def trace_hopfield_step(weights, vector)
  n = vector.length
  Array.new(n) { |i| n.times.sum { |j| weights[i][j] * vector[j] } }
end

def hamming_trace(pattern_vectors, input_vec)
  n = input_vec.length
  k = pattern_vectors.length
  dots = pattern_vectors.map { |pv| pv.zip(input_vec).sum { |a, b| a * b } }
  initial = dots.map { |dot| (dot.to_f + n) / 2.0 }
  {
    eps:             (0.9 / k).round(6),
    k:               k,
    n:               n,
    dot_products:    dots,
    initial_outputs: initial.map { |v| v.round(2) }
  }
end