## §0 TL;DR Cheat Sheet

> 💡 **VLM in 8 sentences** — one page covering the core interview points for vision-language models (see §1–§13 below for derivations and code).

1. **Vision encoder = ViT-dominated**: Dosovitskiy et al. 2021 (ICLR) slice images into $P\times P$ patches (typically $P=14$ or $16$), apply a linear projection + learnable positional embedding + optional `[CLS]` token, and feed them into a Transformer encoder. **The vision side of CLIP / SigLIP / LLaVA is all a ViT variant.**

2. **CLIP symmetric InfoNCE (must derive)**: Radford et al. 2021 (ICML) make image embeddings $\mathbf{u}_i$ and text embeddings $\mathbf{v}_i$ do contrastive learning in a shared space, with loss = **average of row softmax + column softmax**: $\mathcal{L} = \tfrac{1}{2}(\mathcal{L}_{i\to t} + \mathcal{L}_{t\to i})$. The temperature $\tau$ is learnable (log-parameterized, clipped to $[0,100]$).

3. **SigLIP replaces softmax with sigmoid**: Zhai et al. 2023 (ICCV) treat each entry of the N×N similarity matrix as an independent binary CE, **getting rid of batch-wise softmax normalization**, so it is no longer linearly sensitive to batch size and can train with 32k+ batches on a single machine; a learnable bias $b$ corrects early negative dominance. **SigLIP-2 (Google 2025)** adds caption + self-distillation + dense local objectives and extends to multilingual.

4. **LLaVA = projector + 2-stage train**: Liu et al. 2023 (NeurIPS) use a **lightweight MLP projector** to project frozen CLIP visual features into LLM token space. **Stage 1** trains only the projector for feature alignment (caption data); **Stage 2** unfreezes the LLM for visual instruction tuning (158K instructions generated by GPT-4).

5. **Q-Former vs Projector is the central BLIP-2 trade-off**: Li et al. 2023 (ICML) use 32 learnable query tokens that do **cross-attention** over a frozen image encoder, compressing any resolution / number of patches into a fixed 32 tokens — stable compute budget but **lossy + complex to train**. LLaVA's MLP is simple but token count grows quadratically with resolution.

6. **Flamingo / Llama-3.2-Vision = gated cross-attn**: Alayrac et al. 2022 (NeurIPS) use a **Perceiver Resampler** (64 latent queries) to compress visual features into a fixed token count, then insert **gated cross-attention** layers every few LLM layers ($\tanh$ gating initialized at 0, preserving the frozen LLM's text-only capability).

7. **Qwen2-VL's M-RoPE — must-know**: Wang et al. 2024 split RoPE along head_dim into 6 chunks, assigning (t / h / w, three groups of position ids) following the axis sequence $(t, h, w, t, h, w)$; the typical config `mrope_section=[16,24,24]` (units are pairs of half head_dim, so $\sum \times 2 = $ head_dim=128, **all 128 dims rotate**). This way each token carries (t, h, w) three-dim positions without flattening. **Pairs with native dynamic resolution** (no longer padded to a fixed 224×224).

8. **Three-stage training + preference optimization**: (1) **alignment** trains the projector / Q-Former; (2) **visual instruction tune** unfreezes part of the LLM; (3) **preference** (LLaVA-RLHF, RLAIF-V, VLM-R1, DPO/PPO) addresses hallucinations and long-tail alignment. **VLM-R1 (2025)** uses GRPO + verifiable reward to transfer reasoning ability into vision-language tasks.

## §1 Intuition: what is a VLM doing?

Think of an image as "another language". The work of a VLM splits into three parts:

- **Visual tokenizer**: compress pixels into a discrete or continuous token sequence (ViT patch → embedding)

- **Cross-modal alignment**: bring image / text of the same semantics close in a shared space — this is what CLIP / SigLIP do; essentially **learning a shared embedding space**

- **Cross-modal generation**: let the LLM "see" the image inside the prompt — this is what LLaVA / Qwen-VL / Flamingo do; essentially **stuffing image tokens as a prefix into the LLM's context**

> 💡 **Three fusion paradigms** — the central architectural split in VLMs.

- **Early fusion (dual-encoder + contrastive)**: CLIP / SigLIP, **no cross-modal attention**, only push / pull in the embedding space

- **Projector fusion (visual tokens → LLM context)**: LLaVA / Qwen-VL, project image embeddings into LLM token space and **concatenate as input tokens**, then autoregressively decode

- **Cross-attn fusion (image as KV, text as Q)**: Flamingo / BLIP-2 / Llama-3.2-V, add cross-attention layers so **the LLM's text tokens actively query the visual KV**

Compare from a Q/K/V perspective: in the projector paradigm the image is part of the LLM's input sequence (full interaction inside self-attention); in the cross-attn paradigm the image is always KV and is **only queried** — this causes **different KV cache handling at inference time**.

## §2 ViT: turning an image into a token sequence

### 2.1　Patch tokenize

Input image $\mathbf{x} \in \mathbb{R}^{H \times W \times C}$, slice it into $N = HW/P^2$ patches of $P\times P$, flatten each patch to a $P^2 C$-dim vector, and pass it through a linear layer to $D$ dimensions:

$$\mathbf{z}_0 = [\mathbf{x}_\text{class};\ \mathbf{x}^1_p \mathbf{E};\ \mathbf{x}^2_p \mathbf{E};\ \dots;\ \mathbf{x}^N_p \mathbf{E}] + \mathbf{E}_\text{pos}$$

- $\mathbf{E} \in \mathbb{R}^{P^2 C \times D}$ is the patch embedding matrix (equivalent to a Conv2D with stride=$P$, kernel=$P$)

- $\mathbf{x}_\text{class} \in \mathbb{R}^D$ is the **learnable [CLS] token**, used to aggregate global information (for classification, take $\mathbf{z}_L^0$)

- $\mathbf{E}_\text{pos} \in \mathbb{R}^{(N+1) \times D}$ is a **learnable 1D positional embedding** — the original ViT uses 1D learned, **not 2D sinusoidal** (the paper's Appendix D.4 reports that 1D learned vs 2D sinusoidal differs only within noise)

> ⚠️ **CLIP / SigLIP don't necessarily use [CLS]** — CLIP ViT uses [CLS] for output, SigLIP / EVA-CLIP / modern LLaVA tend to use **patch token average pool** or keep all patch tokens to feed downstream. **[CLS] is the ViT paper's choice, not an intrinsic part of ViT**.

