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Just like the classic Notepad Ctrl+Click RCE behavior, terminals on Windows, Linux, and macOS also support clickable file/URI handlers. printf "\x1b]8;;file:///C:/windows/system32/calc.exe\x07Click here\x1b]8;;\x1b\\n"
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![I told you to claim your free 16GB NVIDIA GPU for learning Local LLMs. Now I’m going to show you how to double its inference speed without touching the hardware. Google Colab gives you an enterprise grade NVIDIA Tesla T4 GPU for free, roughly 4 hours every single day. It is the absolute perfect sandbox for learning AI engineering, testing inference flags, and pushing massive context windows. The local AI timeline is moving way too fast. If you aren't using Multi Token Prediction (MTP) yet, you are leaving massive performance on the table. I just pushed DeepMind’s Gemma 4 26B to 64.9 t/s on this exact free tier. Let's look at the raw benchmark data running on an Ubuntu Linux environment with the latest compiled llama.cpp binaries and quantized GGUFs from Unsloth via HuggingFace: # Qwen 3.5 9B (Dense): Base: [ Prompt: 626.7 t/s | Generation: 21.0 t/s ] With MTP: [ Prompt: 539.1 t/s | Generation: 24.8 t/s ] # Gemma 4 26B QAT (MoE): Base: [ Prompt: 634.2 t/s | Generation: 48.3 t/s ] With MTP: [ Prompt: 572.1 t/s | Generation: 64.9 t/s ] If you are paying attention, this single Colab notebook reveals 3 massive observations about the current state of local LLMs: # 1. The MTP Speedup (Software Overclocking) Standard autoregressive decoding guesses one token at a time. MTP acts like a highly optimized, built in speculative decoder. It predicts multiple future tokens at once and the main model verifies them in parallel. The result? Zero accuracy loss and a massive throughput increase. Gemma jumped from 48 to 65 t/s just by flipping a flag. # 2. The MoE Paradox (Bigger is Faster) How does a 26B parameter model absolutely destroy a 9B model in raw speed on the exact same hardware? Architecture. Qwen 3.5 9B is a dense model. it activates all 9 billion parameters for every single token. Gemma 4 26B is a Mixture of Experts (MoE) model. It routes data efficiently, activating only 4B parameters per token. You get the reasoning capabilities of a 26B model with the compute cost of a 4B model. 3. Thinking Efficiency When I ran the exact same complex prompt on both models, the larger MoE spent significantly fewer "thinking" tokens to arrive at the correct answer. A smarter model doesn't just give better answers; it gets to the point faster, saving you compute cycles and preserving your context window. # Want to run this yourself? Here are the exact llama.cpp CLI commands. For Qwen (MTP is baked into the main model): ./llama-cli -m Qwen3.5-9B-UD-Q4_K_XL.gguf -p "Explain quantum computing." -n 2000 -c 8000 -ngl 99 -fa on --spec-type draft-mtp --spec-draft-n-max 4 --spec-draft-p-min 0.7 For Gemma (Using a separate lightweight draft model): ./llama-cli -m gemma-4-26B-A4B-it-qat-UD-Q4_K_XL.gguf --model-draft mtp-gemma-4-26B-A4B-it.gguf -p "Explain quantum computing." -n 2000 -c 8000 -ngl 99 -fa on --spec-type draft-mtp --spec-draft-n-max 4 --spec-draft-p-min 0.7 Stop waiting for a $3,000 rig. Boot up Colab, pull these models, and start building your stack. I’ve put together a completely free, cell by cell Google Colab notebook that automates this entire workflow so you can test it yourself in 5 minutes and learn. Link to the notebook is in the comments below. Experiemt with different MTP parameters, context windows and post your results in the comments.](https://image.24vids.com/tw-2076665127450067116/amplify_video_thumb/2076664980515278849/img/K3GTizaUDbpZHQuo.jpg)
