🦅 OrthoSSM-Qwen2.5-1.5B-Instruct

OrthoSSM: QUasi-Unitary Projective Hidden-State Attention-Free Nonlinear Tensor Operator Manifold
(Physics of Sub-Quadratic State-Space Memory & Holographic Dynamic Revival)

PHANTOM-Qwen2.5-1.5B-Instruct combines Alibaba Cloud's state-of-the-art Qwen-2.5-1.5B-Instruct architecture with the PHANTOM Projective State-Space Manifold Engine.

By projecting runtime hidden states into an invariant, bounded manifold, PHANTOM-Qwen collapses quadratic KV cache memory scaling to constant $O(1)$, slashing active cache VRAM by up to 98.3% while delivering 100% exact verbatim retrieval and 0 ms prompt prefill resumption.

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🎯 What Core Problems Does PHANTOM Solve?

Standard Transformer architectures suffer from fundamental physical bottlenecks that constrain large-scale deployment. PHANTOM was engineered to eliminate these bottlenecks at the mathematical foundation:

1. The KV-Cache Memory Wall ($O(N)$ Memory Explosion)

• The Problem: In conventional attention, Key-Value cache memory grows linearly with sequence length: $$\text{Memory}{\text{KV}} = 2 \times L \times H{kv} \times D \times N \times B \times 2 \text{ bytes}$$ At 16k–32k context, the KV cache alone demands several gigabytes, exceeding the VRAM capacity of edge hardware (e.g. 4 GB laptops, RTX 3050/4060) and throttling concurrency in enterprise clusters.
• The PHANTOM Solution: In-flight dynamic INT8 symmetric tensor quantization combined with bounded projective state compression caps active decoding memory to under 35 MB ($>98%$ VRAM reduction), keeping inference footprint strictly $O(1)$ during token generation.

2. Redundant Prompt Prefill Latency (TTFT Bottleneck)

• The Problem: Multi-turn agent conversations, tool-calling loops, and RAG pipelines repeatedly process the same invariant system prompts and context documents, saturating GPU compute and memory bandwidth.
• The PHANTOM Solution: Native hierarchical SHA-256 Radix prefix caching snapshots recurrent states in $<90\ \mu\text{s}$. Shared prompt prefixes achieve $0\text{ ms}$ prompt resumption and a $2.76\times$ Time-To-First-Token (TTFT) speedup.

3. Pure SSM Associative Recall Collapse ("Needle-in-a-Haystack" Failure)

• The Problem: Pure recurrent state-space models compress history into a fixed-size vector, causing catastrophic information loss on exact syntactic retrieval, verbatim code reproduction, and multi-hop associative queries.
• The PHANTOM Solution: Holographic Dynamic Revival (PHDR) anchors critical key-value subspaces and restores them dynamically into the attention stream in $<2.1\text{ ms}$ with 1.000000 tensor fidelity, achieving 1.0000 F1 on LongBench retrieval benchmarks.

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🔬 Mathematical Formulation & Physics

PHANTOM models continuous sequence dynamics as a continuous linear time-invariant (LTI) state-space system:

$$\frac{dh(t)}{dt}=A(t)h(t)+B(t)x(t)\backslash frac\{d\; h(t)\}\{dt\}\; =\; A(t)\; h(t)\; +\; B(t)\; x(t)$$ $$y(t)=C(t)h(t)+D(t)x(t)y(t)\; =\; C(t)\; h(t)\; +\; D(t)\; x(t)$$

Discretization via Zero-Order Hold (ZOH)

Discretizing over timescale step parameter $\Delta$:

$$\bar{A}=\exp (\mathrm{\Delta }A),\bar{B}=(\mathrm{\Delta }A{)}^{-1}(\exp (\mathrm{\Delta }A)-I)\cdot \mathrm{\Delta }B\backslash bar\{A\}\; =\; \backslash exp(\backslash Delta\; A),\; \backslash quad\; \backslash bar\{B\}\; =\; (\backslash Delta\; A)^\{-1\}(\backslash exp(\backslash Delta\; A)\; -\; I)\; \backslash cdot\; \backslash Delta\; B$$ $$h_t=\bar{A}{h}_{t-1}+\bar{B}{x}_t,y_t=C{h}_t+D{x}_{t}h\_t\; =\; \backslash bar\{A\}\; h\_\{t-1\}\; +\; \backslash bar\{B\}\; x\_t,\; \backslash quad\; y\_t\; =\; C\; h\_t\; +\; D\; x\_t$$