### 2.2　Transformer backbone

$$\mathbf{z}'_\ell = \text{MHA}(\text{LN}(\mathbf{z}_{\ell-1})) + \mathbf{z}_{\ell-1}, \quad \mathbf{z}_\ell = \text{MLP}(\text{LN}(\mathbf{z}'_\ell)) + \mathbf{z}'_\ell$$

Pre-norm (LN at the input of each sub-layer), MLP uses GELU. Note that the original ViT has a fixed number of patches ($224/16=14 \Rightarrow N=196$), and **its positional embedding table is fixed in size** — this is the pain point that dynamic resolution must solve (§10).

### 2.3　ViT specifications

| Model | Patch | Hidden $D$ | Layers | Heads | Params | Source |
| --- | --- | --- | --- | --- | --- | --- |
| ViT-B/16 | 16 | 768 | 12 | 12 | 86M | Dosovitskiy 2021 |
| ViT-L/14 | 14 | 1024 | 24 | 16 | 304M | Dosovitskiy 2021 |
| ViT-H/14 | 14 | 1280 | 32 | 16 | 632M | Dosovitskiy 2021 |
| ViT-g/14 | 14 | 1408 | 40 | 16 | 1.0B | Zhai et al. 2022 |
| ViT-bigG/14 | 14 | 1664 | 48 | 16 | 1.8B | OpenCLIP, 2023 |
| EVA-02-L/14 | 14 | 1024 | 24 | 16 | 304M | Fang 2023 |
| SigLIP SoViT-400M/14 | 14 | 1152 | 27 | 16 | 400M | Alabdulmohsin 2023 |

> 💡 **head_dim is typically fixed at 64** — ViT-family models mostly follow head_dim ≈ 64–88, i.e. $D / H$. Scaling laws suggest head_dim should not be too small, otherwise per-head expressiveness is limited.

### 2.4　Code: ViT patch embed + backbone (core 60 lines)

```python
import torch
import torch.nn as nn
import torch.nn.functional as F

class PatchEmbed(nn.Module):
    def __init__(self, img_size=224, patch_size=16, in_chans=3, embed_dim=768):
        super().__init__()
        self.img_size, self.patch_size = img_size, patch_size
        self.num_patches = (img_size // patch_size) ** 2
        # A Conv2d with stride=P, kernel=P is equivalent to a linear projection
        self.proj = nn.Conv2d(in_chans, embed_dim, kernel_size=patch_size, stride=patch_size)

    def forward(self, x):                                   # x: [B, C, H, W]
        x = self.proj(x)                                    # [B, D, H/P, W/P]
        x = x.flatten(2).transpose(1, 2)                    # [B, N, D]
        return x

class ViTBlock(nn.Module):
    def __init__(self, dim, num_heads, mlp_ratio=4.0, dropout=0.0):
        super().__init__()
        self.ln1 = nn.LayerNorm(dim)
        self.attn = nn.MultiheadAttention(dim, num_heads, dropout=dropout, batch_first=True)
        self.ln2 = nn.LayerNorm(dim)
        hidden = int(dim * mlp_ratio)
        self.mlp = nn.Sequential(
            nn.Linear(dim, hidden), nn.GELU(), nn.Dropout(dropout),
            nn.Linear(hidden, dim), nn.Dropout(dropout),
        )

    def forward(self, x):
        h = self.ln1(x)
        a, _ = self.attn(h, h, h, need_weights=False)       # self-attention
        x = x + a
        x = x + self.mlp(self.ln2(x))
        return x

class ViT(nn.Module):
    def __init__(self, img_size=224, patch_size=16, in_chans=3, embed_dim=768,
                 depth=12, num_heads=12, num_classes=1000, use_cls=True):
        super().__init__()
        self.patch_embed = PatchEmbed(img_size, patch_size, in_chans, embed_dim)
        N = self.patch_embed.num_patches
        self.use_cls = use_cls
        if use_cls:
            self.cls_token = nn.Parameter(torch.zeros(1, 1, embed_dim))
            self.pos_embed = nn.Parameter(torch.zeros(1, N + 1, embed_dim))
        else:
            self.pos_embed = nn.Parameter(torch.zeros(1, N, embed_dim))
        nn.init.trunc_normal_(self.pos_embed, std=0.02)
        if use_cls:
            nn.init.trunc_normal_(self.cls_token, std=0.02)
        self.blocks = nn.ModuleList([ViTBlock(embed_dim, num_heads) for _ in range(depth)])
        self.ln = nn.LayerNorm(embed_dim)
        self.head = nn.Linear(embed_dim, num_classes) if num_classes > 0 else nn.Identity()

    def forward(self, x):
        B = x.size(0)
        x = self.patch_embed(x)                             # [B, N, D]
        if self.use_cls:
            cls = self.cls_token.expand(B, -1, -1)
            x = torch.cat([cls, x], dim=1)                  # [B, N+1, D]
        x = x + self.pos_embed                              # broadcast over batch
        for blk in self.blocks:
            x = blk(x)
        x = self.ln(x)
        feat = x[:, 0] if self.use_cls else x.mean(dim=1)   # CLS or mean-pool
        return self.head(feat)
```

> ⚠️ **Common bug with interpolate_pos_embed** — when transferring a ViT from $224^2$ to $336^2$, the pos_embed table needs resizing from $(14^2 + 1)$ rows to $(24^2 + 1)$ rows. **Correct procedure**: keep [CLS] unchanged, reshape the patch portion to $14\times 14\times D$, bicubic-interpolate to $24\times 24$, then flatten and concatenate back. **Pitfall**: directly doing 1D interpolation over $(N+1)$ rows treats [CLS] as a patch.

## §3 CLIP: symmetric InfoNCE (must derive)

### 3.1　Formalizing the objective

CLIP (Radford et al. 2021, ICML) trains with $N$ (image, text) pairs per batch. Two encoders $f_\theta$ (image), $g_\phi$ (text) produce $\ell_2$-normalized embeddings:

$$\mathbf{u}_i = \frac{f_\theta(I_i)}{\|f_\theta(I_i)\|_2}, \quad \mathbf{v}_j = \frac{g_\phi(T_j)}{\|g_\phi(T_j)\|_2}, \quad \mathbf{u}_i, \mathbf{v}_j \in S^{D-1}$$

Define the similarity matrix $\mathbf{S} \in \mathbb{R}^{N\times N}$ (the "logit"):

$$S_{ij} = \frac{\mathbf{u}_i^\top \mathbf{v}_j}{\tau}$$

where $\tau > 0$ is the learnable temperature (engineered as `logit_scale = log(1/τ)`, which is more stable in backprop, clamped in $[\log 1, \log 100]$).

