arXiv subjects

Saleh Bunaiyan

Publications and source records attributed to Saleh Bunaiyan.

8 recordsLinked to original sources

arXiv2026

IsingFormer: Augmenting Parallel Tempering With Learned Proposals

Generative models have been extensively used to accelerate MCMC mixing for sampling and optimization, but their effective integration with standard MCMC remains an open question. Here, we introduce a global proposal move in which finite-temperature configurations from an external generator are used as proposals within Parallel Tempering (PT). We examine a specific generator, IsingFormer, a Transformer trained on long-run MCMC configurations intended to approximate equilibrium distributions, and call the resulting framework Transformer-Augmented Parallel Tempering (TAPT). The IsingFormer exhibits two useful capabilities: interpolation to untrained $β$ values and conditional completion under clamped settings absent from training. On 3D spin-glass instances, TAPT reaches substantially lower residual energies than standard PT in fewer Monte Carlo sweeps. On integer factorization, we show how a structured problem encoding can amortize the training cost by training IsingFormer once and reusing the same model across target products that were not imposed during training. Finally, in a scaling study that uses long-run MCMC configurations as proposals, with proposal generation excluded from the timing, TAPT reduces the fitted time-to-solution exponent by approximately $33\%$ relative to PT over the tested problem sizes.

cs.LG↗

arXiv2026

Spin Vector Control for Heisenberg-Inspired Probabilistic Computing

Probabilistic bits (p-bits) have emerged as a cornerstone of probabilistic computing, enabling energy-efficient hardware implementation for probabilistic inference and combinatorial optimization. A critical challenge in advancing this field beyond binary p-bits lies in realizing and manipulating vector spin information, essential for mapping complex energy-based models such as the Heisenberg Hamiltonian.Here, we demonstrate a spintronic platform capable of real-space vector summation by using dual ferromagnetic spin injections into a monolayer graphene channel. By electrically tuning the spin polarization through independently controlled injection currents, we achieve continuous control over the magnitude and direction of the resulting spin accumulation vector. Experimental observations, supported by theoretical vector summation models and spin-circuit simulations, reveal coherent vector interactions and angular tunability of the spin state. This approach enables direct implementation of vector-based spin logic and lays the groundwork for mapping classical Heisenberg models using stochastic low-barrier magnets. Our results establish a scalable pathway for realizing probabilistic spin circuits based on two-dimensional materials, offering new opportunities for low-power, non-Boolean computing architectures.

cond-mat.mes-hall↗

arXiv2026

Programmable Probabilistic Computer with 1,000,000 p-bits

Probabilistic computers built from p-bits have been proposed as hardware accelerators for sampling and optimizing Ising models, but existing systems have been confined to a single chip, capped by its capacity and memory bandwidth. Here we break this limit by networking FPGAs into a single Ising machine far larger than any one device could hold, realizing a programmable probabilistic computer with one million p-bits. The machine performs Gibbs sampling at over a trillion flips per second while keeping every coupling weight in local on-chip memory. During execution, devices exchange nothing but 1-bit boundary states. This architecture exposes a question fundamental to any distributed sampler: how frequently boundary information must be refreshed for a partitioned machine to behave as an unpartitioned one. Using three-dimensional Edwards-Anderson spin glasses, we show that the answer is set by a single timing ratio, eta = f_comm/f_p-bit, of the boundary-exchange frequency to the local p-bit update frequency. Above a topology-dependent threshold, the distributed machine matches a monolithic GPU reference. Below it, residual energy still decays as a power law but with a reduced exponent, turning parallelism into a quantifiable throughput-accuracy tradeoff. A theoretical cluster mean-field model reproduces the same behavior, showing that this tradeoff is a universal property of partitioned stochastic dynamics. These results provide a programmable million-p-bit platform, demonstrated across spin glasses, Max-Cut, and Boolean satisfiability, together with a quantitative design rule for scaling probabilistic computers beyond the single-chip limit.

cs.DC↗

arXiv2026

Adaptive Variation-Resilient Random Number Generator for Embedded Encryption

With a growing interest in securing user data within the internet-of-things (IoT), embedded encryption has become of paramount importance, requiring light-weight high-quality Random Number Generators (RNGs). Emerging stochastic device technologies produce random numbers from stochastic physical processes at high quality, however, their generated random number streams are adversely affected by process and supply voltage variations, which can lead to bias in the generated streams. In this work, we present an adaptive variation-resilient RNG capable of extracting unbiased encryption-grade random number streams from physically driven entropy sources, for embedded cryptography applications. The system's key feature is its adaptive digitizer with an adaptive reference voltage. As a proof of concept, we employ a stochastic magnetic tunnel junction (sMTJ) device as an entropy source. The impact of variations in the sMTJ is mitigated by the adaptive digitizer, which generates an adaptive short-term average reference voltage that dynamically tracks any stochastic signal drift or deviation, leading to unbiased random bit stream generation. The generated bit streams, due to their higher entropy, then only need to undergo simplified post-processing. A prototype of the adaptive RNG system was experimentally implemented using discrete electronic components and an FPGA for entropy source emulation. Statistical randomness tests based on the National Institute of Standards and Technology (NIST) test suite are conducted on bit streams obtained using the simulations as well as the discrete electronic component implementation, demonstrating that the bit streams consistently pass all 16 tests of the NIST SP 800-22 test suite with a 100% pass rate. Leveraging its simplified post-processing, the adaptive RNG shows consistent operation across a wide range of throughputs from 5 to 182 Mbps.

