ETSep 19, 2022Code
NeurOLight: A Physics-Agnostic Neural Operator Enabling Parametric Photonic Device SimulationJiaqi Gu, Zhengqi Gao, Chenghao Feng et al.
Optical computing is an emerging technology for next-generation efficient artificial intelligence (AI) due to its ultra-high speed and efficiency. Electromagnetic field simulation is critical to the design, optimization, and validation of photonic devices and circuits. However, costly numerical simulation significantly hinders the scalability and turn-around time in the photonic circuit design loop. Recently, physics-informed neural networks have been proposed to predict the optical field solution of a single instance of a partial differential equation (PDE) with predefined parameters. Their complicated PDE formulation and lack of efficient parametrization mechanisms limit their flexibility and generalization in practical simulation scenarios. In this work, for the first time, a physics-agnostic neural operator-based framework, dubbed NeurOLight, is proposed to learn a family of frequency-domain Maxwell PDEs for ultra-fast parametric photonic device simulation. We balance the efficiency and generalization of NeurOLight via several novel techniques. Specifically, we discretize different devices into a unified domain, represent parametric PDEs with a compact wave prior, and encode the incident light via masked source modeling. We design our model with parameter-efficient cross-shaped NeurOLight blocks and adopt superposition-based augmentation for data-efficient learning. With these synergistic approaches, NeurOLight generalizes to a large space of unseen simulation settings, demonstrates 2-orders-of-magnitude faster simulation speed than numerical solvers, and outperforms prior neural network models by ~54% lower prediction error with ~44% fewer parameters. Our code is available at https://github.com/JeremieMelo/NeurOLight.
LGJul 10, 2024
INSIGHT: Universal Neural Simulator for Analog Circuits Harnessing Autoregressive TransformersSouradip Poddar, Youngmin Oh, Yao Lai et al. · tsinghua
Analog front-end design heavily relies on specialized human expertise and costly trial-and-error simulations, which motivated many prior works on analog design automation. However, efficient and effective exploration of the vast and complex design space remains constrained by the time-consuming nature of SPICE simulations, making effective design automation a challenging endeavor. In this paper, we introduce INSIGHT, a GPU-powered, technology-agnostic, effective universal neural simulator in the analog front-end design automation loop. INSIGHT accurately predicts the performance metrics of analog circuits across various technologies with just a few microseconds of inference time. Notably, its autoregressive capabilities enable INSIGHT to accurately predict simulation-costly critical transient specifications leveraging less expensive performance metric information. The low cost and high fidelity feature make INSIGHT a good substitute for standard simulators in analog front-end optimization frameworks. INSIGHT is compatible with any optimization framework, facilitating enhanced design space exploration for sample efficiency through sophisticated offline learning and adaptation techniques. Our experiments demonstrate that INSIGHT-M, a model-based batch reinforcement learning sizing framework with INSIGHT as the accurate surrogate, only requires < 20 real-time simulations with 100-1000x lower simulation costs and significant speedup over existing sizing methods.
LGNov 11, 2025
The Path Not Taken: RLVR Provably Learns Off the PrincipalsHanqing Zhu, Zhenyu Zhang, Hanxian Huang et al.
Reinforcement Learning with Verifiable Rewards (RLVR) reliably improves the reasoning performance of large language models, yet it appears to modify only a small fraction of parameters. We revisit this paradox and show that sparsity is a surface artifact of a model-conditioned optimization bias: for a fixed pretrained model, updates consistently localize to preferred parameter regions, highly consistent across runs and largely invariant to datasets and RL recipes. We mechanistically explain these dynamics with a Three-Gate Theory: Gate I (KL Anchor) imposes a KL-constrained update; Gate II (Model Geometry) steers the step off principal directions into low-curvature, spectrum-preserving subspaces; and Gate III (Precision) hides micro-updates in non-preferred regions, making the off-principal bias appear as sparsity. We then validate this theory and, for the first time, provide a parameter-level characterization of RLVR's learning dynamics: RLVR learns off principal directions in weight space, achieving gains via minimal spectral drift, reduced principal-subspace rotation, and off-principal update alignment. In contrast, SFT targets principal weights, distorts the spectrum, and even lags RLVR. Together, these results provide the first parameter-space account of RLVR's training dynamics, revealing clear regularities in how parameters evolve. Crucially, we show that RL operates in a distinct optimization regime from SFT, so directly adapting SFT-era parameter-efficient fine-tuning (PEFT) methods can be flawed, as evidenced by our case studies on advanced sparse fine-tuning and LoRA variants. We hope this work charts a path toward a white-box understanding of RLVR and the design of geometry-aware, RLVR-native learning algorithms, rather than repurposed SFT-era heuristics.