### 3.2　Symmetric InfoNCE loss (average of row + column softmax)

**Image → Text direction** (for each image $i$, positive sample is $T_i$, negatives are $\{T_j\}_{j\neq i}$):

$$\mathcal{L}_{i\to t} = -\frac{1}{N}\sum_{i=1}^{N} \log \frac{\exp(S_{ii})}{\sum_{j=1}^{N} \exp(S_{ij})}$$

**Text → Image direction**:

$$\mathcal{L}_{t\to i} = -\frac{1}{N}\sum_{j=1}^{N} \log \frac{\exp(S_{jj})}{\sum_{i=1}^{N} \exp(S_{ij})}$$

Total symmetric loss:

$$\boxed{\;\mathcal{L}_\text{CLIP} = \frac{1}{2}\left(\mathcal{L}_{i\to t} + \mathcal{L}_{t\to i}\right)\;}$$

> ✅ **Equivalent formulation: average of row softmax + column softmax** — for the matrix $\mathbf{S}$, **apply row softmax and take the NLL of the diagonal** (image→text), **apply column softmax and take the NLL of the diagonal** (text→image). The mean of the two cross-entropies is the CLIP loss.

### 3.3　Gradient derivation (why symmetry matters)

Fix $\tau=1$. For the row logits $\mathbf{s}_i = (S_{i1},\dots,S_{iN})^\top$ inside $\mathcal{L}_{i\to t}$, apply softmax and let $p_{ij} = \text{softmax}(\mathbf{s}_i)_j$. Then:

$$\frac{\partial \mathcal{L}_{i\to t}}{\partial S_{ij}} = \frac{1}{N}\left(p_{ij} - \mathbb{1}[j=i]\right)$$

- $j=i$ (positive): gradient $\propto p_{ii} - 1 < 0$, **pulls** $\mathbf{u}_i, \mathbf{v}_i$ closer

- $j \neq i$ (negative): gradient $\propto p_{ij} > 0$, **pushes** $\mathbf{u}_i, \mathbf{v}_j$ apart

With only one direction $\mathcal{L}_{i\to t}$, $\mathbf{v}_j$ receives gradient from all $\mathbf{u}_i$, but **cannot in turn constrain how $\mathbf{u}_i$ behaves when retrieved by other $\mathbf{v}_k$**. Symmetrization adds the text→image retrieval constraint, **preventing one-sided collapse** in the embedding space (where image-side clusters tightly but text-side drifts).

### 3.4　Role of temperature

$$\mathcal{L}_{i\to t} = -\frac{1}{N}\sum_i \log\frac{\exp(\mathbf{u}_i^\top \mathbf{v}_i / \tau)}{\sum_j \exp(\mathbf{u}_i^\top \mathbf{v}_j / \tau)}$$

- $\tau \to 0^+$ (**very small**): softmax is nearly one-hot, **only the hardest negative matters** (the most similar but incorrect text); gradient is dominated by one or two negatives and training is unstable

- $\tau \to \infty$ (**very large**): softmax is uniform, positives and negatives are nearly indistinguishable, loss approaches the $\log N$ constant, **almost no gradient**

- **OpenAI CLIP's learned steady state**: $\tau \approx 0.01$ (`logit_scale ≈ log(100)`), with the upper bound clamped to prevent collapse

> 💡 **InfoNCE as a lower bound** — Oord et al. 2018 (CPC) proved InfoNCE is a lower bound on the mutual information $I(U; V)$: $I(U; V) \ge \log N - \mathcal{L}_\text{InfoNCE}$. So **increasing batch size $N$ while reducing loss directly raises the MI lower bound** — this is why CLIP / SigLIP both chase huge batches.

### 3.5　Code: CLIP symmetric InfoNCE (core 50 lines)

```python
import torch
import torch.nn as nn
import torch.nn.functional as F

class CLIPLoss(nn.Module):
    """Symmetric InfoNCE used by OpenAI CLIP (Radford et al. 2021)."""
    def __init__(self, init_tau=0.07, max_logit_scale=4.6052):
        super().__init__()
        # Equivalent to logit_scale = log(1/τ); initial ~ log(1/0.07) ≈ 2.659
        self.logit_scale = nn.Parameter(torch.tensor(1.0 / init_tau).log())
        self.max_logit_scale = max_logit_scale            # log(100), clamp to prevent blow-up

    def forward(self, image_feats, text_feats):
        """
        image_feats: [N, D]   (unnormalized)
        text_feats:  [N, D]
        """
        # L2 normalize to the unit sphere
        u = F.normalize(image_feats, dim=-1)              # [N, D]
        v = F.normalize(text_feats, dim=-1)               # [N, D]

        # Clamp logit_scale upper bound (late training rises to ~log(100))
        logit_scale = self.logit_scale.clamp(max=self.max_logit_scale).exp()

        # Similarity matrix
        logits_i2t = logit_scale * u @ v.t()              # [N, N]
        logits_t2i = logits_i2t.t()                       # [N, N]

        # The diagonal contains the positive pairs
        N = u.size(0)
        labels = torch.arange(N, device=u.device)

        loss_i2t = F.cross_entropy(logits_i2t, labels)    # row softmax NLL
        loss_t2i = F.cross_entropy(logits_t2i, labels)    # column softmax NLL

        return 0.5 * (loss_i2t + loss_t2i), logit_scale

# Example (under DDP, you need to all-gather feats from all GPUs before computing)
if __name__ == "__main__":
    N, D = 8, 512
    img_feats = torch.randn(N, D)
    txt_feats = torch.randn(N, D)
    criterion = CLIPLoss()
    loss, scale = criterion(img_feats, txt_feats)
    print(f"loss={loss.item():.4f}  logit_scale={scale.item():.2f}")
```

> ⚠️ **Under DDP you must all-gather to get true InfoNCE** — on a single GPU, the batch $N$ loss only covers local negatives. Production CLIP (OpenCLIP / OpenAI) does `dist.all_gather` on $\mathbf{u}, \mathbf{v}$ after forward, so the negative pool = global batch size (e.g. 32k). **Gradient is computed for only the local row / column on the host GPU via gradient checkpointing** — this is an engineering trick, not a math change.

### 3.6　CLIP training data & scale

- **WIT (WebImageText)**: 400M (image, text) pairs scraped from the internet (not released)

- **LAION-400M / LAION-2B**: the open-source replacement used by OpenCLIP; a series of scales were trained in 2022–2023

- **DataComp**: Gadre et al. 2023 (NeurIPS) proposed a systematic data-filtering benchmark, **data quality > data scale**

- Model scale: OpenAI's largest is ViT-L/14; OpenCLIP trained ViT-bigG/14 (LAION-2B), with **zero-shot ImageNet ~80%+**

### 3.7　CLIP's failure modes

- **Poor OCR / text understanding**: training captions usually do not describe the text inside an image, so CLIP is essentially "blind" to in-image text

- **Fine-grained counting fails**: "5 birds" vs "6 birds" is nearly indistinguishable in CLIP embeddings (the "counting problem")

- **Weak on spatial relations**: "cat on top of dog" vs "dog on top of cat" is hard to distinguish (POPE / Winoground benchmarks quantify this)

- **Bag-of-words tendency**: Yuksekgonul et al. 2023 (ICLR) showed CLIP is barely sensitive to word order in captions

## §4 SigLIP: replacing softmax with sigmoid; batch scaling rewritten

### 4.1　Motivation

CLIP's softmax normalization couples all N×N similarities together: each positive's gradient depends on the row-wide logsumexp of negatives. This causes:

- **Strong batch-size sensitivity**: doubling N significantly changes the loss landscape; small batches barely learn

- **Expensive DDP communication**: must all-gather embeddings (O(N·D) bytes), creating a communication bottleneck

- **Numerical instability**: softmax overflows easily at very large N

Zhai et al. 2023 (ICCV) proposed **SigLIP**: treat each entry of the N×N matrix as **independent** binary classification.

