psilogic 0.2.0

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, and SGD across images · text · audio · language modeling on real 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

Most statistically rigorous 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 on the same hardware, same protocol.

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

Iterative development benchmark showing improvement across ΨLogic 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.
Wins 9 out of 10 epoch×optimizer comparison slots overall.

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

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

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 loss gap (100-epoch runs): ΨLogic's training loss is higher than Adam's despite nearly identical val accuracy. This is residual regularization from the Active Cancellation Term at small slow_t values. Addressed in the next version via hard threshold and cosine γ decay.

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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
slow_t = 0.99 · slow_{t-1} + 0.01 · gn_t   ← stable baseline

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          = 1.2,     # external power scale
    quantum_decay  = 1e-3,    # adaptive per-weight decay
    eps            = 1e-8,
    grad_centralize = True,   # gradient centralization (recommended)
    chaos_tau      = 0.3,     # threshold — term is zero below this
    gamma_T_max    = 0,       # cosine γ decay over N steps (0 = disabled)
)

Recommended Settings

Task	lr	gamma	chaos_tau	gamma_T_max
Image classification	1e-3	0.05	0.3	0
NLP / Transformer	5e-4	0.03	0.2	total_steps
Audio classification	1e-3	0.05	0.3	0
Language modeling	1e-3	0.01	0.2	total_steps

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Reproduce

git clone https://github.com/Troxter222/psilogic
cd psilogic
pip install -e ".[dev]"
python benchmark/benchmark_all.py   # CIFAR-10 10 seeds + nanoGPT 5 seeds on NVIDIA A40

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License

MIT © 2025 Ali (Troxter222)

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"Fire hard when wrong. Disappear when right."