juniper-recurrence-model

The model-specific core for the juniper-recurrence application — the selected model P3-C (LMU + Approach-C).

This package ships the Δt-native Legendre Memory Unit (Approach-C) — a closed-form, variable-step LMU discretisation that is the only first-principles-clean ("C1") option natively handling irregularly-sampled time series — and LMURegressor, the recurrent model implementing the shared juniper-model-core TrainableModel interface (now that that package has landed). The regressor keeps the LMU memory fixed and trains only the readout — a linear closed-form least-squares fit by default (no BPTT, fully deterministic), with an optional nonlinear readout spectrum (ridge/GCV, random Fourier features, and a torch MLP — see Readout spectrum). It passes model-core's conformance kit unchanged, making it the WS-4 refactor template (a non-cascor model on the shared model seam).

Design of record (in juniper-ml): notes/JUNIPER_RECURRENCE_MODEL_DETAILED_DESIGN_2026-06-14.md.

Why Approach-C

An LMU's linear memory obeys theta * m'(t) = A·m(t) + B·u(t) with fixed, closed-form matrices. Because the system is linear, its exact discretisation is a matrix exponential — no ODE solver, no autodiff-through-solver. For irregular sampling, the discrete update is simply evaluated at the real per-step gap dt: the dataset's dt channel is the discretisation step. A/B are never trained; only the read-in/readout are. That is the entire C1-clean, irregular-Δt-native story.

Install

pip install juniper-recurrence-model          # once published
pip install -e ".[test]"                       # local development

numpy-only at the core (the memory is a fixed linear recurrence requiring no autodiff).

Quick start

import numpy as np
from juniper_recurrence_model import VariableStepLMUMemory

mem = VariableStepLMUMemory(d=16, theta=1.0)   # order 16, window 1.0 (same unit as dt)

# Irregularly-sampled input: u driven on a non-uniform time grid
t = np.cumsum(np.r_[0.0, np.random.default_rng(0).uniform(0.02, 0.08, 239)])
dt = np.empty_like(t); dt[0] = 0.0; dt[1:] = np.diff(t)
u = np.sin(2.0 * t)

m = mem.rollout(u, dt)                          # (240, 16) memory trajectory
w = mem.decode_weights(rho=1.0)                 # read the input one full window ago
reconstruction = m @ w

Trainable model (LMURegressor)

The package also exposes LMURegressor, a juniper-model-core TrainableModel. The LMU memory is fixed; the readout is fit — a linear closed-form least-squares solve by default (no BPTT, fully deterministic), or a nonlinear readout from the spectrum below. It is Δt-native: pass per-step gaps dt ((n, T)) and an optional readout_mask to fit / predict; both default to uniform gaps and the final step, so the bare ABC predict(X) works too. It reports canonical regression metrics (mse, rmse, mae, r2).

import numpy as np
from juniper_recurrence_model import LMURegressor, LMUSerializer

n, T, F = 48, 6, 3
X = np.random.default_rng(0).normal(size=(n, T, F))
y = X.reshape(n, -1) @ np.random.default_rng(1).normal(size=(T * F, 1))
dt = np.zeros((n, T)); dt[:, 1:] = np.random.default_rng(2).integers(1, 4, size=(n, T - 1))

model = LMURegressor(d=6)             # theta resolved data-driven from dt at fit time
result = model.fit(X, y, dt=dt)                 # closed-form readout solve
preds = model.predict(X, dt=dt)                 # (n, 1)
print(result.final_metrics["r2"], model.describe_topology()["model_type"])

LMUSerializer().save(model, "/tmp/lmu")   # writes /tmp/lmu.npz (lossless round-trip)

LMURegressor passes model-core's conformance kit unchanged (tests/test_conformance.py), proving the WS-4 refactor template.

Readout spectrum

The LMU memory is always the fixed, closed-form Δt-native recurrence; only the readout on top of the memory trajectory varies. Select it with the readout= constructor argument (DP-3):

from juniper_recurrence_model import LMURegressor, RFFReadoutSpec

model = LMURegressor(d=16, readout=RFFReadoutSpec(n_features_out=256, gamma="median"))

All three rungs keep the closed-form Δt memory and pass the conformance kit (including bit-exact save/load). On the synthetic delay_product capacity benchmark the RFF readout measures +0.83 r² over the linear readout; on the efficient-market equities target the spread is ≈0 (juniper-ml DP-3 findings). Default to linear + ridge="gcv"; reach for rff / mlp when the target has genuine nonlinear structure.

Verified behaviour

Pinned by tests/test_lmu_grid_invariance.py. Numerics match the reference util/ad-hoc/verify_delta_t_reference_code.py in juniper-ml.

Numerical guardrails

• Keep d ≲ 64 — the eigenvector matrix of A becomes ill-conditioned for large d (Padé scaling-and-squaring is the documented fallback for larger orders).
• Stability is automatic for dt > 0 (Re(λ) < 0 ⇒ |e^z| < 1).
• dt may be quantised (e.g. integer calendar-day gaps) and Abar/Bbar cached per bucket.

Versioning

PEP 440 + Keep a Changelog. Consumers should pin juniper-recurrence-model>=A.B,<A+1. See CHANGELOG.md.

License

MIT — see LICENSE.