design principle for implementing prescribed energy-based dynamics in physical oscillator networks.
Yi Cheng, Liangtao Dai, Mircea R. Stan et al.· 0 citations
Large language models (LLMs) offer remarkable capabilities but impose prohibitive compute and energy costs. Quantization governs the trade-offs between accuracy and hardware efficiency across granularity and bit-width. Finer granularity (e.g., group-wise) provides high accuracy but incurs scaling and control overhead, while coarser granularity (e.g., channel-wise) has lower overhead but loses accuracy at low precision. Meanwhile, mixed-precision quantization exposes rich accuracy-efficiency trade-offs algorithmically, but existing LLM accelerators remain limited to discrete precision modes, leaving the fractional design space between them unexplored. FlexPosit bridges these gaps through co-design of Posit-based quantization and a precision-tunable bit-serial architecture. Algorithmically, FlexPosit employs distribution-aware quantization with hardware-aligned, sensitivity-guided mixed-precision allocation, leveraging the Posit format's tapered precision to achieve group-wise-like accuracy with channel-wise-like regularity. Architecturally, FlexPosit is a unified bit-serial systolic array with lightweight per-column decoders, unified Processing Elements (PEs), and a global precision controller, enabling tunable fractional precision while preserving fully regular systolic dataflow. Across diverse LLMs, FlexPosit achieves near-FP16 accuracy with sub-5-bit fractional weights. It achieves 1.8x higher throughput and 1.2x lower energy than BitMoD (group-wise quantization), and 1.5x higher throughput and 2.0x lower energy than OliVe (channel-wise quantization), establishing a new Pareto frontier for precision-tunable LLM acceleration.
Yimin Gao, Liangtao Dai, Jun Yin et al.· 0 citations
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