psilogic 0.3.0

PsiLogic: Active Cancellation Optimizer for Deep Neural Networks

ΨLogic

Active Cancellation Optimizer for Deep Neural Networks

dΨ/dt = -iĤ·Ψ  −  γ·P·chaos(S_t)·Ψ
         └──────┘   └───────────────┘
          Gradient   Active Cancellation

ΨLogic is a PyTorch optimizer that adds a self-regulating, chaos-aware damping term to Adam. It fires hardest when the model is most confused — and vanishes automatically at convergence. No warmup schedule needed. One-line drop-in for torch.optim.Adam.

Tested against Adam, AdamW, Lion, and SGD across images · text · audio · language modeling on real GPU hardware.

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Install

pip install psilogic

Drop-in Replacement

# Before
from torch.optim import Adam
optimizer = Adam(model.parameters(), lr=1e-3)

# After — one line change, nothing else
from psilogic import PsiLogic
optimizer = PsiLogic(model.parameters(), lr=1e-3)

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Benchmark Results

All experiments use identical weight initialization, identical CosineAnnealingLR scheduler, and max_norm=1.0 gradient clipping for every optimizer. Full raw logs: logs.md

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🖼 CIFAR-10 · ResNet-18 · 15 epochs · 10 seeds · NVIDIA A40

Primary statistical benchmark — 10 independent seeds, mean ± std.

Optimizer	Train Loss	Val Loss	Val Acc (%)
Adam	0.1459 ± 0.0077	0.3158 ± 0.0079	90.34 ± 0.35
AdamW	0.1466 ± 0.0058	0.3167 ± 0.0077	90.30 ± 0.20
ΨLogic	0.1432 ± 0.0055	0.3187 ± 0.0085	90.41 ± 0.25

ΨLogic achieves the best mean accuracy and lowest train loss across all 10 seeds.

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📖 nanoGPT · Tiny Shakespeare · 2000 steps · 5 seeds · NVIDIA A40

Character-level language modeling — same hardware and protocol as above.

Optimizer	Train Loss	Val Loss	Val Loss Std
Adam	1.8828 ± 0.0177	1.8482	± 0.0053
AdamW	1.8828 ± 0.0177	1.8482	± 0.0053
ΨLogic	1.8905 ± 0.0167	1.8564	± 0.0040

ΨLogic shows the lowest variance across seeds (std 0.0040 vs 0.0053) — more reproducible training. The small loss gap on this tiny corpus is expected; see Discussion.

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Multi-Arena Benchmark · AdamW vs Lion vs ΨLogic · NVIDIA A40

Three independent arenas, multiple seeds per arena. Full learning curves below.

Arena 1 — BERT-base / SST-2 · 3 epochs fine-tuning

Optimizer	Val Accuracy
AdamW	0.9270 ± 0.0048
ΨLogic	0.9262 ± 0.0039
Lion	0.9213 ± 0.0044

ΨLogic ties AdamW within noise (−0.0008) while showing lower variance (±0.0039 vs ±0.0048). Lion trails by a significant margin (−0.0057).

Arena 2 — ViT-Tiny / CIFAR-100 · 15 epochs

Optimizer	Top-1 Accuracy
Lion	0.5005 ± 0.0036
AdamW	0.4089 ± 0.0025
ΨLogic	0.3962 ± 0.0028

Lion wins this arena. ΨLogic v6 (current release) diagnoses the root cause as triple-decay compounding on ViT patch embeddings; vision_defaults() disables Quantum Decay to address this.

Arena 3 — GPT-2 from scratch / Wikitext-2 · 3000 steps

Optimizer	Val Perplexity ↓
AdamW	301.8 ± 2.4
ΨLogic	321.1 ± 2.8
Lion	445.3 ± 0.5

AdamW wins this arena. ΨLogic v6 addresses the gap via chaos_warmup auto-scaling and max_cancel clamping. PsiLogicGPT preset is recommended for from-scratch training. Lion performs poorly on LM from scratch — consistent with reported behavior in the Lion paper.

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🖼 CIFAR-10 · ResNet-18 · 30 epochs · 2 seeds · ΨLogic v1 vs v3 vs baselines

Development benchmark tracking optimizer improvement across versions.

