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What is a connection weight made of?

The weight of a connection is a count of synapses from one cell to another. CAVE's synapse view has one row per synapse, and champalimaud.fetch counts the rows of each pair of cells (the outputs of a cell by its presynaptic id, its inputs by its postsynaptic id). If that is all a weight is, the rows of one cell should reproduce its stored weights exactly. synapses holds the rows of one LC16 cell, fetched once as the dataset example_synapses.

synapses = load_example_synapses()
cell = synapses["cell"][0]
synapses

shape: (1_273, 4)

cell	id	pre_pt_root_id	post_pt_root_id
i64	i64	i64	i64
720575940606173630	159305691	720575940606173630	720575940615645034
720575940606173630	162802451	720575940606173630	720575940615645034
720575940606173630	159304826	720575940606173630	720575940615645034
720575940606173630	161891568	720575940606173630	720575940615645034
720575940606173630	162803628	720575940606173630	720575940445991679
…	…	…	…
720575940606173630	190197806	720575940616434260	720575940606173630
720575940606173630	190197390	720575940616434260	720575940606173630
720575940606173630	190196942	720575940622648703	720575940606173630
720575940606173630	190193625	720575940622664522	720575940606173630
720575940606173630	190198656	720575940609598475	720575940606173630

Rows per pair

pairs counts the rows between each pair of cells.

pairs = (
    synapses.group_by("pre_pt_root_id", "post_pt_root_id")
    .agg(rows=pl.len())
    .sort("rows", descending=True)
)
pairs

shape: (692, 3)

pre_pt_root_id	post_pt_root_id	rows
i64	i64	u32
720575940606173630	720575940613369586	25
720575940606173630	720575940606609696	24
720575940627497244	720575940606173630	17
720575940606173630	720575940615645034	16
720575940619690968	720575940606173630	14
…	…	…
720575940610984516	720575940606173630	1
720575940611329501	720575940606173630	1
720575940624090493	720575940606173630	1
720575940623775843	720575940606173630	1
720575940637630565	720575940606173630	1

Against the stored weights

stored is every connection in connections.parquet that starts or ends at the cell. The joined table has one row per pair, with the number of rows and the stored weight side by side.

stored = pl.concat(
    [
        load_connections_of([cell]),
        load_connections_of([cell], end="post"),
    ]
).unique()
compared = pairs.join(
    stored, on=["pre_pt_root_id", "post_pt_root_id"], how="full"
)
compared.select(
    pairs=pl.len(),
    only_in_rows=pl.col("weight").is_null().sum(),
    only_stored=pl.col("rows").is_null().sum(),
    equal=(pl.col("rows") == pl.col("weight")).sum(),
)

shape: (1, 4)

pairs	only_in_rows	only_stored	equal
u32	u32	u32	u32
692	0	0	692

How the weight is spread

The number of pairs at each weight, and the synapses they hold. Most connections are one or two synapses, but the heavier ones hold a large share of all synapses.

pairs.group_by("rows").agg(pairs=pl.len()).with_columns(
    synapses=pl.col("rows") * pl.col("pairs")
).sort("rows").rename({"rows": "weight"})

shape: (16, 3)

weight	pairs	synapses
u32	u32	u32
1	486	486
2	101	202
3	36	108
4	25	100
5	11	55
…	…	…
14	2	28
16	1	16
17	1	17
24	1	24
25	1	25