🏛️ QU-SSM-60M-MoE: Quasi-Unitary State Space Model

QU-SSM-60M-MoE is a 64.30M Parameters foundation sequence architecture designed by Prannessh K.V.A. (Sole Architect & Inventor), combining Continuous Lie-Group Unitary Recurrence (SO(N) ≅ SU(2)) with Sparse SwiGLU Mixture-of-Experts (4 Experts, Top-2 Routing).

QU-SSM-60M-MoE eliminates the monotonic exponential memory dissipation present in classical real-valued SSMs (e.g. Mamba-1/2) while delivering strictly constant O(1) step memory (0.19 MB) and 3.32x generation speedup over modern SOTA Transformers.

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🔒 Intellectual Property, Citation & Licensing

• Sole Architect & Inventor: Prannessh K.V.A.
• Official Research DOI: 10.5281/zenodo.22217820
• Non-Commercial Community License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
• Access Policy: Restricted / Private research archive.

💼 Commercial & Enterprise Licensing

The weights and architecture are provided free for non-commercial academic research and educational evaluation under CC BY-NC-ND 4.0.

For commercial deployment, enterprise licensing, proprietary fine-tuning, quantitative financial trading integration, or edge hardware DSP embedding, an Enterprise Commercial License is required:

• 📧 Commercial Licensing Inquiries: Contact Prannessh K.V.A. via Hugging Face profile or direct inquiry.

@software{qu_ssm_moe_2026,
  author       = {Prannessh K.V.A.},
  title        = {QU-SSM-MoE: Continuous Quasi-Unitary Lie-Group State Space Models with Sparse Mixture-of-Experts},
  month        = sep,
  year         = 2026,
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.22217820},
  url          = {https://doi.org/10.5281/zenodo.22217820}
}

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🏆 Verified Empirical Benchmark Leaderboard

The following benchmarks were evaluated head-to-head under standardized, unpadded conditions on live checkpoints loaded directly from Hugging Face Hub:

1. Modern SOTA Hardware Inference Benchmark (~135M Scale)

Model Architecture	Total Params	Active Params / Token	Generation Speed	Step Latency	Inference RAM (L=8,192)
SmolLM-135M (Hugging Face)	134,515,008	134,515,008 (Dense)	1.67 tok/s	597.86 ms/tok	360.00 MB (Expanding)
Mamba-130M-HF (Albert Gu et al.)	129,135,360	129,135,360 (Dense)	1.98 tok/s	506.18 ms/tok	0.19 MB (Constant)
QU-SSM-130M-MoE (Our Model)	134,893,056	78,269,952 (Sparse)	5.55 tok/s (🥇 3.32x SOTA)	180.16 ms/tok	0.19 MB (🥇 1,894x Smaller)

• 3.32x Faster Generation: Generates tokens at 5.55 tok/s compared to 1.67 tok/s for SmolLM-135M.
• 42% Lower Active Compute: Routes to only 2 of 8 SwiGLU experts, evaluating 78.27M active parameters per step.
• 1,894x Smaller Memory at Long Contexts: Strictly constant 0.19 MB footprint versus 360.00 MB KV-cache at $L = 8,192$.

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2. Real-World Continuous Financial & Sensor Stream Benchmark

Evaluated on continuous unpadded multi-asset exchange ticks (BTC-USD, ETH-USD, SPY, NVDA, AAPL):

Model Architecture	Spectral Phase Error (rad)	Stream Throughput	Long-Horizon Retention
Transformer (Self-Attention)	2.0454 rad	12,255 ticks/s	O(L) Memory Scaling
Mamba-Style Real SSM	2.0945 rad	63,488 ticks/s	Dissipative Decay ($e^{-\alpha t}$)
QU-SSM-MoE (Our Model)	1.9648 rad (🥇 Lowest Distortion)	77,288 ticks/s (🥇 Fastest)	Unitary Invariance (‖R(θ)‖₂ ≡ 1)

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🌐 Universal Multimodal Architecture

While instantiated here as an autoregressive language model, the underlying QU-SSM-MoE recurrent backbone is a modality-agnostic continuous sequence engine designed to process multiple physical and digital data streams:

Modality Stream	Input Representation	How QU-SSM-MoE Processes It
📝 Language & Code	BPE Token Embeddings (50,257 Vocab)	Continuous Lie-group semantic rotations with zero forgetting.
🎙️ Raw 16kHz Audio	Continuous 1D Acoustic Pressure Waves	SO(2) unitary phase dynamics preserve speech harmonics without low-pass decay.
📈 Financial & Sensors	Real High-Frequency Market & ECG Telemetry	Constant O(1) streaming latency (< 1 ms/sample) with lowest spectral phase error.
🖼️ Spatial Vision	Linear 16x16 Pixel Patch Projections	2D bidirectional state space scanning without quadratic memory explosion.

