I proposed—She said "No." (s**tpost)

She proceeded to monologue about how I fail to retain her words and am incapable of understanding her emotions.

My world broke, yet I could see so clearly 🌎 💔 👀

A critical limitation to my brain's Recurrent Neural Network (RNN) architecture 🧠:

The Vanishing Gradient Problem 🚩

I've mistakenly designed my mind to process my relationships' communication like an RNN handles sequences: Word by Word.

RNNs are neural nets built for ordered data, like speech, text, or in my case, Her lengthy explanations on why I "need help." 🙄

Basic RNN setup

At each step $t$, take input $x_t$ ("No, I'm never going to marry you") and combine it with hidden state $h_t$ (yesterday's argument) yielding $y_t$:

$$\begin{aligned} h_t &= \tanh\!\left(W_{hh}\,h_{t-1} + W_{xh}\,x_t + b_h\right)\\[2pt] y_t &= W_{hy}\,h_t + b_y \end{aligned} \tag{2}$$

In theory, this loop is magical: Info persists over time 🕰️

Unroll it, find a deep chain sharing weights, and learn the temporal dependencies within sequences ➡️ Backpropagation Through Time (BPTT)

It's like replaying this heartbreaking conversation backwards to learn. Loss sums over the sequence, $\mathcal{L} = \sum_{t} \mathcal{L}_t$, gradients flow from end to start, updating weights.

Where it falls apart

But here's the real heartbreak: long sequences kill it ➡️ The Vanishing Gradient Problem 🚩

These gradients shrink exponentially 📉 as they propagate back. The partial derivative matrix (Jacobian) with respect to $h_{t-k}$ involves repeated multiplications:

$$\frac{\partial h_t}{\partial h_{t-k}} = \prod_{j=t-k+1}^{t} \frac{\partial h_j}{\partial h_{j-1}} = \prod_{j=t-k+1}^{t} \operatorname{diag}\!\big(\tanh'(z_j)\big)\, W_{hh}^{\top} \tag{3}$$

Since $\tanh'$ is always between $0$ and $1$, if $W_{hh}$'s eigenvalues are $< 1$, the gradients vanish over time. Early inputs (like her first hints, years ago) have zero influence on updates. My foolish RNN brain architecture can't remember the start by the end.

RNNs shine on short, concise inputs: "Yes, I'll marry you" or "Ew, No." But long, nuanced conversations over the course of a multi-year relationship? Forget it, it'll struggle to learn deep dependencies.

She said I don't get her feelings and that I need to take responsibility. Fair. But is it really my fault, or is it my brain's faulty architecture? If so, what is there for me to take responsibility for?