# Flowing vs. Thinking: How Liquid Neural Networks Diverge from LLMs

> Source: <https://dev.to/suzuskiee/flowing-vs-thinking-how-liquid-neural-networks-diverge-from-llms-4kal>
> Published: 2026-07-20 16:41:29+00:00

If you follow the world of Artificial Intelligence, it is easy to assume that scaling up is the only path forward. **Large Language Models (LLMs)** have dominated the conversation by scaling to hundreds of billions of parameters, acting as massive, discrete reasoning engines.

But not all problems require a massive library of tokens. In the world of robotics, physical sensors, and continuous time, a different architectural philosophy is thriving: **Liquid Neural Networks (LNNs)**.

LLMs process static, discrete symbols, LNNs use highly expressive fluid equations to navigate the chaotic, continuous flow of the physical world. To understand why an LNN can solve complex physics tasks with just a fraction of the compute of an LLM, we have to look at the actual mathematics.

People often state that LNNs "adapt" according to the input they receive. In the context of LLMs, we usually think of adaptation as shifting attention weights across discrete tokens. When people hear that LNNs adapt dynamically, a common misconception arises: *Do LNNs actually change their weights or biases during the forward pass?*

**The short answer is no.**

Just like an LLM, an LNN's parameters — its input weight matrix ( U ), recurrent weight matrix ( W ), and biases ( b ) — are completely fixed after the training phase is complete.

So, what makes them "liquid"?

The adaptation happens within the **hidden state** (
h(t)
) and the **effective time constant** (
τ(t)
) of each individual neuron, which change continuously with time. Unlike LLMs, which are governed by the discrete-time architecture of the Transformer, LNNs are fundamentally built on **Ordinary Differential Equations (ODEs)**.

Inside an LNN, the equation describing a neuron's state looks like this:

Where f is a standard non-linear activation function (like tanh or sigmoid).

Notice the time constant
τ
. In a traditional continuous-time neural network,
τ
is a fixed number. In an LNN, **
τ
is a dynamic function of the current input
x(t)
and the current hidden state
h(t)
.**

In code, the right-hand side of that ODE is just this:

``` python
import numpy as np

def dh_dt(h, x, W, U, b, tau_fn, f=np.tanh):
    """
    LNN ODE: dh/dt = -h / tau(x, h) + f(W·h + U·x + b)
    tau_fn(x, h) -> the dynamic time constant function.
    """
    # 1. Compute the dynamic, liquid time constant
    tau = tau_fn(x, h)

    # 2. Compute the continuous rate of change
    return -h / tau + f(W @ h + U @ x + b)

# To update the hidden state over a discrete time step (dt):
def euler_step(h, x, W, U, b, tau_fn, dt):
    return h + dt * dh_dt(h, x, W, U, b, tau_fn)
```

Therefore, "adaptation" in an LNN doesn't mean the network is rewriting its own code (altering weights) on the fly. Instead, it means **the speed and trajectory of the neuron's state change based entirely on the input.** If the incoming data suddenly becomes noisy, erratic, or unpredictable, the neuron can mathematically "slow down" its integration to filter out the noise — all without needing new weights.

Because of this unique, continuous-time framework, LNNs are uniquely suited for **physical, real-world, streaming environments**.

Despite the elegance of LNNs, they are not designed to process semantic knowledge. LLMs remain the undisputed engines of **reasoning and massive knowledge retrieval**.

| Feature | Liquid Neural Networks (LNNs) | Large Language Models (LLMs) |
|---|---|---|
Primary Domain |
Robotics, autonomous systems, continuous sensors | Text, code, semantic reasoning |
Time Paradigm |
Continuous (ODEs) | Discrete (Tokens + Attention) |
Scale |
Extremely small (thousands of parameters) | Massive (billions of parameters) |
Adaptation Mechanism |
Dynamic, input-dependent time constants ( τ ) | Contextual attention weights |

Ultimately, we are looking at two brilliant but entirely distinct philosophies of computation. LLMs are built to store, parse, and reason through the accumulated, discrete data of human history. LNNs are built like agile nervous systems to react, filter noise, and adapt to the chaotic, continuous flow of the physical world.