Help with my training data
There are a couple of problems and things you might want to add to your existing script.

Below I separate your example data into two NumPy arrays:


input values x
labels y


It is also important to make sure they are of type float32, because Tensorflow will complain if you pass it integers (as they otherwise would be interpreted).

The following works for me, the model trains to completion:

import numpy as np
import tensorflow as tf
from tensorflow.keras import layers

syslog_data = [
    [302014, 0, 0, 63878, 30, 3, 1],
    [302014, 0, 0, 3891, 0, 0, 0],
    [302014, 0, 0, 15928, 0, 0, 2],
    [305013, 5, 0, 123, 99999, 0, 3],
    [302014, 0, 0, 5185, 0, 0, 0],
    [305013, 5, 0, 123, 99999, 0, 3],
    [302014, 0, 0, 56085, 0, 0, 0],
    [110002, 4, 2, 50074, 99999, 0, 4],
]

print(tf.VERSION)
print(tf.keras.__version__)

x = np.array([arr[:-1] for arr in syslog_data], dtype=np.float32)
y = np.array([arr[-1:] for arr in syslog_data], dtype=np.float32)

model = tf.keras.Sequential()
# Adds a densely-connected layer with 64 units to the model:
model.add(layers.Dense(64, activation="relu"))
# Add another:
model.add(layers.Dense(64, activation="relu"))
# Add a softmax layer with 10 output units:
model.add(layers.Dense(10, activation="softmax"))

model.compile(optimizer=tf.train.AdamOptimizer(0.001), loss="categorical_crossentropy", metrics=["accuracy"])

model.fit(x, y, epochs=10, steps_per_epoch=30)