Solver Overview — UMAP + Matrix Heatmaps

C — Observed Connectome

X axisPostsynaptic neuron type (741 types, hover to identify)

Y axisPresynaptic neuron type (741 types, hover to identify)

What it's saying: Binary — 1 where a synapse was measured between that type pair. ~6.3% density: most possible type pairs never connect. Full resolution, no subsampling.

Ĉ — Reconstructed Connectome

X axisPostsynaptic neuron type (same 741 types, same order as C)

Y axisPresynaptic neuron type (same 741 types)

What it's saying: The solver's continuous reconstruction of C from the learned P and β. corr(C, Ĉ) ≈ 0.47 after 15 iterations. Full resolution, no subsampling.

P — Solved Type Assignment

X axisMetacell — 500 of the 6,099 solved metacells, evenly sampled by index (real metacells, not averaged)

Y axisNeuron type (all 741 types)

What it's saying: Log color scale. A confident metacell shows one bright cell in its column; a genuinely ambiguous one spreads across a few types. Full 741×6,099 matrix is ~4.5M cells — too large to embed live, so columns are subsampled (not binned/averaged) to keep every shown value a real solved entry.

P Constraints — Candidate Types Allowed (input to the solver, before any optimisation)

X axisMetacell — 500 of 7,982 metacells (built pre-solve; this run's actual solve used a filtered 6,099), evenly sampled

Y axisNeuron type (all 741 types)

What it's saying: This is the input to the P update, not an output — a binary support mask (step 9 of build_all_matrices.py: P_constraints_metacell = (P_meta > 0), transposed). Orange = that type is even allowed as a candidate for that metacell; gray = ruled out entirely. On average each metacell starts with 162.5 candidate types allowed out of 741. The solver's P update (see the "P — Solved Type Assignment" tab) can only move probability mass onto orange cells here — everything gray stays exactly 0 no matter how many iterations run. Compare the two tabs side by side: P's non-zero pattern should sit strictly inside this mask's orange cells.

β — Learned Gene-Gene Weights

X axisGene index — first gene in the pair (3,000 genes)

Y axisGene index — second gene in the pair (3,000 genes)

What it's saying: Only the top ~150 of 9,000,000 gene-pair entries are shown — an L1 sparsity penalty (λ=0.001) drives 99.999% of β to ~0, so a full heatmap would just be noise. This run's top hit: CG31688 × Rpn3 (β≈3.92).

G — Metacell Expression Probability

X axisGene — 250 of 3,000 highly-variable genes, evenly sampled

Y axisMetacell — 250 of 7,982 metacells, evenly sampled

What it's saying: Linear [0,1] scale — the fraction of cells in that metacell detected expressing that gene. This is the version (G_metacell_p) the solver's β update actually regresses against. Full matrix is ~24M cells; shown here as a 250×250 subsample of real (metacell, gene) pairs.

Gene Correlation (ref) — diagnostic only, not the solver's β

X axisGene — 250 of 3,000 genes, evenly sampled (same subsample on both axes)

Y axisGene — same 250 genes

What it's saying: This is NOT a solver output — it's a plain co-expression baseline, computed once before the solver ever runs, so you have something to compare β against. Formula: Gᵀ·G / n_cells, where G is the same z-scored per-cell expression used for clustering (not metacells — all 109,743 individual cells). Because each gene column is z-scored (mean≈0, std≈1), this is mathematically the Pearson correlation between every pair of genes — diagonal ≈1 (a gene perfectly correlates with itself), shown here as |value| on a log scale so both strong positive and negative correlations stand out. Compare a bright cell here against the same gene pair in β: if β is near-zero there despite this correlation being high, the connectome constraint is actively rejecting a co-expression pattern that raw correlation alone would have flagged. (Saved in the code as B_matrix.npy, hence the internal name "B".)

Solver Convergence

X axisSolver iteration (1 to 15)

Y axisObjective / loss value

What it's saying: Loss drops from 29,449 to 25,403 (13.7%) and flattens by iteration ~10 — 15 iterations is close to converged for this configuration. Hover any point on any of the 3 curves; toggle series via the legend.