88.4OPTICSApr 12
Harnessing Photonics for Machine IntelligenceHanqing Zhu, Shupeng Ning, Hongjian Zhou et al.
The exponential growth of machine-intelligence workloads is colliding with the power, memory, and interconnect limits of the post-Moore era, motivating compute substrates that scale beyond transistor density alone. Integrated photonics is emerging as a candidate for artificial intelligence (AI) acceleration by exploiting optical bandwidth and parallelism to reshape data movement and computation. This review reframes photonic computing from a circuits-and-systems perspective, moving beyond building-block progress toward cross-layer system analysis and full-stack design automation. We synthesize recent advances through a bottleneck-driven taxonomy that delineates the operating regimes and scaling trends where photonics can deliver end-to-end sustained benefits. A central theme is cross-layer co-design and workload-adaptive programmability to sustain high efficiency and versatility across evolving application domains at scale. We further argue that Electronic-Photonic Design Automation (EPDA) will be pivotal, enabling closed-loop co-optimization across simulation, inverse design, system modeling, and physical implementation. By charting a roadmap from laboratory prototypes to scalable, reproducible electronic-photonic ecosystems, this review aims to guide the CAS community toward an automated, system-centric era of photonic machine intelligence.
LGNov 5, 2024Code
PACE: Pacing Operator Learning to Accurate Optical Field Simulation for Complicated Photonic DevicesHanqing Zhu, Wenyan Cong, Guojin Chen et al.
Electromagnetic field simulation is central to designing, optimizing, and validating photonic devices and circuits. However, costly computation associated with numerical simulation poses a significant bottleneck, hindering scalability and turnaround time in the photonic circuit design process. Neural operators offer a promising alternative, but existing SOTA approaches, NeurOLight, struggle with predicting high-fidelity fields for real-world complicated photonic devices, with the best reported 0.38 normalized mean absolute error in NeurOLight. The inter-plays of highly complex light-matter interaction, e.g., scattering and resonance, sensitivity to local structure details, non-uniform learning complexity for full-domain simulation, and rich frequency information, contribute to the failure of existing neural PDE solvers. In this work, we boost the prediction fidelity to an unprecedented level for simulating complex photonic devices with a novel operator design driven by the above challenges. We propose a novel cross-axis factorized PACE operator with a strong long-distance modeling capacity to connect the full-domain complex field pattern with local device structures. Inspired by human learning, we further divide and conquer the simulation task for extremely hard cases into two progressively easy tasks, with a first-stage model learning an initial solution refined by a second model. On various complicated photonic device benchmarks, we demonstrate one sole PACE model is capable of achieving 73% lower error with 50% fewer parameters compared with various recent ML for PDE solvers. The two-stage setup further advances high-fidelity simulation for even more intricate cases. In terms of runtime, PACE demonstrates 154-577x and 11.8-12x simulation speedup over numerical solver using scipy or highly-optimized pardiso solver, respectively. We open sourced the code and dataset.
AIJun 7, 2024Code
LLM-Enhanced Bayesian Optimization for Efficient Analog Layout Constraint GenerationGuojin Chen, Keren Zhu, Seunggeun Kim et al.
Analog layout synthesis faces significant challenges due to its dependence on manual processes, considerable time requirements, and performance instability. Current Bayesian Optimization (BO)-based techniques for analog layout synthesis, despite their potential for automation, suffer from slow convergence and extensive data needs, limiting their practical application. This paper presents the \texttt{LLANA} framework, a novel approach that leverages Large Language Models (LLMs) to enhance BO by exploiting the few-shot learning abilities of LLMs for more efficient generation of analog design-dependent parameter constraints. Experimental results demonstrate that \texttt{LLANA} not only achieves performance comparable to state-of-the-art (SOTA) BO methods but also enables a more effective exploration of the analog circuit design space, thanks to LLM's superior contextual understanding and learning efficiency. The code is available at https://github.com/dekura/LLANA.
ETMay 31, 2023Code
M3ICRO: Machine Learning-Enabled Compact Photonic Tensor Core based on PRogrammable Multi-Operand Multimode InterferenceJiaqi Gu, Hanqing Zhu, Chenghao Feng et al.