cs.ET↗

arXiv2026

Probabilistic Sensing: Intelligence in Data Sampling

Extending the intelligence of sensors to the data-acquisition process - deciding whether to sample or not - can result in transformative energy-efficiency gains. However, making such a decision in a deterministic manner involves risk of losing information. Here we present a sensing paradigm that enables making such a decision in a probabilistic manner. The paradigm takes inspiration from the autonomous nervous system and employs a probabilistic neuron (p-neuron) driven by an analog feature extraction circuit. The response time of the system is on the order of microseconds, over-coming the sub-sampling-rate response time limit and enabling real-time intelligent autonomous activation of data-sampling. Validation experiments on active seismic survey data demonstrate lossless probabilistic data acquisition, with a normalized mean squared error of 0.41%, and 93% saving in the active operation time of the system and the number of generated samples.

cs.LG↗

arXiv2026

Configurable p-Neurons Using Modular p-Bits

Probabilistic bits (p-bits) have recently been employed in neural networks (NNs) as stochastic neurons with sigmoidal probabilistic activation functions. Nonetheless, there remain a wealth of other probabilistic activation functions that are yet to be explored. Here we re-engineer the p-bit by decoupling its stochastic signal path from its input data path, giving rise to a modular p-bit that enables the realization of probabilistic neurons (p-neurons) with a range of configurable probabilistic activation functions, including a probabilistic version of the widely used Logistic Sigmoid, Tanh and Rectified Linear Unit (ReLU) activation functions. We present spintronic (CMOS + sMTJ) designs that show wide and tunable probabilistic ranges of operation. Finally, we experimentally implement digital-CMOS versions on an FPGA, with stochastic unit sharing, and demonstrate an order of magnitude (10x) saving in required hardware resources compared to conventional digital p-bit implementations.

cs.ET↗

arXiv2024

Connecting physics to systems with modular spin-circuits

An emerging paradigm in modern electronics is that of CMOS + $\sf X$ requiring the integration of standard CMOS technology with novel materials and technologies denoted by $\sf X$. In this context, a crucial challenge is to develop accurate circuit models for $\sf X$ that are compatible with standard models for CMOS-based circuits and systems. In this perspective, we present physics-based, experimentally benchmarked modular circuit models that can be used to evaluate a class of CMOS + $\sf X$ systems, where $\sf X$ denotes magnetic and spintronic materials and phenomena. This class of materials is particularly challenging because they go beyond conventional charge-based phenomena and involve the spin degree of freedom which involves non-trivial quantum effects. Starting from density matrices $-$ the central quantity in quantum transport $-$ using well-defined approximations, it is possible to obtain spin-circuits that generalize ordinary circuit theory to 4-component currents and voltages (1 for charge and 3 for spin). With step-by-step examples that progressively become more complex, we illustrate how the spin-circuit approach can be used to start from the physics of magnetism and spintronics to enable accurate system-level evaluations. We believe the core approach can be extended to include other quantum degrees of freedom like valley and pseudospins starting from corresponding density matrices.

cond-mat.mes-hall↗

arXiv2024

Heisenberg machines with programmable spin-circuits

We show that we can harness two recent experimental developments to build a compact hardware emulator for the classical Heisenberg model in statistical physics. The first is the demonstration of spin-diffusion lengths in excess of microns in graphene even at room temperature. The second is the demonstration of low barrier magnets (LBMs) whose magnetization can fluctuate rapidly even at sub-nanosecond rates. Using experimentally benchmarked circuit models, we show that an array of LBMs driven by an external current source has a steady-state distribution corresponding to a classical system with an energy function of the form $E = -1/2\sum_{i,j} J_{ij} (\hat{m}_i \cdot \hat{m}_j$). This may seem surprising for a non-equilibrium system but we show that it can be justified by a Lyapunov function corresponding to a system of coupled Landau-Lifshitz-Gilbert (LLG) equations. The Lyapunov function we construct describes LBMs interacting through the spin currents they inject into the spin neutral substrate. We suggest ways to tune the coupling coefficients $J_{ij}$ so that it can be used as a hardware solver for optimization problems involving continuous variables represented by vector magnetizations, similar to the role of the Ising model in solving optimization problems with binary variables. Finally, we train a Heisenberg XOR gate based on a network of four coupled stochastic LLG equations, illustrating the concept of probabilistic computing with a programmable Heisenberg model.

cond-mat.mes-hall↗