Initial release
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-- ============================================================================
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-- SPDX-License-Identifier: GPL-3.0-or-later
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-- Copyright (C) 2026 Alexander Allan (MDMAchine) -- A&E Concepts
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-- ============================================================================
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-- MD Eigenflow V1 -- PCA Trajectory Filtering Sampler
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-- MDMAchine | A&E Concepts (c) 2026
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--
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-- PCA trajectory filtering via power iteration on velocity history window.
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-- Separates dominant denoising direction from oscillatory noise.
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-- Euler advance with filtered velocity. owns_loop = true. Single NFE.
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-- ============================================================================
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local C = require("md_solver_commons")
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-- ── POWER ITERATION (per-batch) ─────────────────────────────────────────────
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local function power_iteration_batch(window, win_len, off, cnt, M, iters)
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local eigvecs, eigvals = {}, {}
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for m = 1, M do
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local q = {}
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for i = 0, cnt - 1 do q[i] = window[1][off + i] end
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for prev = 1, m - 1 do
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local d = 0.0
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for i = 0, cnt - 1 do d = d + q[i] * eigvecs[prev][i] end
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for i = 0, cnt - 1 do q[i] = q[i] - d * eigvecs[prev][i] end
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end
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for _iter = 1, iters do
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local Cq = {}
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for i = 0, cnt - 1 do Cq[i] = 0.0 end
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for k = 1, win_len do
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local dot = 0.0
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for i = 0, cnt - 1 do dot = dot + window[k][off + i] * q[i] end
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local scale = dot / win_len
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for i = 0, cnt - 1 do Cq[i] = Cq[i] + window[k][off + i] * scale end
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end
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for prev = 1, m - 1 do
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local d = 0.0
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for i = 0, cnt - 1 do d = d + Cq[i] * eigvecs[prev][i] end
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for i = 0, cnt - 1 do Cq[i] = Cq[i] - d * eigvecs[prev][i] end
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end
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local nrm = 0.0
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for i = 0, cnt - 1 do nrm = nrm + Cq[i] * Cq[i] end
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nrm = math.sqrt(nrm + C.EPSILON)
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for i = 0, cnt - 1 do q[i] = Cq[i] / nrm end
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end
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local lam = 0.0
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for k = 1, win_len do
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local dot = 0.0
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for i = 0, cnt - 1 do dot = dot + window[k][off + i] * q[i] end
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lam = lam + dot * dot
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end
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eigvecs[m] = q
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eigvals[m] = lam / win_len
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end
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return eigvecs, eigvals
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end
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local function filter_velocity_batch(v_curr, off, cnt, eigvecs, M, ratio)
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local projections = {}
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for m = 1, M do
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local dot = 0.0
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for i = 0, cnt - 1 do dot = dot + v_curr[off + i] * eigvecs[m][i] end
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projections[m] = dot
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end
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local filtered = {}
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for i = 0, cnt - 1 do
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local dominant = 0.0
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for m = 1, M do dominant = dominant + projections[m] * eigvecs[m][i] end
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filtered[i] = dominant + ratio * (v_curr[off + i] - dominant)
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end
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return filtered
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end
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-- ── SOLVER DEFINITION ───────────────────────────────────────────────────────
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solver = {
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name = "md_eigenflow_v1",
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display = "MD Eigenflow V1",
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description = "PCA trajectory filtering sampler. Power iteration on velocity history, batch-aware, shared anchor stack.",
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nfe = 1,
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order = 1,
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needs_model = false,
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stateful = true,
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stochastic = true,
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owns_loop = true,
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params = {
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{ key = "window_size", type = "slider", label = "Velocity Window Size",
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default = 6, min = 3, max = 12, step = 1,
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hint = "Velocity snapshots in sliding window." },
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{ key = "num_modes", type = "slider", label = "Principal Modes",
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default = 2, min = 1, max = 4, step = 1,
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hint = "Dominant eigenvectors to keep. 1 = aggressive, 3+ = conservative." },
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{ key = "power_iterations", type = "slider", label = "Power Iterations",
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default = 4, min = 2, max = 8, step = 1,
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hint = "Convergence iterations for power method." },
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{ key = "eigenflow_ratio", type = "slider", label = "Eigenflow Ratio",
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default = 0.3, min = 0.0, max = 1.0, step = 0.05,
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hint = "Residual to keep. 0 = pure dominant mode. 1 = passthrough (Euler)." },
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{ key = "sigma_warmup", type = "slider", label = "Sigma Warmup",
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default = 0.85, min = 0.5, max = 1.0, step = 0.05,
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hint = "Sigma fraction above which filtering is disabled." },
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{ key = "adaptive_ratio", type = "toggle", label = "Adaptive Ratio",
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default = true,
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hint = "Modulates eigenflow_ratio by dominance ratio." },
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},
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}
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C.append_common_params(solver.params)
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-- ── SAMPLE ──────────────────────────────────────────────────────────────────
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function sample(xt, vt_buf, schedule, n, model_fn)
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local p = params or {}
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local B, NPB = C.get_batch_routing(n)
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local win_size = math.floor(C.num_param(p, "window_size", 6))
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local num_modes = math.floor(C.num_param(p, "num_modes", 2))
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local pw_iters = math.floor(C.num_param(p, "power_iterations", 4))
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local ef_ratio = C.num_param(p, "eigenflow_ratio", 0.3)
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local sigma_warmup = C.num_param(p, "sigma_warmup", 0.85)
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local f_adaptive = C.bool_param(p, "adaptive_ratio", true)
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local opts = C.read_common_opts(p)
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local state = C.new_state()
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-- Engine schedule has NO trailing 0 (fix ported from 46c081e): iterate all ns
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-- entries so the last iteration gets sigma_next = 0.0 and the terminal branch
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-- performs the final x0 projection. With ns - 1 that branch is dead code and
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-- the output keeps ~final-sigma noise.