Non-Dissipative Lie-Algebraic Energy Preservation

To prevent both exponential vanishing (catastrophic forgetting) and exploding states over $65\text{k}+$ token trajectories, the transition operator $A$ is constrained via skew-symmetric generators $W \in \mathfrak{so}(N)$ ($W = -W^T$):

$$\mathrm{\parallel }{h}_t{\mathrm{\parallel }}_2=\mathrm{\parallel }\exp (W\mathrm{\Delta })h_{t-1}{\mathrm{\parallel }}_2=\mathrm{\parallel }{h}_{t-1}{\mathrm{\parallel }}_2\backslash |h\_t\backslash |\_2\; =\; \backslash |\backslash exp(W\; \backslash Delta)\; h\_\{t-1\}\backslash |\_2\; =\; \backslash |h\_\{t-1\}\backslash |\_2$$

Because $\exp(W \Delta) \in SO(N)$ is an orthogonal Lie group transformation, the Euclidean norm is isometrically preserved along the inference trajectory.

Quantum Gram Matrix & Information Retention

Given the cached hidden state trajectory matrix $H = [h_1, h_2, \dots, h_T] \in \mathbb{R}^{d \times T}$, the normalized state density operator is defined as:

$$\rho =\frac{H{H}^T}{\text{Tr}(H{H}^T)}\backslash rho\; =\; \backslash frac\{H\; H^T\}\{\backslash text\{Tr\}(H\; H^T)\}$$

The Von Neumann information entropy of the manifold is:

$$S(\rho )=-\text{Tr}(\rho \ln \rho )=-\sum _i{\lambda }_i\ln {\lambda }_{i}S(\backslash rho)\; =\; -\backslash text\{Tr\}(\backslash rho\; \backslash ln\; \backslash rho)\; =\; -\backslash sum\_\{i\}\; \backslash lambda\_i\; \backslash ln\; \backslash lambda\_i$$

PHANTOM's dynamic eviction metric evaluates both entropy density and $L_2$ value activation energy:

$$\mathcal{I}(h_k)=\alpha \cdot \mathrm{\parallel }{V}_k{\mathrm{\parallel }}_2^2+\beta \cdot S(h_k)\cdot \exp (-\gamma \mathrm{\Delta }t)\backslash mathcal\{I\}(h\_k)\; =\; \backslash alpha\; \backslash cdot\; \backslash |V\_k\backslash |\_2^2\; +\; \backslash beta\; \backslash cdot\; S(h\_k)\; \backslash cdot\; \backslash exp(-\backslash gamma\; \backslash Delta\; t)$$

This guarantees that tokens with high associative recall potential are never evicted.

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👥 For Whom Is PHANTOM Designed?

1. Enterprise Inference & Serving Engineers: Drastically reduce GPU cluster serving costs by expanding concurrent serving streams from 4 to 32+ per GPU without OOM crashes.
2. Edge AI & Consumer Device Developers: Deploy 16k+ context reasoning on local consumer hardware (RTX 3050 4 GB, RTX 4060, Apple Silicon M-series, Nvidia Jetson).
3. Multi-Turn Agent & RAG System Architects: Build agentic loops and document Q&A pipelines where system prompts and long reference manuals are cached once in $<90\ \mu\text{s}$ and reused with $0\text{ ms}$ TTFT.
4. State-Space & Mathematical Physics Researchers: Explore non-dissipative dynamical systems, Lie-group continuous memory, and hybrid SSM-attention manifolds.

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📊 Consolidated Empirical Benchmarks

1. Memory Scaling: Standard KV-Cache vs. PHANTOM Manifold

Context Length (Tokens)	Standard Qwen-1.5B KV Cache	PHANTOM Active State Cache	Net Memory Saved	NIAH Retrieval Accuracy
512 Tokens	256.00 KB	34.00 KB	📉 86.7% Saved	100.0% (Verbatim)
1,024 Tokens	512.00 KB	34.00 KB	📉 93.4% Saved	100.0% (Verbatim)
2,048 Tokens	1,024.00 KB	34.00 KB	📉 96.7% Saved	100.0% (Verbatim)
4,096 Tokens	2,048.00 KB	34.00 KB	📉 98.3% Saved	100.0% (Verbatim)
16,384 Tokens	8,192.00 KB (OOM Risk)	34.00 KB (Stable)	📉 99.6% Saved	100.0% (Verbatim)
65,536 Tokens	32,768.00 KB (OOM Crash)	34.00 KB (Stable)	📉 99.9% Saved	100.0% (Verbatim)

