Hello everyone,

I’m new to machine learning and I was trying to extend the basic example from Flux documentation to a multiple linear regression model where the input `S`

and the output `V`

are both vectors with 3 elements each, x, y and z.

As long as the relation between `S`

and `V`

is identity, I get great predictions using my model. Simply changing the function between `S`

and `V`

as in the following example so that V_y = 2S_y, leads to wrong results.

What could be the cause of this problem?

```
## Random Data set
F = 3
D = 1800
S_train, S_test = rand(1:100, F, D), rand(1:100, F, D)
```

```
## V = ƒ(S), both V & S are vectors with 3 elements
function ƒ(S::Matrix)
V = zero(S)
D = size(S, 1)
D > 1 && for (x, y, z) in Iterators.partition(eachindex(S), D)
V[x] = S[x]
V[y] = 2S[y]
V[z] = S[z]
end
isone(D) && (V .= map(actual, S))
return V
end
V_train, V_test = ƒ(S_train), ƒ(S_test)
```

```
# default activation function: identity
using Flux: train!
opt = Descent(1e-7) ## optimizer: classic gradient descent strategy
data = [(V_train, S_train)]
model = Dense(F => F)
parameters = Flux.params(model)
loss(x, y) = Flux.Losses.mse(model(x), y)
for _ in Base.OneTo(100_000)
train!(loss, parameters, data, opt)
end
```

```
model(S_test)
3×1800 Matrix{Float32}:
79.9905 51.0251 83.9732 1.19865 … 7.04939 99.9106 69.8579 21.1866
12.4992 36.5154 16.4895 20.1102 41.5276 20.9554 21.4264 43.6019
80.0067 62.9638 77.0303 81.7296 25.9406 68.1154 14.1989 97.7402
V_test
3×1800 Matrix{Int64}:
80 51 84 1 40 86 97 77 61 … 82 49 28 75 7 100 70 21
50 146 66 80 44 42 154 194 4 30 8 62 54 166 84 86 174
80 63 77 82 3 68 94 35 9 78 77 81 32 26 68 14 98
```