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local ns, n_steps = #schedule, #schedule
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if n_steps < 1 then return end
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local sigma_max = schedule[1]
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local v_window, v_win_len, v_win_pos = {}, 0, 0
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for k = 1, win_size do v_window[k] = nil end
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local x = C.fa_to_tbl(xt, n)
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if opts.verbose then
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print(string.format("[EIGENFLOW V1] Schedule: %d steps | B=%d NPB=%d n=%d | win=%d modes=%d ratio=%.2f",
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n_steps, B, NPB, n, win_size, num_modes, ef_ratio))
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end
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for i = 1, n_steps do
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local sigma_curr = schedule[i]
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local sigma_next = (i < ns) and schedule[i + 1] or 0.0
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local step_idx = i - 1
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local sigma_ratio = C.clamp(sigma_curr / math.max(sigma_max, C.EPSILON), 0.0, 1.0)
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if sigma_next == 0.0 then
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C.tbl_to_fa(x, xt, n)
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model_fn(xt, sigma_curr)
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local v_final = C.fa_to_tbl(vt_buf, n)
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for j = 0, n - 1 do x[j] = x[j] - v_final[j] * sigma_curr end
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break
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end
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C.tbl_to_fa(x, xt, n)
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model_fn(xt, sigma_curr)
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local v_curr = C.fa_to_tbl(vt_buf, n)
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local dt = sigma_next - sigma_curr
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-- Relational decomposition (shape/scale cleanup on velocity)
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if opts.rw > 0 then
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C.apply_relational(v_curr, n, B, NPB, sigma_ratio, sigma_max,
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opts.rw, opts.rw_sigma_pow, opts.drift_on, opts.drift_thr, x)
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end
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-- Push into ring buffer
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v_win_pos = (v_win_pos % win_size) + 1
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v_window[v_win_pos] = C.vec_clone(v_curr, n)
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if v_win_len < win_size then v_win_len = v_win_len + 1 end
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-- Build ordered window
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local win_ordered = {}
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for k = 1, v_win_len do
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local idx = ((v_win_pos - v_win_len + k - 1) % win_size) + 1
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win_ordered[k] = v_window[idx]
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end
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-- Eigenflow filtering
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local v_use = v_curr
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local filtered = false
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local dominance_ratio = 0.0
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if v_win_len >= win_size and sigma_ratio < sigma_warmup then
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local actual_modes = math.min(num_modes, win_size - 1)
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local v_filtered = C.vec_clone(v_curr, n)
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for b = 0, B - 1 do
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local off = b * NPB
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local eigvecs, eigvals = power_iteration_batch(
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win_ordered, v_win_len, off, NPB, actual_modes, pw_iters)
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if actual_modes >= 2 and eigvals[2] > C.EPSILON then
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local dr = eigvals[1] / eigvals[2]
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if dr > dominance_ratio then dominance_ratio = dr end
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end
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local eff_ratio = ef_ratio
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if f_adaptive and dominance_ratio > 1.0 then
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eff_ratio = ef_ratio * C.clamp(1.0 / math.sqrt(dominance_ratio), 0.1, 1.0)
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end
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local batch_filtered = filter_velocity_batch(
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v_curr, off, NPB, eigvecs, actual_modes, eff_ratio)
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for j = 0, NPB - 1 do v_filtered[off + j] = batch_filtered[j] end
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end
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if not C.has_nan_inf(v_filtered, n) then
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v_use = v_filtered
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filtered = true
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end
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end
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-- Euler advance
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local x_new = {}
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for j = 0, n - 1 do x_new[j] = x[j] + dt * v_use[j] end
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if C.has_nan_inf(x_new, n) then
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for j = 0, n - 1 do x_new[j] = x[j] + dt * v_curr[j] end
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end
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-- Post-advance stack
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opts.sigma_next = sigma_next
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opts.step_idx = step_idx
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C.post_advance(x_new, n, B, NPB, sigma_ratio, opts, state)
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if opts.verbose then
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print(string.format("[EIGENFLOW V1] step %02d | %s | dom=%.2f | rms=%.3f",
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step_idx, filtered and "FILTERED" or "raw", dominance_ratio, C.rms(x_new, n)))
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end
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x = x_new
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C.tbl_to_fa(x, xt, n)
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C.tbl_to_fa(v_curr, vt_buf, n)
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if on_step(step_idx, sigma_curr, sigma_next) then return end
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x = C.fa_to_tbl(xt, n)
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end
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C.tbl_to_fa(x, xt, n)
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end
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