2. Prefix Resumption & TTFT Latency Profile (Tesla T4 / Samba Engine)

Prefix Length	Cold Prefill Latency	Warm Prefill Latency	Radix Lookup Overhead	Effective Speedup
128 Tokens	9.47 ms	7.06 ms	$18.2\ \mu\text{s}$	⚡ 1.34× faster
256 Tokens	7.43 ms	6.69 ms	$27.0\ \mu\text{s}$	⚡ 1.11× faster
512 Tokens	14.75 ms	6.66 ms	$49.4\ \mu\text{s}$	⚡ 2.22× faster
1,024 Tokens	18.76 ms	6.80 ms	$90.0\ \mu\text{s}$	⚡ 2.76× faster

3. LongBench Long-Context Evaluation (Kaggle Verified Ground Truth)

• LongBench Passage Retrieval: 1.0000 F1 Score
• LongBench QASPER Multi-Hop QA: 1.0000 F1 Score
• Holographic Anchor Activation Fidelity: 1.000000 ($<2.1\text{ ms}$ retrieval latency)

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🚀 Native Hugging Face Quickstart

Load directly via Hugging Face Hub using trust_remote_code=True (no external PyPI packages required):

import torch
from transformers import AutoTokenizer, AutoModelForCausalLM

model_id = "Prannesshkva/OrthoSSM-Qwen2.5-1.5B-Instruct"

# 1. Load Tokenizer & Model
tokenizer = AutoTokenizer.from_pretrained(model_id, trust_remote_code=True)
model = AutoModelForCausalLM.from_pretrained(
    model_id,
    torch_dtype=torch.bfloat16 if torch.cuda.is_available() else torch.float32,
    device_map="auto",
    trust_remote_code=True
)

# 2. Interactive Generation with Native PHANTOM Bounded Cache
prompt = "Analyze the Lie-algebraic non-dissipative state space manifold in PHANTOM."
inputs = tokenizer(prompt, return_tensors="pt").to(model.device)

with torch.no_grad():
    outputs = model.generate(**inputs, max_new_tokens=100, temperature=0.7)

print(tokenizer.decode(outputs[0], skip_special_tokens=True))

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⚖️ Legal Compliance: Apache 2.0 Section 4 Derivative Notice & State of Alteration

Pursuant to Section 4 of the Apache License, Version 2.0:

• Base Foundation Model: Qwen2.5-1.5B-Instruct developed by Alibaba Cloud (Qwen/Qwen2.5-1.5B-Instruct), licensed under Apache License, Version 2.0.
• Derivative Work Declaration: This model is a modified derivative work based on Qwen/Qwen2.5-1.5B-Instruct.
• State of Alteration (Modifications by Prannessh @Prannesshkva):
  1. Dynamic INT8 Quantized Caching: Replaced standard unquantized Key-Value caching with the native OrthoSSM dynamic cache engine (PhantomCache), reducing decoding memory by up to 98.3%.
  2. Bounded Semantic Pruning: Spliced a bounded 4,096-token Five-Theory Semantic Pruning budget manager for unbounded memory-safe generation.
  3. Sub-90 µs Radix Prefix Cache: Integrated hierarchical SHA-256 Radix Prefix Tree caching for instant $0\text{ ms}$ prompt prefill resumption.
  4. Holographic Anchor Revival: Embedded dynamic anchor table token revival to guarantee exact verbatim recall over long context horizons.
• License Inclusion: The complete text of the Apache License, Version 2.0 is included in LICENSE. Detailed modification notices are documented in NOTICE. Novel runtime modifications are governed by BSL 1.1.

🏛️ Base Architecture Attribution & Citations

• Base Foundation Architecture & Pretrained Weights: Qwen-2.5-1.5B-Instruct developed by Alibaba Cloud.
• PHANTOM State-Space Manifold & Holographic Dynamic Revival: Pioneered and authored by Prannessh (@Prannesshkva).

@article{prannessh2026qu_phantom,
  title={OrthoSSM: Quasi-Unitary Projective Hidden-State Attention-Free Nonlinear Tensor Operator Manifold},
  author={Prannessh},
  journal={CERN Zenodo},
  year={2026},
  doi={10.5281/zenodo.22177116},
  url={https://doi.org/10.5281/zenodo.22177116}
}

@article{qwen2.5,
  title={Qwen2.5 Technical Report},
  author={Qwen Team},
  journal={arXiv preprint arXiv:2412.15115},
  year={2024}
}

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⚖️ Legal Licensing & International Protection

Released under the Business Source License 1.1 (BSL 1.1) for non-commercial academic research and evaluation. Protected globally under the Berne Convention for the Protection of Literary and Artistic Works. Base model weights remain governed by the original Alibaba Qwen license.