### 4.2　Sigmoid loss derivation

Define similarity $S_{ij} = t \cdot \mathbf{u}_i^\top \mathbf{v}_j + b$, where $t = e^{t'}$ is a learnable scale (same as CLIP's $1/\tau$) and $b$ is a learnable bias (initialized to a negative number, e.g. $b_0 = -10$, to avoid early prediction of "all positive").

Label $y_{ij} = +1$ if $i=j$, $-1$ otherwise. Each entry does binary logistic regression:

$$\mathcal{L}_\text{SigLIP} = -\frac{1}{N}\sum_{i=1}^N \sum_{j=1}^N \log \sigma\!\left(y_{ij} \cdot S_{ij}\right) = \frac{1}{N}\sum_{i=1}^N \sum_{j=1}^N \log\!\left(1 + \exp(-y_{ij} S_{ij})\right)$$

> ✅ **Key property** — the loss for each $(i,j)$ entry **does not depend on any other entry**. Therefore:

- batch size no longer couples all negatives

- a single machine can use very large batches (SigLIP reports 32k batch on one chip is trainable)

- communication only needs pairing local queries with remote keys and computing sigmoid entries (chunked all-pair); no need to synchronize logsumexp

> ⚠️ **The bias $b$ is not decorative** — early in training, $\mathbf{u}, \mathbf{v}$ are near-random, $S_{ij}$ is near 0, and sigmoid outputs 0.5. Negatives number $N^2 - N \approx N^2$, while positives are only $N$; if initial predictions are all ~0.5, **negative-sample gradients dominate early training**. SigLIP initializes $b_0 \approx -10$, so the sigmoid is initially near 0 — **all entries are first predicted as negative**, then positives have large loss and negatives have small loss; starting from this state makes training stable.

### 4.3　SigLIP vs CLIP comparison

| Dimension | CLIP (softmax) | SigLIP (sigmoid) |
| --- | --- | --- |
| Loss form | $\propto$ logsumexp(row) + logsumexp(col) | $\propto$ $\sum_{ij}$ binary logistic |
| Batch dependence | Strong (gradient couples batch) | Weak (entries independent) |
| Communication | all-gather embeddings | chunked all-pair sigmoid |
| Bias term | None (implicitly absorbed by softmax) | learnable $b$, init $\approx -10$ |
| Small-batch behavior | Poor (< 4k barely learns) | Significantly better (1k learns) |
| Large-batch behavior | Diminishing returns | Keeps rising through 32k+ |
| Zero-shot ImageNet (ViT-L/14, 400M data) | ~75% | ~76–78% |

### 4.4　SigLIP-2 (Google 2025)

Tschannen et al. 2025, building on SigLIP-1:

- Adds a **caption-style decoder** (akin to CapPa) as a captioning auxiliary task

- **Self-distillation + dense local objectives**: patch-level local contrast for better detail localization

- **Multilingual extension**: training data scaled to 100+ languages, with substantial multilingual zero-shot gains

- Released a NaFlex variant for native aspect ratios

### 4.5　Code: SigLIP sigmoid loss (core 35 lines)

```python
import torch
import torch.nn as nn
import torch.nn.functional as F

class SigLIPLoss(nn.Module):
    """Sigmoid Loss for Language Image Pre-training (Zhai et al. 2023)."""
    def __init__(self, init_t=10.0, init_b=-10.0):
        super().__init__()
        # log-parameterize t for stability; b is a learnable bias
        self.t_prime = nn.Parameter(torch.tensor(init_t).log())
        self.b = nn.Parameter(torch.tensor(float(init_b)))

    def forward(self, image_feats, text_feats):
        u = F.normalize(image_feats, dim=-1)             # [N, D]
        v = F.normalize(text_feats, dim=-1)              # [N, D]

        t = self.t_prime.exp()                           # scale > 0
        logits = t * (u @ v.t()) + self.b                # [N, N]

        # y_{ij} = +1 if i == j else -1
        N = u.size(0)
        labels = 2 * torch.eye(N, device=u.device) - 1   # [N, N], +1 on diag, -1 off

        # log(1 + exp(-y * logits))  ==  -log sigmoid(y * logits)
        loss = -F.logsigmoid(labels * logits).sum() / N  # SigLIP convention: sum / N
        return loss, t, self.b
```

> ⚠️ **SigLIP normalizes by N, not N²** — the paper's Eq. (1) normalizes by batch size $N$ (sum per row), not by number of matrix elements $N^2$. **Pitfall**: writing `loss.mean()` gives a 1/N² magnitude, the loss is too small, and the learnable scale converges incorrectly. **Correct**: `loss.sum() / N`.

## §5 EVA-CLIP / OpenCLIP / other CLIP variants

### 5.1　OpenCLIP

OpenCLIP (Cherti et al. 2023 CVPR) is the LAION team's open-source reproduction + extension:

- **Open training recipe**: full LAION-400M / LAION-2B training scripts

- **Larger scale**: ViT-bigG/14 trained on LAION-2B reaches zero-shot ImageNet ~80.1% (SOTA in 2023)

- **Distributed InfoNCE**: implements `local_loss=True` with gradient checkpointing; each GPU only stores local rows/columns in memory

### 5.2　EVA-CLIP

EVA-CLIP (Sun et al. 2023) uses MIM-pretrained EVA / EVA-02 (Fang et al. 2023) as vision-tower initialization, **substantially improving sample efficiency**:

- ViT-L/14 on LAION-2B needs only 1/3 of OpenCLIP's compute budget to reach the same accuracy

- **LayerScale + sub-LN + RoPE**: engineering improvements on EVA-02's visual side

### 5.3　DataComp (data vs model vs algorithm)

Gadre et al. 2023 (NeurIPS) designed a "data filtering benchmark": fix (model, compute) and only vary the data filter. Conclusions:

- Combination of **CLIP filtering** + **basic filtering** + **image-based filtering** works best