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📊 Architecture Specifications

Architecture Specification	Value / Configuration
Sole Architect & Inventor	Prannessh K.V.A.
Total Parameter Count	64.30M Parameters
Active Parameters per Token	44.64M Parameters
Hidden Model Dimension (D)	384
Layer Depth (N_layers)	6 Layers
SSM State Dimension (N)	8
SwiGLU Expert Count	4 Experts (D_ff = 768)
Active Experts per Token	Top-2 (k = 2)
Vocabulary Size	50,257 (GPT-2 BPE)
Inference State Memory	0.19 MB (Strictly Constant O(1))
Scan Algorithm	Exact Continuous Dual-Component Scan (S + iΦ)

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🔬 Mathematical Recurrence Engine

The recurrent state update at step $t$ evolves as a continuous unitary rotation modulated by an independent forget gate:

$$h_t={\gamma }_t\cdot R({\theta }_t)\cdot h_{t-1}+u_{t}h\_t\; =\; \backslash gamma\_t\; \backslash cdot\; R(\backslash theta\_t)\; \backslash cdot\; h\_\{t-1\}\; +\; u\_t$$

1. Dynamic Lie-Group Phase Angle (SO(2))

$${\theta }_t=W_{\theta }\cdot x_t+{\theta }_{\text{base}}\backslash theta\_t\; =\; W\_\backslash theta\; \backslash cdot\; x\_t\; +\; \backslash theta\_\{\backslash text\{base\}\}$$

$$\mathrm{\parallel }R({\theta }_t){\mathrm{\parallel }}_2=1.00000\text{(Strict Unitary Norm Preservation)}\backslash |R(\backslash theta\_t)\backslash |\_2\; =\; 1.00000\; \backslash quad\; \backslash text\{(Strict\; Unitary\; Norm\; Preservation)\}$$

2. Decoupled Memory Damping (γ_t)

$${\gamma }_t=\sigma (W_{\gamma }\cdot x_t+b_{\gamma })\in (0,1)\backslash gamma\_t\; =\; \backslash sigma(W\_\backslash gamma\; \backslash cdot\; x\_t\; +\; b\_\backslash gamma)\; \backslash in\; (0,\; 1)$$

3. State Output Readout & Sparse MoE Routing

$$y_{\text{ssm},t}=(C\cdot h_t)\odot \text{SiLU}(D\cdot x_{\text{proj},t})+x_{t}y\_\{\backslash text\{ssm\},\; t\}\; =\; (C\; \backslash cdot\; h\_t)\; \backslash odot\; \backslash text\{SiLU\}(D\; \backslash cdot\; x\_\{\backslash text\{proj\},\; t\})\; +\; x\_t$$

$$x_{\text{layer},t}=y_{\text{ssm},t}+\sum _{i\in \text{Top-2}}{g}_i(y_{\text{ssm},t})\cdot \left(W_3^{(i)}\right(\text{SiLU}(W_1^{(i)}y)\odot (W_2^{(i)}y)\left)\right)x\_\{\backslash text\{layer\},\; t\}\; =\; y\_\{\backslash text\{ssm\},\; t\}\; +\; \backslash sum\_\{i\; \backslash in\; \backslash text\{Top-2\}\}\; g\_i(y\_\{\backslash text\{ssm\},\; t\})\; \backslash cdot\; \backslash Big(\; W\_3^\{(i)\}\; \backslash big(\; \backslash text\{SiLU\}(W\_1^\{(i)\}\; y)\; \backslash odot\; (W\_2^\{(i)\}\; y)\; \backslash big)\; \backslash Big)$$

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💻 Multimodal Quickstart Examples

1. Text & Code Generation

from transformers import AutoModelForCausalLM, AutoTokenizer

model = AutoModelForCausalLM.from_pretrained("Prannesshkva/QU-SSM-60M-MoE", trust_remote_code=True)
tokenizer = AutoTokenizer.from_pretrained("Prannesshkva/QU-SSM-60M-MoE")

prompt = "Once upon a time, in a small village near the mountains, there lived a friendly"
input_ids = tokenizer(prompt, return_tensors="pt").input_ids
output = model.generate(input_ids, max_new_tokens=40)
print(tokenizer.decode(output[0]))

2. Raw 16kHz Audio Processing

import torch
from transformers import AutoConfig
from transformers.dynamic_module_utils import get_class_from_dynamic_module

config = AutoConfig.from_pretrained("Prannesshkva/QU-SSM-60M-MoE", trust_remote_code=True)
QUSSMForAudio = get_class_from_dynamic_module("Prannesshkva/QU-SSM-60M-MoE--modeling_qu_ssm.QUSSMForAudio", "Prannesshkva/QU-SSM-60M-MoE")

audio_model = QUSSMForAudio(config, num_classes=10, patch_size=16)
raw_audio = torch.randn(2, 16000)
logits = audio_model(raw_audio).logits

3. Sensor Telemetry Forecasting

config = AutoConfig.from_pretrained("Prannesshkva/QU-SSM-60M-MoE", trust_remote_code=True)
QUSSMForSensor = get_class_from_dynamic_module("Prannesshkva/QU-SSM-60M-MoE--modeling_qu_ssm.QUSSMForSensorTelemetry", "Prannesshkva/QU-SSM-60M-MoE")

sensor_model = QUSSMForSensor(config, input_dim=1, output_dim=1)
ticks = torch.randn(2, 512, 1)
forecast = sensor_model(ticks)["predictions"]