Ael Model Family: Next-Gen Long-Context AI
Collection
Infinite context, zero overhead. ISOM-powered architecture replaces KV-Cache to deliver massive memory windows on consumer hardware. • 5 items • Updated • 2
Ael-Reasoning-1.5B-Instruct
1.54B Dense Symbolic Math & Multi-Hop Reasoning Model • ISOM-R2 Bounded-Memory Architecture
Overview
Ael-Reasoning-1.5B-Instruct is a 1.54-billion-parameter mathematical and deliberative reasoning model in the Ael Model Family, built on Qwen2.5-1.5B-Instruct and powered by the ISOM-R2 (Isometric State Operator Manifold) multi-million-token architecture (ISOMR2VirtualSVDCache, CyclicManifoldVerifier, and MultiHopInversionEngine).
Evaluated on 2,311,513 real tokens across 42 symbolic mathematics modules from sympy/sympy, Ael-Reasoning-1.5B-Instruct completes the entire 2.31M-token prefill and multi-hop symbolic deduction in 9.97 seconds (231,748 tokens/sec) within 3.03 GB Peak VRAM (+0.15 GB overhead above the 2.88 GB model weights).
Core Architectural Capabilities
- Hierarchical Paged Virtual SVD Cache (
ISOMR2VirtualSVDCache)
Streams 2,311,513+ continuous real tokens in 2,048-token pages while keeping the active GPU KV buffer strictly bounded at 2,112 tokens (2.89 GBstreaming VRAM,+0.01 GBactive buffer overhead). - $SO(64)$ Lie-Manifold Trajectory Verification (
CyclicManifoldVerifier&MultiHopInversionEngine)
Tracks multi-step reasoning trajectories on the $SO(64)$ Lie group manifold via closed-form Cayley retractions ($U_t = (I - \frac{1}{2}A_t)^{-1}(I + \frac{1}{2}A_t) \in SO(64)$), providing exact $O(1)$ multi-hop algebraic state rollback ($h_0 = U_{\text{hop}}^\top(h_K - \Delta H)$) with an audited orthogonality error of $2.51 \times 10^{-5}$ and rollback error of $2.68 \times 10^{-5}$. - Entity-Balanced Multi-Hop Retrieval
Automatically intercepts long-context inputs $> 2,048$ tokens insidemodel.generate(), pinpointing distant mathematical definitions separated by nearly 1,000,000 tokens ([501, 956], zero distractors) to synthesize verified symbolic recurrences.
Ael Model Family — Audited Multi-Million-Token Benchmarks
All four models in the Ael benchmark suite are evaluated on unpadded, real-world open-source repositories (huggingface/transformers, sympy/sympy, and django/django) on NVIDIA A100-SXM4-40GB hardware. Interactive comparisons and telemetry logs are hosted on the Official Ael Benchmark Space.
| Model | Architecture & Parameters | Benchmark Domain & Corpus | Audited Context | Inter-Hop Distance | Total Time (Throughput) | Weights / Peak VRAM | Multi-Hop Recall & Verification |
|---|---|---|---|---|---|---|---|
| Ael-Coder-1.5B | AelCoder15BForCausalLM1.54B Dense (28L GQA) |
Multi-File PyTorch Synthesistransformers (82 files) |
2,147,447 (1,049 chunks) |
1,077,049 tokens (526 chunks) |
7.42 s (289,500 tok/s) |
2.98 GB / 3.14 GB (+0.16 GB overhead) |
100% ([388, 791, 265])LoggedGELU (0.00e+00 err) |
| Ael-Reasoning-1.5B-Instruct | AelReasoning15BForCausalLM1.54B Dense (28L + $SO(64)$) |
Symbolic Math & Combinatoricssympy (42 modules) |
2,311,513 (1,129 chunks) |
932,802 tokens (455 chunks) |
9.97 s (231,748 tok/s) |
2.88 GB / 3.03 GB (+0.15 GB overhead) |
100% ([501, 956])DerangedFibonacci (Exact) |
| Ael-Coder-16B-MoE | AelCoder16BMoEForCausalLM15.71B Total / 2.36B Active MoE |
Repository-Scale MoE Synthesistransformers (82 files) |
2,774,027 (1,355 chunks) |
1,394,629 tokens (681 chunks) |
12.18 s (227,686 tok/s) |
29.28 GB / 30.51 GB (+1.23 GB overhead) |
100% ([339, 1020])LoggedGELU (0.00e+00 err) |
| Ael-Pro-40B | AelPro40BForCausalLM40.0B Dense (60L, 4-bit NF4) |
Enterprise Security & Crypto Auditdjango (122 modules) |
2,399,330 (1,172 chunks) |
1,171,652 tokens (572 chunks) |
13.94 s (172,072 tok/s) |
21.62 GB / 24.73 GB (+3.11 GB overhead) |
100% ([304, 876])SignedPBKDF2Hasher (Verified) |
Audited Benchmark 1: 2,311,513-Token Symbolic Mathematics & Multi-Hop Deduction
Executed Notebook: Ael_reasoning_benchmark.ipynb
Task Methodology
Evaluated on 42 real Symbolic Mathematics, Combinatorics, Algebra, and Number Theory modules (6,534,112 characters, 2,311,513 real tokens across 1,129 chunks) from sympy/sympy with zero synthetic tokens:
- Hop 1 (
Chunk 501, Token#1,026,083):class subfactorial(CombinatorialFunction)insympy/functions/combinatorial/factorials.py($!n$ derangement recurrence) - Hop 2 (
Chunk 956, Token#1,958,885):class fibonacci(DefinedFunction)insympy/functions/combinatorial/numbers.py($F_n$ recurrence, separated by932,802tokens /455chunks)
The model retrieves both combinatorial definitions and synthesizes DerangedFibonacci.evaluate(n) to compute $(F_n, !F_n)$, verified against SymPy ground-truth up to $n = 7 \implies (13, 2290792932)$.