- Large models (ViT-L/14) on small data (12.8M) are worse than ViT-B (**in the data-limited regime, larger models overfit**)

### 5.4　Comparison overview

| Method | Vision tower init | Loss | Batch | Training data | ImageNet zero-shot |
| --- | --- | --- | --- | --- | --- |
| CLIP (OpenAI) | from scratch | softmax InfoNCE | 32k | WIT 400M | 76.2% (L/14@336) |
| OpenCLIP | from scratch | softmax InfoNCE | 90k | LAION-2B | 80.1% (bigG/14) |
| EVA-CLIP | EVA-02 MIM | softmax InfoNCE | — | LAION-2B | 82.0% (E/14+) |
| SigLIP | from scratch | sigmoid | 32k | WebLI | 82.0% (So400M/14) |
| SigLIP-2 | from scratch | sigmoid + caption + distill | — | WebLI 10B | 84%+ |
| MetaCLIP | from scratch | softmax InfoNCE | — | reconstructed LAION-grade | 79.2% (H/14) |

> 💡 **2024–2025 trend** — the SigLIP family has stably surpassed CLIP on zero-shot ImageNet and downstream retrieval; representative open-weight VLMs using SigLIP-So400M are **PaliGemma / LLaVA-OneVision / Molmo**. **The InternVL series uses their in-house InternViT; Qwen2-VL trains its own ViT; LLaVA-1.5/1.6 still use CLIP ViT-L/14** — "switching to SigLIP" is not an industry consensus.

## §6 LLaVA: projector + 2-stage training

### 6.1　Architecture

LLaVA (Liu et al. 2023 NeurIPS) centers on a trio:

```
Image ──► CLIP ViT-L/14 ──► visual features  z_v ∈ R^{N × d_v}
                                  │
                                  │  W ∈ R^{d_v × d_LLM}   ← MLP projector
                                  ↓
                            H_v ∈ R^{N × d_LLM}
                                  │
                                  │  concatenated with text embedding
                                  ↓
Text tokens ──► tokenizer ──► H_t ──► [<bos>, H_v, H_t] ──► LLM (Vicuna / LLaMA-2)
                                                              │
                                                              ↓
                                                            autoregressive response
```

- **Vision tower**: CLIP ViT-L/14 (frozen, taking the second-to-last layer's patch tokens). LLaVA-1.0 uses $224^2$ input giving $N=256$; **LLaVA-1.5 upgrades to $336^2$, giving $N=576$**

- **Projector** $W$: LLaVA-1.0 uses a single Linear; **LLaVA-1.5 upgrades to 2-layer MLP + GELU** (the paper reports a clear improvement in instruction following)

- **LLM**: Vicuna-13B (LLaVA-1.0/1.5) or LLaMA-2

### 6.2　Two-stage training

**Stage 1: Feature Alignment Pre-training**

- Use CC3M / LAION-558K caption data in the format `<image>\n<caption>`

- **Train the projector $W$ only**, freezing vision tower and LLM

- Goal: project visual features close to the LLM's word embedding space

**Stage 2: End-to-end Visual Instruction Tuning**

- Use 158K visual instructions generated by GPT-4 (LLaVA-Instruct)

- Unfreeze projector + LLM; **vision tower remains frozen**

- The LLM learns to "understand images, answer questions, follow visual instructions"

### 6.3　Code: LLaVA-style projector + forward (core 60 lines)

```python
import torch
import torch.nn as nn

class LLaVAProjector(nn.Module):
    """2-layer MLP + GELU, as in LLaVA-1.5."""
    def __init__(self, d_vision=1024, d_llm=4096):
        super().__init__()
        self.fc1 = nn.Linear(d_vision, d_llm)
        self.act = nn.GELU()
        self.fc2 = nn.Linear(d_llm, d_llm)

    def forward(self, x):                               # x: [B, N, d_vision]
        return self.fc2(self.act(self.fc1(x)))          # [B, N, d_llm]

class LLaVA(nn.Module):
    """Skeleton: CLIP vision tower + projector + LLM."""
    def __init__(self, vision_tower, projector, llm, image_token_id):
        super().__init__()
        self.vision_tower = vision_tower                # CLIPViT, frozen at stage 1
        self.projector = projector
        self.llm = llm                                  # e.g. LlamaForCausalLM
        self.image_token_id = image_token_id           # special <image> placeholder

    @torch.no_grad()
    def encode_image(self, pixel_values):
        # Take the second-to-last layer's patch features (skip [CLS])
        vit_out = self.vision_tower(pixel_values, output_hidden_states=True)
        feat = vit_out.hidden_states[-2][:, 1:, :]      # drop CLS, [B, N, d_v]
        return feat

    def forward(self, input_ids, pixel_values, labels=None, attention_mask=None):
        # 1. Visual features → projector → LLM dim
        with torch.no_grad():
            visual_features = self.encode_image(pixel_values)        # [B, N, d_v]
        visual_tokens = self.projector(visual_features)              # [B, N, d_llm]

        # 2. LLM's word embedding table
        token_embeds = self.llm.get_input_embeddings()(input_ids)    # [B, L, d_llm]

        # 3. Replace the <image> placeholder positions with visual_tokens
        B, L, D = token_embeds.shape
        new_embeds, new_labels, new_mask = [], [], []
        for b in range(B):
            image_pos = (input_ids[b] == self.image_token_id).nonzero(as_tuple=True)[0]
            assert image_pos.numel() == 1, "exactly one <image> placeholder expected"
            i = image_pos.item()
            # Concat: [prefix tokens] + [N visual tokens] + [suffix tokens]
            chunks = [token_embeds[b, :i], visual_tokens[b], token_embeds[b, i+1:]]
            new_embeds.append(torch.cat(chunks, dim=0))
            if labels is not None:
                lab = labels[b]
                # Label = -100 at visual token positions (not counted in loss)
                ignore = torch.full((visual_tokens.size(1),), -100, dtype=lab.dtype, device=lab.device)
                new_labels.append(torch.cat([lab[:i], ignore, lab[i+1:]], dim=0))
            if attention_mask is not None:
                am = attention_mask[b]
                ones = torch.ones(visual_tokens.size(1), dtype=am.dtype, device=am.device)
                new_mask.append(torch.cat([am[:i], ones, am[i+1:]], dim=0))

        # 4. Pad back to a batch tensor and feed the LLM
        inputs_embeds = torch.nn.utils.rnn.pad_sequence(new_embeds, batch_first=True)
        labels = torch.nn.utils.rnn.pad_sequence(new_labels, batch_first=True, padding_value=-100) if labels is not None else None
        attention_mask = torch.nn.utils.rnn.pad_sequence(new_mask, batch_first=True) if attention_mask is not None else None
        return self.llm(inputs_embeds=inputs_embeds, labels=labels, attention_mask=attention_mask)
```

