SoftOpt

A standalone optimizer that excels against leading market optimizers like Adam, in problems with a known, differentiable computation graph.

Each step is an update followed by an exact Newton correction computed from your own model, through Klein–Maimon soft-number calculus (Foundations of Soft Logic, Klein & Maimon, Springer 2024). Free, open source, and runs locally.

Where it helps

If your problem has a known computation graph — a quantum circuit, a physical simulator, a projection or measurement model, anything you can write down exactly, even if the measurements of it are noisy — SoftOpt computes an exact directional derivative and curvature of that model on every step, and uses them to correct the optimizer's trajectory. Validated, with real hardware-noise-model data, across:

• Quantum chemistry (VQE) — H₂, H₄, BeH₂, HeH⁺, and larger multireference molecules
• Quantum control (GRAPE) — the single cleanest result across every domain tested
• Computer vision — multi-camera bundle adjustment / camera calibration
• Finance — portfolio optimization (Markowitz mean-variance)
• Condensed-matter physics — quasicrystal and spin-chain models (Ising, XY, Heisenberg, SSH, Kitaev)
• Pharmacokinetics, logistic regression, and more

Where it does not help

Full reinforcement learning (or anything else with a continuously moving target — a policy, an adversary, a non-stationary distribution) is outside SoftOpt's validated scope. The mechanism needs a fixed objective to compute a meaningful correction against; a moving target breaks that assumption. Use plain Adam/SGD there.

Installation

pip install softopt

Quick start

import numpy as np
from softopt import SoftOpt, soft_compile

# Write your model once, in plain Python. No special arithmetic.
def my_model(theta):
    x, y = theta
    return (x - 2.0)**2 + np.exp(y) * x

# soft_compile turns it into the exact directional-derivative function
# SoftOpt needs, and verifies the result against your own model.
g_delta = soft_compile(my_model, n_params=2)

opt = SoftOpt(2, g_delta, lr=0.02)

for step in range(num_steps):
    grad_estimate = my_gradient_estimate(theta)   # e.g. from SPSA on real hardware
    theta = opt.step(theta, grad_estimate)

Your model needs to be built from arithmetic and the elementary functions the soft algebra defines: + - * / ** (including negative and fractional exponents, and 2.0 ** x), abs, sqrt, exp, log, log10, sin, cos, tanh, comparisons, and numpy's versions of those. Loops and if/else branching on parameter values work too — the compiled derivative is then valid on the branch your parameters are actually in.

The one thing to avoid is converting a traced value back to a plain number mid-model — float(x), or np.array(params) on the parameter list, both silently discard the derivative. soft_compile's verification catches this and says so.

If you'd rather write the derivative function yourself — because your model lives in a simulator SoftOpt can't trace, or because you want the speed of a hand-tuned implementation — pass any g_delta(theta, delta) that returns the exact directional derivative, and skip soft_compile entirely.

Validated results

All results below use IBM's FakeFez noise model via Qiskit + Aer, or realistic finite-sample/measurement noise for the non-quantum domains, with torch.optim.Adam as the baseline. Improvement is the reduction in gap to the known optimum (or, for Portfolio, the reduction in loss).

Quantum chemistry (VQE)

Quantum control

Condensed-matter & spin models

Computer vision

Finance

See benchmarks/ for the exact, runnable scripts behind every one of these numbers, including the raw per-seed results.

A performance table cannot show why a method wins. tests/test_causal.py runs the optimizer's own code path while replacing the genuine soft-computed curvature with a frozen constant, or with real curvature measured at an unrelated point. Both perform worse than using no correction at all — the specific computed value is doing the work. Run it directly for the full report:

python3 tests/test_causal.py

The math

The full soft-number algebra is available from the package (from softopt import SoftNumber, sadd, smul, ...), each operation cited to its exact source in Foundations of Soft Logic (Klein & Maimon, Springer 2024):

SoftNumber wraps these with operator syntax (x + y, x * y, x ** 3, x.sqrt()) and is verified, axiom by axiom, against the book's own proofs that bridge numbers form an abelian group under addition and a ring under both operations (tests/test_soft_number.py).

What SoftOpt is not

• Not a claim to beat specialized full-Jacobian second-order solvers (Levenberg–Marquardt, L-BFGS) where those are already practical — SoftOpt's validated niche is genuine improvement over first-order optimizers (Adam, SGD) already in use, particularly where switching to a full second-order method isn't practical (embedded in a larger pipeline, high dimensionality, or measurement noise).
• Not a general-purpose black-box optimizer — it requires a known computation graph, as described above.

License

MIT. See LICENSE.