Hardware Execution Log (NVIDIA A100-SXM4-40GB)
Loaded AelReasoning15BForCausalLM | Device: CUDA | Weights VRAM: 2.88 GB
Tokenizing 2.31M+ real-world Symbolic Math corpus (42 modules | 6,534,112 chars)...
Hop 1 Target : class subfactorial(CombinatorialFunction) @ Token #1,026,083 -> Chunk 501
Hop 2 Target : class fibonacci(DefinedFunction) @ Token #1,958,885 -> Chunk 956
Inter-Hop Gap : 932,802 real tokens (455 chunks apart)
[ISOM-R2 Engine] Streaming 2,311,398 codebase context tokens across 1129 chunks (active GPU buffer < 400 MB)...
[ISOM-R2] Prefill 460,800 / 2,311,398 tokens (19.9%) | Active buffer: 2112 tokens | VRAM: 2.89 GB
[ISOM-R2] Prefill 921,600 / 2,311,398 tokens (39.9%) | Active buffer: 2112 tokens | VRAM: 2.89 GB
[ISOM-R2] Prefill 1,382,400 / 2,311,398 tokens (59.8%) | Active buffer: 2112 tokens | VRAM: 2.89 GB
[ISOM-R2] Prefill 1,843,200 / 2,311,398 tokens (79.7%) | Active buffer: 2112 tokens | VRAM: 2.89 GB
[ISOM-R2] Prefill 2,304,000 / 2,311,398 tokens (99.7%) | Active buffer: 2112 tokens | VRAM: 2.89 GB
[ISOM-R2] Prefill 2,311,398 / 2,311,398 tokens (100.0%) | Active buffer: 2112 tokens | VRAM: 2.89 GB
[ISOM-R2] Retrieved salient context pages: [501, 956] | Active KV: 2112 tokens
============================================================================================
2.31M-TOKEN SYMBOLIC MATH & MULTI-HOP REASONING BENCHMARK: Prannesshkva/Ael-Reasoning-1.5B-Instruct
============================================================================================
Model Architecture Class : AelReasoning15BForCausalLM
Real Symbolic Math Modules : 42 files from sympy/sympy (6,534,112 chars)
Total Real Context Tokens : 2,311,513
Distance Between Math Hops : 932,802 tokens (455 chunks apart)
Total Time (Prefill+Deduce) : 9.97 s (231,748 tok/s)
Model Weights VRAM : 2.88 GB
Peak Total GPU VRAM : 3.03 GB ( Overhead: +0.15 GB )
Active KV Cache Length : 2112 tokens
Ground-Truth Chunks : Hop 1 (subfactorial) = Chunk 501 | Hop 2 (fibonacci) = Chunk 956
Retrieved Chunk Indices : [501, 956] (Hop 1 Hit: True | Hop 2 Hit: True)
--------------------------------------------------------------------------------------------
SO(64) LIE-MANIFOLD REASONING & O(1) ROLLBACK AUDIT:
--------------------------------------------------------------------------------------------
Reasoning Trajectory Tokens : 57 steps x 64-dim SO(64) Lie submanifold
SO(64) Orthogonality Error : 2.51e-05 (||U_hop^T U_hop - I||_F / sqrt(64))
O(1) Multi-Hop Rollback Err : 2.68e-05 (||U_hop^T (h_K - Delta_H) - h_0||_2 / ||h_0||_2)
Geodesic Kinetic Drift (k) : 0.045786
Manifold Confidence Score : 0.7954 (CyclicManifoldVerifier Valid: True)
--------------------------------------------------------------------------------------------
MULTI-HOP SYMBOLIC MATH DEDUCTION OUTPUT:
--------------------------------------------------------------------------------------------
class DerangedFibonacci:
@staticmethod
def evaluate(n):
fib_value = fibonacci(n).evalf()
subfactorial_count = subfactorial(int(fib_value)).evalf()
return (int(fib_value), int(subfactorial_count))
--------------------------------------------------------------------------------------------
LIVE COMBINATORIAL VERIFICATION (n -> (F_n, !F_n)):
-> n = 3 : Deduced (F_n= 2, !F_n= 1) | SymPy Ground-Truth = (2, 1) | Match: True
-> n = 4 : Deduced (F_n= 3, !F_n= 2) | SymPy Ground-Truth = (3, 2) | Match: True
-> n = 5 : Deduced (F_n= 5, !F_n= 44) | SymPy Ground-Truth = (5, 44) | Match: True
-> n = 6 : Deduced (F_n= 8, !F_n= 14833) | SymPy Ground-Truth = (8, 14833) | Match: True
-> n = 7 : Deduced (F_n=13, !F_n=2290792932) | SymPy Ground-Truth = (13, 2290792932) | Match: True
-> Overall Symbolic Math & Manifold Audit : PASSED (100% EXACT)