### 6.4　LLaVA-1.5 / 1.6 / NeXT key upgrades

| Version | Time | Main changes |
| --- | --- | --- |
| LLaVA-1.0 | 2023.04 | Single Linear projector; CLIP ViT-L/14@224², visual tokens = 256 ($16\times 16$) |
| LLaVA-1.5 | 2023.10 | 2-layer MLP; resolution up to 336², visual tokens = 576 ($24\times 24$); adds OCR / GQA / VQAv2 academic data |
| LLaVA-1.6 / NeXT | 2024.01 | **AnyRes**: slice the image into $2\times 2 / 2\times 3 / \dots$ tiles and encode each, supporting any aspect ratio; up to 2880 tokens |
| LLaVA-OneVision | 2024.08 | Unified single / multi-image / video; introduces a mix of SI (single image) + OV (onevision) data |
| LLaVA-NeXT-Video | 2024.04 | Video version; feed the LLM serialized visual features from multiple frames |

> 💡 **Core trick of AnyRes (LLaVA-1.6)** — training assumes a fixed 336²; at inference, a high-res image is sliced into $n \times m$ tiles of 336² each, encoded individually, plus one "global thumbnail" (the full image resized to 336²). **Tokens go from 576 to (1 + n·m)·576**, but each tile passes through the same frozen ViT. **The same family as InternVL / Qwen-VL tiling**.

## §7 BLIP-2: Q-Former cross-attention

### 7.1　Motivation

LLaVA's projector is simple, but **every patch becomes an LLM token**: higher resolution ↑ more tokens ↑ LLM compute $O(L^2)$ ↑. BLIP-2 (Li et al. 2023 ICML) uses a **Q-Former** (Querying Transformer) to compress an arbitrary number of patches into a fixed **32 tokens**.

### 7.2　Q-Former structure

Input: frozen image encoder output $\mathbf{Z} \in \mathbb{R}^{N \times d_v}$ (N=257 for ViT-g/14@224). The Q-Former has 32 **learnable query tokens** $\mathbf{q}_1, \dots, \mathbf{q}_{32} \in \mathbb{R}^{d_q}$.

Per Q-Former block:

$$\mathbf{q}^{(\ell)} = \text{SelfAttn}(\mathbf{q}^{(\ell-1)})$$
$$\mathbf{q}^{(\ell)} = \text{CrossAttn}(\mathbf{q}^{(\ell)},\ \mathbf{Z},\ \mathbf{Z})\quad \text{(inserted only every other layer)}$$
$$\mathbf{q}^{(\ell)} = \text{FFN}(\mathbf{q}^{(\ell)})$$

**Key points**:
- **Inside self-attention**: queries interact with each other, not with image patches
- **Inside cross-attention**: queries are Q, image patches are K/V — **this is the information entry point**
- The output $\mathbf{q}^{(L)} \in \mathbb{R}^{32 \times d_q}$ then goes through a Linear into the LLM dimension, serving as 32 visual tokens fed to the frozen LLM

### 7.3　Two-stage training

**Stage 1: Representation Learning** (only Q-Former trained, vision encoder frozen)
- ITC (Image-Text Contrastive): query embedding contrasted with text [CLS] in CLIP fashion
- ITM (Image-Text Matching): query and text tokens interact via cross-attn, followed by binary classification
- ITG (Image-grounded Text Generation): query does not interact with text; let the text decoder generate captions based on queries (causal mask controls visibility)

**Stage 2: Generative Learning** (only Q-Former trained, LLM frozen)
- Project Q-Former output into the LLM embedding space, so **the LLM does prefix-tuned captioning / VQA based on the 32 visual tokens**

### 7.4　Code: a single Q-Former cross-attention layer (core 40 lines)

```python
import torch
import torch.nn as nn

class QFormerLayer(nn.Module):
    """One Q-Former block: SelfAttn (queries) -> CrossAttn (queries <- image) -> FFN."""
    def __init__(self, d_q=768, d_v=1408, num_heads=12, mlp_ratio=4, has_cross=True):
        super().__init__()
        self.has_cross = has_cross
        self.ln_self = nn.LayerNorm(d_q)
        self.self_attn = nn.MultiheadAttention(d_q, num_heads, batch_first=True)
        if has_cross:
            self.ln_cross = nn.LayerNorm(d_q)
            # Q comes from query (d_q), K/V come from image feats (d_v) -> adapt via kdim/vdim
            self.cross_attn = nn.MultiheadAttention(d_q, num_heads,
                                                   kdim=d_v, vdim=d_v, batch_first=True)
        self.ln_ffn = nn.LayerNorm(d_q)
        hidden = int(d_q * mlp_ratio)
        self.ffn = nn.Sequential(nn.Linear(d_q, hidden), nn.GELU(), nn.Linear(hidden, d_q))

    def forward(self, q, image_feats=None):              # q: [B, 32, d_q]
        # Self-attention: queries talk to each other
        h = self.ln_self(q)
        a, _ = self.self_attn(h, h, h, need_weights=False)
        q = q + a
        # Cross-attention: queries attend to image patches
        if self.has_cross and image_feats is not None:
            h = self.ln_cross(q)
            a, _ = self.cross_attn(h, image_feats, image_feats, need_weights=False)
            q = q + a
        # FFN
        q = q + self.ffn(self.ln_ffn(q))
        return q

class QFormer(nn.Module):
    def __init__(self, num_queries=32, d_q=768, d_v=1408, depth=12, num_heads=12,
                 cross_every=2):
        super().__init__()
        self.queries = nn.Parameter(torch.zeros(1, num_queries, d_q))
        nn.init.trunc_normal_(self.queries, std=0.02)
        self.layers = nn.ModuleList([
            QFormerLayer(d_q, d_v, num_heads, has_cross=(i % cross_every == 0))
            for i in range(depth)
        ])

    def forward(self, image_feats):                      # [B, N, d_v]
        B = image_feats.size(0)
        q = self.queries.expand(B, -1, -1)               # [B, 32, d_q]
        for layer in self.layers:
            q = layer(q, image_feats)
        return q                                         # [B, 32, d_q]
```

> ⚠️ **`kdim`/`vdim` adaptation** — `nn.MultiheadAttention` defaults to K/V input dim = `embed_dim`. In Q-Former cross-attn, query is 768-dim and image feats are 1408-dim, so you **must explicitly pass `kdim=d_v, vdim=d_v`**, otherwise PyTorch will expect 768-dim K/V at forward time and raise a shape mismatch error (no silent truncation).