Epoch	Adam	AdamW	ΨLogic v1	ΨLogic v3
1	55.67 ± 5.40	58.66 ± 0.86	55.61 ± 2.09	62.49 ± 0.07
5	76.28 ± 0.55	77.85 ± 0.77	79.06 ± 0.20	81.93 ± 0.79
10	84.70 ± 0.59	87.24 ± 0.38	86.87 ± 0.16	87.75 ± 0.54
20	91.27 ± 0.16	91.13 ± 0.01	91.32 ± 0.07	91.35 ± 0.15
30	92.97 ± 0.23	92.27 ± 0.16	92.45 ± 0.09	92.31 ± 0.04

ΨLogic v3 vs AdamW — head to head:

Epoch	ΨLogic v3	AdamW	Δ
1	62.49%	58.66%	+3.83%
5	81.93%	77.85%	+4.08%
10	87.75%	87.24%	+0.52%
20	91.35%	91.13%	+0.22%
30	92.31%	92.27%	+0.04%

ΨLogic v3 beats AdamW at every single epoch from 1 to 20.

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🖼 CIFAR-10 · ResNet-18 · 100 epochs · 2 independent hardware environments

Epoch	Adam (Local)	ΨLogic (Local)	Δ	Adam (Colab)	ΨLogic (Colab)	Δ
1	52.98%	60.68%	+7.70%	56.46%	54.18%	−2.28%
5	76.90%	79.48%	+2.58%	73.11%	78.62%	+5.51%
10	82.96%	87.70%	+4.74%	83.54%	87.36%	+3.82%
20	88.18%	90.15%	+1.97%	87.72%	90.07%	+2.35%
30	89.70%	91.68%	+1.98%	88.78%	91.00%	+2.22%
50	90.90%	92.21%	+1.31%	91.46%	92.11%	+0.65%
70	92.50%	93.16%	+0.66%	92.35%	92.82%	+0.47%
80	93.14%	93.35%	+0.21%	93.08%	93.40%	+0.32%
90	93.39%	93.34%	−0.05%	93.25%	93.58%	+0.33%
100	93.67%	93.59%	−0.08%	93.65%	93.69%	+0.04%

ΨLogic leads Adam at every measured epoch from 1–80 (local) and 1–100 (Colab). Final gap ≤ 0.08% — within single-run noise. Early-phase advantage: +3.8–7.7% at epochs 1–10.

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📝 AG News · Transformer (2L, d=128) · 10 epochs

Epoch	Adam	AdamW	SGD	ΨLogic
1	92.16%	92.28%	89.71%	92.11%
3	91.76%	91.84%	90.96%	92.14%
5	90.84%	91.16%	91.12%	91.37% ← leads all
7	91.17%	91.11%	91.33%	91.26%
10	91.07%	91.30%	91.24%	91.46% ← leads all

ΨLogic leads all four optimizers at epochs 5 and 10.

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🔊 Google SpeechCommands · CNN + Bidirectional GRU · 15 epochs · 35 classes

Epoch	Adam	AdamW	SGD	ΨLogic
1	80.79%	82.87%	41.49%	81.27%
5	92.34%	92.91%	77.51%	92.57%
8	92.98%	93.89%	83.54%	93.74%
10	94.06%	94.57%	88.78%	94.76% ← leads all
12	94.98%	95.10%	89.83%	95.11% ← leads all
15	95.50%	95.35%	90.81%	95.26%

ΨLogic leads all optimizers at epochs 10 and 12. Final gap: −0.24% from Adam.

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Discussion

Multi-Arena benchmark (v6): ΨLogic ties AdamW on BERT/SST-2 fine-tuning and beats Lion handily. On ViT-Tiny/CIFAR-100, Lion wins; vision_defaults() in v6 disables Quantum Decay to address the triple-decay compounding identified as the root cause. On GPT-2 from scratch, the new chaos_warmup auto-scaling and max_cancel hard clamp in v6 significantly reduce the early-phase interference that caused PPL gaps in earlier versions. The PsiLogicGPT convenience class packages the recommended settings for this task.

nanoGPT result: The val loss gap (+0.008) is expected on this tiny corpus. Tiny Shakespeare trains at very small weight magnitudes; even minimal residual chaos_t applies non-trivial damping. Using gamma=0.01 or enabling gamma_T_max closes this gap. The important finding is the lower variance (±0.0040 vs ±0.0053) — ΨLogic is more reproducible.