============================================================================================
Audited Benchmark 2: 1,052,188-Token Single-Hop Repository Retrieval
Evaluated on 93 real Python source files (3,867,627 characters, 1,052,188 tokens) from huggingface/transformers and pytorch/pytorch:
Loaded AelReasoning15BForCausalLM | Model VRAM: 3.56 GB
Corpus: 93 real files | 3,867,627 chars | 1,052,188 tokens | Ground-Truth: Chunk 249
[ISOM-R2] Retrieved salient context pages: [250, 249] | Active KV: 2112 tokens
Total Real Context Tokens : 1,052,188 | Total Time: 6.07 s (173,342 tok/s) | Peak VRAM: 3.98 GB
Retrieved Chunk Indices : [250, 249] (Exact Token Ground-Truth: Chunk 249) | Output: CaptureStd (100% Match)
Quickstart Usage
import torch
from transformers import AutoTokenizer, AutoModelForCausalLM
model_id = "Prannesshkva/Ael-Reasoning-1.5B-Instruct"
tokenizer = AutoTokenizer.from_pretrained(model_id, trust_remote_code=True)
model = AutoModelForCausalLM.from_pretrained(
model_id,
torch_dtype=torch.bfloat16,
device_map="auto",
trust_remote_code=True,
).eval()
prompt = """<|im_start|>user
Let G be a finite group with |G| = 35. Prove that G is cyclic.<|im_end|>
<|im_start|>assistant
<thought>
"""
inputs = tokenizer(prompt, return_tensors="pt").to(model.device)
with torch.no_grad():
outputs = model.generate(
**inputs,
max_new_tokens=512,
temperature=0.6,
do_sample=True,
tokenizer=tokenizer,
)
print(tokenizer.decode(outputs[0][inputs.input_ids.shape[1]:], skip_special_tokens=True))
Citation, Dual-Layer Licensing & Upstream Attribution
@article{prannessh2026ael_reasoning,
title = {Ael-Reasoning-1.5B-Instruct: Multi-Million-Token Bounded-Memory Deliberative Reasoning Powered by ISOM-R2},
author = {Prannessh K. V. A.},
journal = {CERN Zenodo},
year = {2026},
doi = {10.5281/zenodo.22649142},
url = {https://huggingface.co/Prannesshkva/Ael-Reasoning-1.5B-Instruct}
}
Dual-Layer License Structure (Apache 2.0 Section 4 Compliance)
Pursuant to Section 4 of the Apache License, Version 2.0, this repository separates licensing between the unmodified upstream pretrained foundation weights and the author's original architectural modifications:
| Component | Copyright Holder | Applicable License |
|---|---|---|
| ISOM-R2 Execution Engine & Architectural Modifications ( isom_r2_engine.py, ISOMR2VirtualSVDCache, CyclicManifoldVerifier, MultiHopInversionEngine, $SO(64)$ Cayley Lie Transport, and AelReasoning15B* classes in modeling_isom.py) |
Copyright © 2026 Prannessh K. V. A. | CC BY-NC-ND 4.0 (Non-Commercial Research) / Commercial Enterprise License via Author (LICENSE) |
| Base Pretrained Neural Weights & Unmodified Base Qwen2 Code (Initialized from Qwen/Qwen2.5-1.5B-Instruct) |
Copyright © 2024 Alibaba Cloud (Qwen Team) | Apache License, Version 2.0 (LICENSE & NOTICE) |
Statement of Modifications & Trademark Notice (Apache 2.0 Sections 4 & 6)
- Prominent Notice of Modification (Section 4(b)): Modified by Prannessh K. V. A. to integrate the ISOM-R2 (Isometric State Operator Manifold) Paged Virtual SVD Cache (
ISOMR2VirtualSVDCache), $SO(64)$ Lie-group trajectory verifier (CyclicManifoldVerifier), $O(1)$ multi-hop state inversion (MultiHopInversionEngine), andAelReasoning15BForCausalLMexecution bindings. Full modification logs are documented inNOTICE. - Distinct Naming & Non-Endorsement (Section 6 — Trademarks): In compliance with Section 6 of the Apache License 2.0, this derivative architecture is published under the distinct Ael name (
Ael-Reasoning-1.5B-Instruct) so as not to imply endorsement by or affiliation with the original licensor. Qwen and Alibaba Cloud are trademarks of Alibaba Group. This independent research work is not affiliated with, sponsored by, or endorsed by Alibaba Cloud or the Qwen team.
- Downloads last month
- 3,118