Photonic computing shows promise for transformative advancements in machine learning (ML) acceleration, offering ultra-fast speed, massive parallelism, and high energy efficiency. However, current photonic tensor core (PTC) designs based on standard optical components hinder scalability and compute density due to their large spatial footprint. To address this, we propose an ultra-compact PTC using customized programmable multi-operand multimode interference (MOMMI) devices, named M3ICRO. The programmable MOMMI leverages the intrinsic light propagation principle, providing a single-device programmable matrix unit beyond the conventional computing paradigm of one multiply-accumulate (MAC) operation per device. To overcome the optimization difficulty of customized devices that often requires time-consuming simulation, we apply ML for optics to predict the device behavior and enable a differentiable optimization flow. We thoroughly investigate the reconfigurability and matrix expressivity of our customized PTC, and introduce a novel block unfolding method to fully exploit the computing capabilities of a complex-valued PTC for near-universal real-valued linear transformations. Extensive evaluations demonstrate that M3ICRO achieves a 3.4-9.6x smaller footprint, 1.6-4.4x higher speed, 10.6-42x higher compute density, 3.7-12x higher system throughput, and superior noise robustness compared to state-of-the-art coherent PTC designs, while maintaining close-to-digital task accuracy across various ML benchmarks. Our code is open-sourced at https://github.com/JeremieMelo/M3ICRO-MOMMI.
LGOct 27, 2021Code
L2ight: Enabling On-Chip Learning for Optical Neural Networks via Efficient in-situ Subspace OptimizationJiaqi Gu, Hanqing Zhu, Chenghao Feng et al.
Silicon-photonics-based optical neural network (ONN) is a promising hardware platform that could represent a paradigm shift in efficient AI with its CMOS-compatibility, flexibility, ultra-low execution latency, and high energy efficiency. In-situ training on the online programmable photonic chips is appealing but still encounters challenging issues in on-chip implementability, scalability, and efficiency. In this work, we propose a closed-loop ONN on-chip learning framework L2ight to enable scalable ONN mapping and efficient in-situ learning. L2ight adopts a three-stage learning flow that first calibrates the complicated photonic circuit states under challenging physical constraints, then performs photonic core mapping via combined analytical solving and zeroth-order optimization. A subspace learning procedure with multi-level sparsity is integrated into L2ight to enable in-situ gradient evaluation and fast adaptation, unleashing the power of optics for real on-chip intelligence. Extensive experiments demonstrate our proposed L2ight outperforms prior ONN training protocols with 3-order-of-magnitude higher scalability and over 30X better efficiency, when benchmarked on various models and learning tasks. This synergistic framework is the first scalable on-chip learning solution that pushes this emerging field from intractable to scalable and further to efficient for next-generation self-learnable photonic neural chips. From a co-design perspective, L2ight also provides essential insights for hardware-restricted unitary subspace optimization and efficient sparse training. We open-source our framework at https://github.com/JeremieMelo/L2ight.
LGDec 6, 2024
APOLLO: SGD-like Memory, AdamW-level PerformanceHanqing Zhu, Zhenyu Zhang, Wenyan Cong et al.
Large language models (LLMs) are notoriously memory-intensive during training, particularly with the popular AdamW optimizer. This memory burden necessitates using more or higher-end GPUs or reducing batch sizes, limiting training scalability and throughput. To address this, various memory-efficient optimizers have been proposed to reduce optimizer memory usage. However, they face critical challenges: (i) reliance on costly SVD operations; (ii) significant performance trade-offs compared to AdamW; and (iii) still substantial optimizer memory overhead to maintain competitive performance. In this work, we identify that AdamW's learning rate adaptation rule can be effectively coarsened as a structured learning rate update. Based on this insight, we propose Approximated Gradient Scaling for Memory-Efficient LLM Optimization (APOLLO), which approximates learning rate scaling using an auxiliary low-rank optimizer state based on pure random projection. This structured learning rate update rule makes APOLLO highly tolerant to further memory reductions while delivering comparable pre-training performance. Even its rank-1 variant, APOLLO-Mini, achieves superior pre-training performance compared to AdamW with SGD-level memory costs. Extensive experiments demonstrate that the APOLLO series performs on-par with or better than AdamW, while achieving greater memory savings by nearly eliminating the optimization states of AdamW. These savings provide significant system-level benefits: (1) Enhanced Throughput: 3x throughput on an 8xA100-80GB setup compared to AdamW by supporting 4x larger batch sizes. (2) Improved Model Scalability: Pre-training LLaMA-13B with naive DDP on A100-80GB GPUs without system-level optimizations. (3) Low-End GPU Friendly Pre-training: Pre-training LLaMA-7B on a single GPU using less than 12 GB of memory with weight quantization.