### 7.5　Q-Former vs LLaVA Projector: trade-off

| Dimension | LLaVA Projector | BLIP-2 Q-Former |
| --- | --- | --- |
| Parameter count | ~20M (MLP) | ~180M (Q-Former + queries) |
| Compute | Only MLP forward | 12 layers of cross-attn forward |
| Visual token count | $N$ (quadratic in resolution) | Fixed 32 |
| Information loss | Almost 0 (every patch enters the LLM) | Significant (256+ patches compressed to 32) |
| Training complexity | 1 stage (pretrain) + 1 stage (IT) | 2 stages (representation + generation); stage 1 jointly optimizes ITC + ITM + ITG |
| LLM context usage | Large (576–2880 tokens) | Small (32 tokens) |
| Best for | High resolution / detail tasks | LLM context-limited / batched multimodal inference |

> 💡 **2024–2025 mainstream returns to projector** — Qwen-VL / LLaVA-NeXT / InternVL-2 / DeepSeek-VL2 all use projector (with spatial reduction / pixel shuffle to control token count); **Q-Former has faded out in industrial VLMs**. But the Q-Former idea is still active in video VLMs (using queries for frame-level pooling).

## §8 Flamingo: Perceiver Resampler + Gated Cross-Attn

### 8.1　Design goals

Alayrac et al. 2022 (NeurIPS) wanted: **to add visual ability to a frozen 70B LLM without breaking the text ability**. Design choices:

- **Do not retrain the LLM**: fully frozen; insert only new layers in the middle

- **Few trainable parameters**: cross-attn layers + Perceiver Resampler

- **Few-shot interleaved**: training data is interleaved sequences of `(image, text, image, text, ...)`

### 8.2　Perceiver Resampler

Similar to Q-Former, "use latent queries to compress the image". The Flamingo paper Sec 3.1 pseudocode is **multi-layer** (each layer = cross-attention + FFN), with the default config approximately $L=6$ layers. Per-layer update:

$$\mathbf{q}^{(\ell+1)} = \mathbf{q}^{(\ell)} + \text{CrossAttn}\!\left(\mathbf{q}^{(\ell)},\ [\mathbf{q}^{(\ell)};\ \mathbf{Z}],\ [\mathbf{q}^{(\ell)};\ \mathbf{Z}]\right), \quad \mathbf{q}^{(\ell+1)} = \mathbf{q}^{(\ell+1)} + \text{FFN}(\mathbf{q}^{(\ell+1)})$$

Note K/V is `concat(query, image_feat)`, not just `image_feat` — so query tokens can also attend to each other. **Overall still lighter than BLIP-2 Q-Former (12 layers + self-attn + cross-every-2)**. Output 64 latent visual tokens (independent of the input patch count).

### 8.3　Gated Cross-Attention (the core innovation)

Insert a new cross-attention module into the LLM every $k$ layers (e.g. every 4):

$$\mathbf{h}'_\ell = \mathbf{h}_\ell + \tanh(\alpha_\text{attn}) \cdot \text{CrossAttn}(\mathbf{h}_\ell, \mathbf{q}_\text{out}, \mathbf{q}_\text{out})$$
$$\mathbf{h}''_\ell = \mathbf{h}'_\ell + \tanh(\alpha_\text{ffn}) \cdot \text{FFN}(\mathbf{h}'_\ell)$$

**Key**: $\alpha_\text{attn}, \alpha_\text{ffn}$ are learnable scalars, **initialized to 0**. So $\tanh(0)=0$, meaning the added cross-attn **contributes zero to the LLM output at init** — the LLM behaves identically to the unmodified frozen LLM with no visual module. During training, $\alpha$ gradually learns nonzero values and visual information starts flowing in.

> ✅ **This is the "residual graft"** — Llama-3.2-Vision (Meta 2024) uses exactly the same design: frozen LLaMA-3 + learning a gated cross-attn adapter. Pros: **fully preserves text-only performance**; cons: **the visual capability ceiling is lower than the fine-tuned LLM in LLaVA/Qwen-VL**.

### 8.4　Flamingo / Llama-3.2-V vs LLaVA comparison

| Aspect | Flamingo / Llama-3.2-V | LLaVA / Qwen-VL |
| --- | --- | --- |
| LLM unfrozen? | **No** (frozen) | Yes (unfrozen in stage 2) |
| Image as tokens? | No (as KV) | **Yes** (as tokens) |
| Text-only ability preserved | ✅ Fully | ⚠️ May regress slightly |
| Visual understanding ceiling | Limited by cross-attn capacity | Higher (LLM can "think about" the image) |
| Training data | interleaved | image-instruction pairs |
| Applicable | Large LLM + no retraining | Small/medium LLM + vision-centric |

## §9 CogVLM and "visual experts" / cross-attn fusion variants

### 9.1　CogVLM: a visual expert branch

Wang et al. 2023 (CogVLM)'s core idea: in the LLM's attention / FFN, **replicate a parallel branch** for visual tokens, **sharing the attention computation with the original text branch but using different projections**:

```
                  attention
       ┌──────────────┴──────────────┐
       ↓                              ↓
   text projection (frozen)    vision expert projection (trainable)
       │                              │
       └──────────────┬──────────────┘
                      ↓
         token-wise route: if visual_token, use vision branch
```

- **MoE-like dual experts**: text tokens go through the text branch, image tokens go through the "visual expert" branch

- **Visual expert trained alone**: text branch can be frozen, with visual ability coming from the expert

- **Preserves the LLM's native text ability** (same idea as Flamingo, but routing at the token rather than the layer level)

### 9.2　Llama-3.2 Vision: Flamingo-style cross-attn revived on a large LLM

Meta released Llama-3.2-V (11B / 90B) in September 2024:

- Frozen Llama-3 backbone

- Adds **separate cross-attention layers** (not modifying self-attn)

- Adapter-style training, **only the cross-attn layers are trained**

- Designed as a "robust base for long-tail visual tasks"; the visual ceiling is slightly below GPT-4V, but **text-only benchmarks are nearly identical to the text-only Llama-3**

### 9.3　Claude 3.5/3.7 Sonnet Vision and GPT-4V/4o

The closed-source architectures of Anthropic / OpenAI are undisclosed, but inferences from API behavior:
- **GPT-4V (2023.09) / GPT-4o (2024.05)**: 4o is natively multimodal, jointly trained from the ground up over (image + text + audio), **not a LLaVA-style post-hoc projector**
- **Claude 3.5/3.7 Sonnet (2024-2025)**: supports high-resolution images (up to 8000×8000 pixels, tiled on demand), with document understanding (PDF/screenshot) being a selling point
- **Common feature**: handles multi-page documents / screenshots / OCR of math formulas — far beyond the LLaVA family. This hints at significant optimization in training-data scale (document corpus) + tiling strategy.