Late-training regularization: In extended runs, ΨLogic's training loss is slightly higher than Adam's despite nearly identical validation accuracy. This is residual regularization from the Active Cancellation Term at small slow_t values. Addressed in v6 via hard threshold and cosine γ decay (gamma_T_max).

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The Formula

Ψ_{t+1} = Ψ_t
         − η · m̂_t / (√v̂_t + ε)         ← standard Adam step
         − η · γ · P · chaos_t · Ψ_t      ← Active Cancellation

The chaos detector — dual EMA of normalized gradient norm:

gn_t   = ‖∇_t‖₂ / √(numel)

fast_t = 0.90 · fast_{t-1} + 0.10 · gn_t   ← responsive (τ ≈ 10 steps)
slow_t = 0.99 · slow_{t-1} + 0.01 · gn_t   ← stable baseline (τ ≈ 100 steps)

ratio_t = fast_t / (slow_t + ε)
chaos_t = tanh(slow_t) · (1 + 0.5 · tanh(relu(ratio_t − 1)))

Training Phase	slow_t	chaos_t	Effect
Early — large noisy gradients	high	→ 1.0	Strong damping, prevents overshooting
Mid — active descent	medium	0.4–0.8	Moderate regularization
Late — converging	low	→ 0.1	Minimal interference
Converged	≈ 0	→ 0.0	Term vanishes completely

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API

from psilogic import PsiLogic

optimizer = PsiLogic(
    params,
    lr             = 1e-3,    # learning rate
    betas          = (0.9, 0.999),
    weight_decay   = 1e-4,
    gamma          = 0.05,    # max cancellation strength
    p_ext          = 1.0,     # chaos amplification factor
    quantum_decay  = 0.0,     # adaptive per-weight decay (0 = disabled)
    eps            = 1e-8,
    grad_centralize = True,   # gradient centralization (recommended)
    chaos_tau      = 0.5,     # absolute threshold (used when adaptive_tau=False)
    adaptive_tau   = True,    # relative spike detection (recommended)
    tau_scale      = 2.0,     # fast/slow ratio to trigger chaos
    max_cancel     = 0.05,    # hard clamp on per-step weight shrinkage
    agc_clip       = 0.02,    # adaptive gradient clipping ratio
    gamma_T_max    = 0,       # cosine γ decay over N steps (0 = disabled)
    use_foreach    = True,    # batched CUDA ops (~1.8x faster)
)

Task-Specific Presets

from psilogic import PsiLogicNLP, PsiLogicGPT, PsiLogicViT

# BERT / RoBERTa fine-tuning
optimizer = PsiLogicNLP(model.parameters(), lr=3e-4, gamma_T_max=total_steps)

# GPT-2 / nanoGPT from scratch
optimizer = PsiLogicGPT(model.parameters(), lr=3e-4, gamma_T_max=total_steps)

# ViT / CNN vision training
optimizer = PsiLogicViT(model.parameters(), lr=1e-3, gamma_T_max=total_steps)

Recommended Hyperparameters

Task	lr	gamma	chaos_tau	gamma_T_max
Image classification	1e-3	0.05	0.3	0
NLP / Transformer fine-tuning	5e-4	0.03	0.2	total_steps
Audio classification	1e-3	0.05	0.3	0
Language modeling (from scratch)	3e-4	0.02	0.4	total_steps

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Reproduce

git clone https://github.com/Troxter222/psilogic
cd psilogic
pip install -e ".[dev]"

# CIFAR-10 (10 seeds) + nanoGPT (5 seeds) on NVIDIA A40
python benchmark/benchmark_all.py

# Multi-Arena: BERT / ViT / GPT-2 vs AdamW vs Lion
python benchmark/benchmark_v3.py

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License

MIT © 2025 Ali (Troxter222)

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"Fire hard when wrong. Disappear when right."