CVJan 3, 2025
VideoLifter: Lifting Videos to 3D with Fast Hierarchical Stereo AlignmentWenyan Cong, Hanqing Zhu, Kevin Wang et al.
Efficiently reconstructing 3D scenes from monocular video remains a core challenge in computer vision, vital for applications in virtual reality, robotics, and scene understanding. Recently, frame-by-frame progressive reconstruction without camera poses is commonly adopted, incurring high computational overhead and compounding errors when scaling to longer videos. To overcome these issues, we introduce VideoLifter, a novel video-to-3D pipeline that leverages a local-to-global strategy on a fragment basis, achieving both extreme efficiency and SOTA quality. Locally, VideoLifter leverages learnable 3D priors to register fragments, extracting essential information for subsequent 3D Gaussian initialization with enforced inter-fragment consistency and optimized efficiency. Globally, it employs a tree-based hierarchical merging method with key frame guidance for inter-fragment alignment, pairwise merging with Gaussian point pruning, and subsequent joint optimization to ensure global consistency while efficiently mitigating cumulative errors. This approach significantly accelerates the reconstruction process, reducing training time by over 82% while holding better visual quality than current SOTA methods.
CVMar 31, 2025
Can Test-Time Scaling Improve World Foundation Model?Wenyan Cong, Hanqing Zhu, Peihao Wang et al.
World foundation models, which simulate the physical world by predicting future states from current observations and inputs, have become central to many applications in physical intelligence, including autonomous driving and robotics. However, these models require substantial computational resources for pretraining and are further constrained by available data during post-training. As such, scaling computation at test time emerges as both a critical and practical alternative to traditional model enlargement or re-training. In this work, we introduce SWIFT, a test-time scaling framework tailored for WFMs. SWIFT integrates our extensible WFM evaluation toolkit with process-level inference strategies, including fast tokenization, probability-based Top-K pruning, and efficient beam search. Empirical results on the COSMOS model demonstrate that test-time scaling exists even in a compute-optimal way. Our findings reveal that test-time scaling laws hold for WFMs and that SWIFT provides a scalable and effective pathway for improving WFM inference without retraining or increasing model size. Project page: https://scalingwfm.github.io/.
ARFeb 1, 2025
Hardware-Efficient Photonic Tensor Core: Accelerating Deep Neural Networks with Structured CompressionShupeng Ning, Hanqing Zhu, Chenghao Feng et al.
The rapid growth in computing demands, particularly driven by artificial intelligence applications, has begun to exceed the capabilities of traditional electronic hardware. Optical computing offers a promising alternative due to its parallelism, high computational speed, and low power consumption. However, existing photonic integrated circuits are constrained by large footprints, costly electro-optical interfaces, and complex control mechanisms, limiting the practical scalability of optical neural networks (ONNs). To address these limitations, we introduce a block-circulant photonic tensor core for a structure-compressed optical neural network (StrC-ONN) architecture. The structured compression technique substantially reduces both model complexity and hardware resources without sacrificing the versatility of neural networks, and achieves accuracy comparable to uncompressed models. Additionally, we propose a hardware-aware training framework to compensate for on-chip nonidealities to improve model robustness and accuracy. Experimental validation through image processing and classification tasks demonstrates that our StrC-ONN achieves a reduction in trainable parameters of up to 74.91%,while still maintaining competitive accuracy levels. Performance analyses further indicate that this hardware-software co-design approach is expected to yield a 3.56 times improvement in power efficiency. By reducing both hardware requirements and control complexity across multiple dimensions, this work explores a new pathway toward practical and scalable ONNs, highlighting a promising route to address future computational efficiency challenges.
OPTICSMay 31, 2023
Integrated multi-operand optical neurons for scalable and hardware-efficient deep learningChenghao Feng, Jiaqi Gu, Hanqing Zhu et al.