![[Discrete Fourier Transform] by Hand ✍️ In signal processing, the Discrete Fourier Transform (DFT) is no doubt the most important method. But the math involved is extremely complex, literally, involving a summation over a complex number term e^(-iwt). I developed this exercise to demonstrate that underneath such complexity, DFT is just a series of matrix multiplications you can calculate by hand. ✍️ Once you see that, it should not surprise you that a deep neural network, which is also a series of matrix multiplications, with activation functions in-between, can learn to perform DFT to process and analyze signals so effectively. How does DFT work? [1] Given ↳ Signals A, B, and C in the 🟧 frequency domain: ◦ A = cos(w) + 2cos(2w) ◦ B = cos(w) + cos(3w) + cos(4w) ◦ C = -cos(2w) + cos(3w) ◦ Each signal is a weighed sum of four cosine waves at frequencies 1w, 2w, 3w, and 4w. ◦ We will apply Inverse DFT to convert the signals to time domain representations, and then demonstrate DFT can convert back to their original frequency domain representations. ↳ Signal X in the 🟩 time domain. X is sampled at 10 time points 1t, 2t, …, 10t: ◦ X = [-2.5, -1.8, 3, -0.7, -1.0, -0.7, 3, -1.8, -2.5, 5] ◦ Suppose X is also a weighted sum of the same four cosine waves, but we don’t already know their weights. We will apply DFT to discover them. [2] 🟧 Frequency Matrix (F) ↳ Write the coefficients of A, B, C as a matrix F. Each signal is a row. Each frequency is a column. ↳ A → [1, 2, 0, 0] ↳ B → [1, 0, 1, 1] ↳ C → [0, 1-, 1, 0] [3] Cosine → Discrete ↳ Sample from the continuous cosine waves at discrete time points 1t, 2t, 3t, to 10t. [4] Cosine Matrix (W) ↳ Write the samples as a matrix, Each frequency is a row. Each time point is a column. [5] Inverse DFT: 🟧 Frequency → 🟩 Time ↳ Multiply the frequency matrix F and the cosine matrix W. ↳ The meaning of this multiplication is to linearly combine the four cosine waves (rows in W) into time-domain signals (rows in T) using the weights specified in F. ↳ The result is matrix T, which are signals A, B, C converted to the time domain. Each signal is a row. Each time point is a column. [6] Transpose ↳ Transpose T, converting each signal’s time domain representation from a row to a column. [7] DFT: 🟩 Time → 🟧 Frequency ↳ Multiply the cosine matrix W with the transpose of matrix T. ↳ The purpose of this multiplication is to take a dot-product between each time-domain signal (columns in the transpose of T) and each cosine wave (rows in W), which has the effect of projecting the signal onto a cosine wave to determine how much they are correlated. Zero means not correlated at all. ↳ The result is an intermediate version of the “recovered” frequency matrix where each column corresponds to a signal and each row corresponds to a frequency. ↳ Compared to the original frequency matrix F, this intermediate matrix has non-zero weights in the correct places, but scaled up by a factor of 5 (n/2, n=10). For example, signal A, originally [1,2,0,0], is recovered at [5,10,0,0]. [8] Scale ↳ Multiply each value by 2/n = 1/5 to scale down the intermediate matrix to match the magnitude of the original frequency matrix F. [9] Transpose ↳ Transpose the recovered frequency matrix back to the same orientation of the original frequency matrix F. ↳ Like magic 🪄, the result is identical to the original F, which means DFT successfully recovered the frequency components of signals A, B, C. [10] Apply DFT to X: 🟩 Time → 🟧 Frequency ↳ Now that we have some confidence in DFT’s ability to recover frequency components, we apply DFT to X’s time-domain representation by multiplying W with X. ↳ The result is the an intermediate matrix. [11] Scale ↳ Similarly, we scale down by a factor of 5 to obtain the recovered frequency components of X (a column). [12] Transpose ↳ Similarly, we transpose the recovered column to row to match the orientation of the frequency matrix. ↳ Using the coefficients [0,0,3,2], we can write the equation of X as 3cos(3w) + 2cos(4w). Notes: I hope this by hand exercise helps you understand the essence of DFT. But there is more technical details, such as: • Sine: The complete DFT math also includes sine waves that follow a similar calculation process. • Phase: Here, we assume all the cosine waves are aligned at the origin, namely, phase is 0. If a phase p is added, for example, cos(w+p), we will need to calculate the sine component and use their ratio to figure out what p is. • Magnitude: If phase is not zero, the magnitude will need to be calculated by combining both cosine and sine terms.](https://image.24vids.com/tw-1805694219031662799/ext_tw_video_thumb/1805693963464327168/pu/img/kOcpELm1j7wfqJlR.jpg)
