# Drill 15 Incomplete mini batch

Subject: Deep Learning

Exam: MT2

Reader: https://deep-learning-study-room.vercel.app/#mt2/read/17/mt2-c17-s15

Canonical: https://deep-learning-study-room.vercel.app/read/dl/mt2/section/mt2-c17-s15/

## Question

**Question.** N = 103, B = 20, epochs = 3. Count updates for batch GD, SGD, mini-batch keeping the remainder, and mini-batch dropping it.

## Answer — step by step

### Given

N = 103 samples; B = 20 samples per mini-batch.

E = 3 epochs.

Compare both remainder policies: keep or drop the final 3 examples.

### To find

Find total updates for full-batch GD, SGD, and both mini-batch policies.

### Formula — which one and why

**Number of updates.** An update occurs after one processed batch. Full-batch GD uses one batch per epoch; SGD uses one sample per batch. Mini-batches need a stated remainder policy.

N = dataset size; B = batch size; E = number of epochs. Ceiling rounds upward to include a smaller final batch; floor drops it.



$$
U_{\mathrm{batch}}=E
$$





$$
U_{\mathrm{SGD}}=EN
$$





$$
U_{\mathrm{keep}}=E\left\lceil\frac NB\right\rceil
$$





$$
U_{\mathrm{drop}}=E\left\lfloor\frac NB\right\rfloor
$$



**Yaad rakhne ka cue:** Kitne batches process hue, utne updates hue.

### Solution — step by step

### Meaning and formulas

An epoch means one pass through the dataset. An update happens once per batch used. N is the number of samples, B is the chosen batch size, and E is the number of epochs.



$$
U_{\mathrm{batch}}=E,\qquad U_{\mathrm{SGD}}=NE
$$





$$
U_{\mathrm{keep}}=E\left\lceil\frac NB\right\rceil,\qquad U_{\mathrm{drop}}=E\left\lfloor\frac NB\right\rfloor
$$



Ceiling rounds up to the next integer; floor rounds down. The final incomplete batch needs an update only if it is retained.

### Step 1: batch GD

All 103 samples form one batch per epoch.



$$
U_{\mathrm{batch}}=3\times1=3
$$



### Step 2: SGD

Each sample gets its own update.



$$
U_{\mathrm{SGD}}=103\times3=309
$$



### Step 3: mini-batches with the remainder



$$
103=5\times20+3
$$



The batch sizes are 20, 20, 20, 20, 20 and 3. Six batches per epoch give:



$$
U_{\mathrm{keep}}=6\times3=18
$$



### Step 4: mini-batches without the remainder

Only the five complete batches are used each epoch.



$$
U_{\mathrm{drop}}=5\times3=15
$$



**Final answer:** 3, 309, 18 and 15 updates respectively.