The optical neural network (ONN) is a promising hardware platform for next-generation neuromorphic computing due to its high parallelism, low latency, and low energy consumption. However, previous integrated photonic tensor cores (PTCs) consume numerous single-operand optical modulators for signal and weight encoding, leading to large area costs and high propagation loss to implement large tensor operations. This work proposes a scalable and efficient optical dot-product engine based on customized multi-operand photonic devices, namely multi-operand optical neurons (MOON). We experimentally demonstrate the utility of a MOON using a multi-operand-Mach-Zehnder-interferometer (MOMZI) in image recognition tasks. Specifically, our MOMZI-based ONN achieves a measured accuracy of 85.89% in the street view house number (SVHN) recognition dataset with 4-bit voltage control precision. Furthermore, our performance analysis reveals that a 128x128 MOMZI-based PTCs outperform their counterparts based on single-operand MZIs by one to two order-of-magnitudes in propagation loss, optical delay, and total device footprint, with comparable matrix expressivity.
LGMay 24, 2023
Pre-RMSNorm and Pre-CRMSNorm Transformers: Equivalent and Efficient Pre-LN TransformersZixuan Jiang, Jiaqi Gu, Hanqing Zhu et al.
Transformers have achieved great success in machine learning applications. Normalization techniques, such as Layer Normalization (LayerNorm, LN) and Root Mean Square Normalization (RMSNorm), play a critical role in accelerating and stabilizing the training of Transformers. While LayerNorm recenters and rescales input vectors, RMSNorm only rescales the vectors by their RMS value. Despite being more computationally efficient, RMSNorm may compromise the representation ability of Transformers. There is currently no consensus regarding the preferred normalization technique, as some models employ LayerNorm while others utilize RMSNorm, especially in recent large language models. It is challenging to convert Transformers with one normalization to the other type. While there is an ongoing disagreement between the two normalization types, we propose a solution to unify two mainstream Transformer architectures, Pre-LN and Pre-RMSNorm Transformers. By removing the inherent redundant mean information in the main branch of Pre-LN Transformers, we can reduce LayerNorm to RMSNorm, achieving higher efficiency. We further propose the Compressed RMSNorm (CRMSNorm) and Pre-CRMSNorm Transformer based on a lossless compression of the zero-mean vectors. We formally establish the equivalence of Pre-LN, Pre-RMSNorm, and Pre-CRMSNorm Transformer variants in both training and inference. It implies that Pre-LN Transformers can be substituted with Pre-(C)RMSNorm counterparts at almost no cost, offering the same arithmetic functionality along with free efficiency improvement. Experiments demonstrate that we can reduce the training and inference time of Pre-LN Transformers by 1% - 10%.
IRFeb 13, 2022
Uni-Retriever: Towards Learning The Unified Embedding Based Retriever in Bing Sponsored SearchJianjin Zhang, Zheng Liu, Weihao Han et al.
Embedding based retrieval (EBR) is a fundamental building block in many web applications. However, EBR in sponsored search is distinguished from other generic scenarios and technically challenging due to the need of serving multiple retrieval purposes: firstly, it has to retrieve high-relevance ads, which may exactly serve user's search intent; secondly, it needs to retrieve high-CTR ads so as to maximize the overall user clicks. In this paper, we present a novel representation learning framework Uni-Retriever developed for Bing Search, which unifies two different training modes knowledge distillation and contrastive learning to realize both required objectives. On one hand, the capability of making high-relevance retrieval is established by distilling knowledge from the ``relevance teacher model''. On the other hand, the capability of making high-CTR retrieval is optimized by learning to discriminate user's clicked ads from the entire corpus. The two training modes are jointly performed as a multi-objective learning process, such that the ads of high relevance and CTR can be favored by the generated embeddings. Besides the learning strategy, we also elaborate our solution for EBR serving pipeline built upon the substantially optimized DiskANN, where massive-scale EBR can be performed with competitive time and memory efficiency, and accomplished in high-quality. We make comprehensive offline and online experiments to evaluate the proposed techniques, whose findings may provide useful insights for the future development of EBR systems. Uni-Retriever has been mainstreamed as the major retrieval path in Bing's production thanks to the notable improvements on the representation and EBR serving quality.
ETDec 15, 2021
ELight: Enabling Efficient Photonic In-Memory Neurocomputing with Life EnhancementHanqing Zhu, Jiaqi Gu, Chenghao Feng et al.
