What numbers that I can put in numpy.random.seed()?

Consider a very basic random number generator:

Z[i] = (a*Z[i-1] + c) % m

Here, Z[i] is the ith random number, a is the multiplier and c is the increment - for different a, c and m combinations you have different generators. This is known as the linear congruential generator introduced by Lehmer. The remainder of that division, or modulus (%), will generate a number between zero and m-1 and by setting U[i] = Z[i] / m you get random numbers between zero and one.

As you may have noticed, in order to start this generative process - in order to have a Z[1] you need to have a Z[0] - an initial value. This initial value that starts the process is called the seed. Take a look at this example:

The initial value, the seed is determined as 7 to start the process. However, that value is not used to generate a random number. Instead, it is used to generate the first Z.

The most important feature of a pseudo-random number generator would be its unpredictability. Generally, as long as you don't share your seed, you are fine with all seeds as the generators today are much more complex than this. However, as a further step you can generate the seed randomly as well. You can skip the first n numbers as another alternative.

Main source: Law, A. M. (2007). Simulation modeling and analysis. Tata McGraw-Hill.

The short answer:

There are three ways to seed() a random number generator in numpy.random:

• use no argument or use None -- the RNG initializes itself from the OS's random number generator (which generally is cryptographically random)

• use some 32-bit integer N -- the RNG will use this to initialize its state based on a deterministic function (same seed → same state)

• use an array-like sequence of 32-bit integers n₀, n₁, n₂, etc. -- again, the RNG will use this to initialize its state based on a deterministic function (same values for seed → same state). This is intended to be done with a hash function of sorts, although there are magic numbers in the source code and it's not clear why they are doing what they're doing.

If you want to do something repeatable and simple, use a single integer.

If you want to do something repeatable but unlikely for a third party to guess, use a tuple or a list or a numpy array containing some sequence of 32-bit integers. You could, for example, use numpy.random with a seed of None to generate a bunch of 32-bit integers (say, 32 of them, which would generate a total of 1024 bits) from the OS's RNG, store in some seed S which you save in some secret place, then use that seed to generate whatever sequence R of pseudorandom numbers you wish. Then you can later recreate that sequence by re-seeding with S again, and as long as you keep the value of S secret (as well as the generated numbers R), no one would be able to reproduce that sequence R. If you just use a single integer, there's only 4 billion possibilities and someone could potentially try them all. That may be a bit on the paranoid side, but you could do it.

Longer answer

The numpy.random module uses the Mersenne Twister algorithm, which you can confirm yourself in one of two ways:

• Either by looking at the documentation for numpy.random.RandomState, of which numpy.random uses an instance for the numpy.random.* functions (but you can also use an isolated independent instance of)

• Looking at the source code in mtrand.pyx which uses something called Pyrex to wrap a fast C implementation, and randomkit.c and initarray.c.

In any case here's what the numpy.random.RandomState documentation says about seed():

Compatibility Guarantee A fixed seed and a fixed series of calls to RandomState methods using the same parameters will always produce the same results up to roundoff error except when the values were incorrect. Incorrect values will be fixed and the NumPy version in which the fix was made will be noted in the relevant docstring. Extension of existing parameter ranges and the addition of new parameters is allowed as long the previous behavior remains unchanged.

Parameters:
seed : {None, int, array_like}, optional

Random seed used to initialize the pseudo-random number generator. Can be any integer between 0 and 2**32 - 1 inclusive, an array (or other sequence) of such integers, or None (the default). If seed is None, then RandomState will try to read data from /dev/urandom (or the Windows analogue) if available or seed from the clock otherwise.

It doesn't say how the seed is used, but if you dig into the source code it refers to the init_by_array function: (docstring elided)

def seed(self, seed=None):
    cdef rk_error errcode
    cdef ndarray obj "arrayObject_obj"
    try:
        if seed is None:
            with self.lock:
                errcode = rk_randomseed(self.internal_state)
        else:
            idx = operator.index(seed)
            if idx > int(2**32 - 1) or idx < 0:
                raise ValueError("Seed must be between 0 and 2**32 - 1")
            with self.lock:
                rk_seed(idx, self.internal_state)
    except TypeError:
        obj = np.asarray(seed).astype(np.int64, casting='safe')
        if ((obj > int(2**32 - 1)) | (obj < 0)).any():
            raise ValueError("Seed must be between 0 and 2**32 - 1")
        obj = obj.astype('L', casting='unsafe')
        with self.lock:
            init_by_array(self.internal_state, <unsigned long *>PyArray_DATA(obj),
                PyArray_DIM(obj, 0))