With the recent advances in optical phase change material (PCM), photonic in-memory neurocomputing has demonstrated its superiority in optical neural network (ONN) designs with near-zero static power consumption, time-of-light latency, and compact footprint. However, photonic tensor cores require massive hardware reuse to implement large matrix multiplication due to the limited single-core scale. The resultant large number of PCM writes leads to serious dynamic power and overwhelms the fragile PCM with limited write endurance. In this work, we propose a synergistic optimization framework, ELight, to minimize the overall write efforts for efficient and reliable optical in-memory neurocomputing. We first propose write-aware training to encourage the similarity among weight blocks, and combine it with a post-training optimization method to reduce programming efforts by eliminating redundant writes. Experiments show that ELight can achieve over 20X reduction in the total number of writes and dynamic power with comparable accuracy. With our ELight, photonic in-memory neurocomputing will step forward towards viable applications in machine learning with preserved accuracy, order-of-magnitude longer lifetime, and lower programming energy.
ETNov 11, 2021
A compact butterfly-style silicon photonic-electronic neural chip for hardware-efficient deep learningChenghao Feng, Jiaqi Gu, Hanqing Zhu et al.
The optical neural network (ONN) is a promising hardware platform for next-generation neurocomputing due to its high parallelism, low latency, and low energy consumption. Previous ONN architectures are mainly designed for general matrix multiplication (GEMM), leading to unnecessarily large area cost and high control complexity. Here, we move beyond classical GEMM-based ONNs and propose an optical subspace neural network (OSNN) architecture, which trades the universality of weight representation for lower optical component usage, area cost, and energy consumption. We devise a butterfly-style photonic-electronic neural chip to implement our OSNN with up to 7x fewer trainable optical components compared to GEMM-based ONNs. Additionally, a hardware-aware training framework is provided to minimize the required device programming precision, lessen the chip area, and boost the noise robustness. We experimentally demonstrate the utility of our neural chip in practical image recognition tasks, showing that a measured accuracy of 94.16% can be achieved in hand-written digit recognition tasks with 3-bit weight programming precision.
LGAug 25, 2021
Towards Memory-Efficient Neural Networks via Multi-Level in situ GenerationJiaqi Gu, Hanqing Zhu, Chenghao Feng et al.
Deep neural networks (DNN) have shown superior performance in a variety of tasks. As they rapidly evolve, their escalating computation and memory demands make it challenging to deploy them on resource-constrained edge devices. Though extensive efficient accelerator designs, from traditional electronics to emerging photonics, have been successfully demonstrated, they are still bottlenecked by expensive memory accesses due to tremendous gaps between the bandwidth/power/latency of electrical memory and computing cores. Previous solutions fail to fully-leverage the ultra-fast computational speed of emerging DNN accelerators to break through the critical memory bound. In this work, we propose a general and unified framework to trade expensive memory transactions with ultra-fast on-chip computations, directly translating to performance improvement. We are the first to jointly explore the intrinsic correlations and bit-level redundancy within DNN kernels and propose a multi-level in situ generation mechanism with mixed-precision bases to achieve on-the-fly recovery of high-resolution parameters with minimum hardware overhead. Extensive experiments demonstrate that our proposed joint method can boost the memory efficiency by 10-20x with comparable accuracy over four state-of-the-art designs, when benchmarked on ResNet-18/DenseNet-121/MobileNetV2/V3 with various tasks.
AIMay 3, 2017
A Rule-Based Computational Model of Cognitive ArithmeticAshis Pati, Kantwon Rogers, Hanqing Zhu
Cognitive arithmetic studies the mental processes used in solving math problems. This area of research explores the retrieval mechanisms and strategies used by people during a common cognitive task. Past research has shown that human performance in arithmetic operations is correlated to the numerical size of the problem. Past research on cognitive arithmetic has pinpointed this trend to either retrieval strength, error checking, or strategy-based approaches when solving equations. This paper describes a rule-based computational model that performs the four major arithmetic operations (addition, subtraction, multiplication and division) on two operands. We then evaluated our model to probe its validity in representing the prevailing concepts observed in psychology experiments from the related works. The experiments specifically explore the problem size effect, an activation-based model for fact retrieval, backup strategies when retrieval fails, and finally optimization strategies when faced with large operands. From our experimental results, we concluded that our model's response times were comparable to results observed when people performed similar tasks during psychology experiments. The fit of our model in reproducing these results and incorporating accuracy into our model are discussed.