And here's what the init_by_array function looks like:

extern void
init_by_array(rk_state *self, unsigned long init_key[], npy_intp key_length)
{
    /* was signed in the original code. RDH 12/16/2002 */
    npy_intp i = 1;
    npy_intp j = 0;
    unsigned long *mt = self->key;
    npy_intp k;

    init_genrand(self, 19650218UL);
    k = (RK_STATE_LEN > key_length ? RK_STATE_LEN : key_length);
    for (; k; k--) {
        /* non linear */
        mt[i] = (mt[i] ^ ((mt[i - 1] ^ (mt[i - 1] >> 30)) * 1664525UL))
            + init_key[j] + j;
        /* for > 32 bit machines */
        mt[i] &= 0xffffffffUL;
        i++;
        j++;
        if (i >= RK_STATE_LEN) {
            mt[0] = mt[RK_STATE_LEN - 1];
            i = 1;
        }
        if (j >= key_length) {
            j = 0;
        }
    }
    for (k = RK_STATE_LEN - 1; k; k--) {
        mt[i] = (mt[i] ^ ((mt[i-1] ^ (mt[i-1] >> 30)) * 1566083941UL))
             - i; /* non linear */
        mt[i] &= 0xffffffffUL; /* for WORDSIZE > 32 machines */
        i++;
        if (i >= RK_STATE_LEN) {
            mt[0] = mt[RK_STATE_LEN - 1];
            i = 1;
        }
    }

    mt[0] = 0x80000000UL; /* MSB is 1; assuring non-zero initial array */
    self->gauss = 0;
    self->has_gauss = 0;
    self->has_binomial = 0;
}

This essentially "munges" the random number state in a nonlinear, hash-like method using each value within the provided sequence of seed values.

What is normally called a random number sequence in reality is a "pseudo-random" number sequence because the values are computed using a deterministic algorithm and probability plays no real role.

The "seed" is a starting point for the sequence and the guarantee is that if you start from the same seed you will get the same sequence of numbers. This is very useful for example for debugging (when you are looking for an error in a program you need to be able to reproduce the problem and study it, a non-deterministic program would be much harder to debug because every run would be different).

Basically the number guarantees the same 'randomness' every time.

More properly, the number is a seed, which can be an integer, an array (or other sequence) of integers of any length, or the default (none). If seed is none, then random will try to read data from /dev/urandom if available or make a seed from the clock otherwise.

Edit: In most honesty, as long as your program isn't something that needs to be super secure, it shouldn't matter what you pick. If this is the case, don't use these methods - use os.urandom() or SystemRandom if you require a cryptographically secure pseudo-random number generator.

The most important concept to understand here is that of pseudo-randomness. Once you understand this idea, you can determine if your program really needs a seed etc. I'd recommend reading here.

To understand the meaning of random seeds, you need to first understand the "pseudo-random" number sequence because the values are computed using a deterministic algorithm.

So you can think of this number as a starting value to calulate the next number you get from the random generator. Putting the same value here will make your program getting the same "random" value everytime, so your program becomes deterministic.

As said in this post

they (numpy.random and random.random) both use the Mersenne twister sequence to generate their random numbers, and they're both completely deterministic - that is, if you know a few key bits of information, it's possible to predict with absolute certainty what number will come next.

If you really care about randomness, ask the user to generate some noise (some arbitary words) or just put the system time as seed.

If your codes run on Intel CPU (or AMD with newest chips) I also suggest you to check the RdRand package which uses the cpu instruction rdrand to collect "true" (hardware) randomness.

Refs:

1. Random seed
2. What is a seed in terms of generating a random number

One very specific answer: np.random.seed can take values from 0 and 2**32 - 1, which interestingly differs from random.seed which can take any hashable object.

A side comment: better set your seed to a rather large number but still within the generator limit. Doing so can let the seed number have a good balance of 0 and 1 bits. Avoid having many 0 bits in the seed.

Reference: pyTorch documentation