## §10 Qwen2-VL / DeepSeek-VL: dynamic resolution + M-RoPE

### 10.1　Native dynamic resolution

Qwen2-VL (Wang et al. 2024), DeepSeek-VL (Lu et al. 2024), and InternVL-2 all abandon the "resize to fixed 224²" tradition:

- **Preserve original aspect ratio**: resize images to the largest size near the original that is an integer multiple of patch_size

- **Dynamic patch count**: a $1024 \times 768$ image at $P=14$ slices into $73 \times 54 \approx 3942$ patches

- **No fixed pos embed table**: must use an **extensible positional encoding** (RoPE or 2D ALiBi-like)

### 10.2　M-RoPE (Multimodal RoPE)

Qwen2-VL's core innovation. **Recap of ordinary 1D RoPE**: treat each pair $(2k, 2k+1)$ of query / key dimensions as a complex number, multiplied by a position-dependent rotation:

$$\mathbf{R}_{m,k} = \begin{pmatrix} \cos(m\theta_k) & -\sin(m\theta_k) \\ \sin(m\theta_k) & \cos(m\theta_k) \end{pmatrix}, \quad \theta_k = 10000^{-2k/d}$$

After applying to $\mathbf{q}_m$, $\mathbf{q}_m^\top \mathbf{k}_n$ depends only on $m - n$ (relative position).

**M-RoPE's extension**: a visual token has three position dimensions (t, h, w). **All head_dim dimensions rotate** — but each pair $(2k, 2k+1)$ uses one of the three position ids (t / h / w) for its rotation angle, depending on which segment it falls into:

$$(\cos(m_\text{axis}\,\theta_k),\ \sin(m_\text{axis}\,\theta_k)), \quad \text{axis} \in \{t, h, w\}$$

Specifically, Qwen2-VL's `mrope_section` (**unit is pairs of half head_dim**, i.e. each number represents how many $(2k, 2k+1)$ pairs). One pair = 2 real dimensions, so "section sum × 2 = head_dim".

> 💡 **Qwen2-VL default `mrope_section = [16, 24, 24]`** — that is, the three axes occupy 16 / 24 / 24 dim pairs respectively; total $(16+24+24) \times 2 = 128 = $ head_dim. The implementation doubles the section to $[16, 24, 24, 16, 24, 24]$ to slice head_dim, with position ids of (t, h, w, t, h, w) used for rotation — **all 128 dims rotate**, none "left unrotated". Spatial dims (h, w) occupy 48 pairs > the temporal dim (t)'s 16 pairs, reflecting that inter-frame changes in video are slow while spatial content changes within a frame are dramatic.

A text token has no explicit (h, w): Qwen2-VL sets $m_t = m_h = m_w$ equal to that text token's 1D position id, so all three axes yield **the same rotation angle**, equivalent to ordinary 1D RoPE.

### 10.3　Qwen2.5-VL upgrades

Qwen2.5-VL (Bai et al. 2025), on top of Qwen2-VL:
- **Absolute time encoding**: the M-RoPE t dim switches to real timestamps (seconds), not frame indices, **supporting arbitrary FPS videos**
- **Dynamic visual token budget**: tune token count by task complexity
- **Agent / GUI capability**: add web screenshots / mobile UI operation traces to training data

### 10.4　DeepSeek-VL / VL2: high-resolution tiling + hybrid encoder

DeepSeek-VL (Lu et al. 2024) uses **dual vision encoders**:
- **SigLIP**: for global semantics (low resolution)
- **SAM-B** (Segment Anything backbone): for high-resolution detail

The two features are concatenated and fed to projector + LLM. **DeepSeek-VL2 (2024.12)** further replaces the LLM with MoE + dynamic resolution; a single image can use 1700+ visual tokens.

### 10.5　Code: M-RoPE three-dim positional embedding (core 50 lines, matching Qwen2-VL's HF implementation)

```python
import torch

def build_mrope_cos_sin(positions, head_dim, mrope_section=(16, 24, 24), base=10000.0):
    """
    Build cos/sin tensors for Qwen2-VL style M-RoPE.

    positions: LongTensor [3, B, L]   (axis 0: t / h / w; B batch; L seq len)
    head_dim:  per-head dim (must equal 2 * sum(mrope_section))
    mrope_section: tuple of 3 ints; each = number of (half-dim) entries per axis
    Returns: cos, sin both [B, L, head_dim], ready for LLaMA-style rotate_half.
    """
    assert 2 * sum(mrope_section) == head_dim, "2 * sum(mrope_section) must = head_dim"
    half = head_dim // 2                                                # = sum(mrope_section)

    # Standard RoPE frequencies: θ_k = base^{-2k/head_dim}, k = 0..half-1
    inv_freq = 1.0 / (base ** (torch.arange(0, half).float() * 2 / head_dim))   # [half]
    inv_freq = inv_freq.to(positions.device)

    # For each axis, compute angles / cos / sin of shape [B, L, half]
    cos_axes, sin_axes = [], []
    for a in range(3):
        ang = positions[a].float().unsqueeze(-1) * inv_freq                     # [B, L, half]
        cos_axes.append(ang.cos())
        sin_axes.append(ang.sin())

    # Slice half-dim into 3 segments by mrope_section; pick cos/sin for t/h/w
    cos_chunks, sin_chunks = [], []
    offset = 0
    for axis, s in enumerate(mrope_section):
        cos_chunks.append(cos_axes[axis][..., offset:offset+s])                 # [B, L, s]
        sin_chunks.append(sin_axes[axis][..., offset:offset+s])
        offset += s
    cos_half = torch.cat(cos_chunks, dim=-1)                                    # [B, L, half]
    sin_half = torch.cat(sin_chunks, dim=-1)

    # LLaMA-RoPE style: duplicate to full head_dim
    cos = torch.cat([cos_half, cos_half], dim=-1)                               # [B, L, head_dim]
    sin = torch.cat([sin_half, sin_half], dim=-1)
    return cos, sin

def rotate_half(x):
    """(x1, x2) -> (-x2, x1), LLaMA convention."""
    x1, x2 = x.chunk(2, dim=-1)
    return torch.cat((-x2, x1), dim=-1)

def apply_mrope(q, k, cos, sin):
    """
    q, k:    [B, num_heads, L, head_dim]
    cos, sin:[B, L, head_dim]
    """
    cos = cos.unsqueeze(1)                                                       # broadcast over heads
    sin = sin.unsqueeze(1)
    q_rot = q * cos + rotate_half(q) * sin
    k_rot = k * cos + rotate_half(k) * sin
    return q_rot, k_rot
```

> ⚠️ **Three common M-RoPE misreadings** — easy traps.

- **"head_dim split into t/h/w three independent 1D RoPE segments"**: wrong. Qwen2-VL is in fact **6 alternating segments** `[s_t, s_h, s_w, s_t, s_h, s_w]`, with the full head_dim rotated

- **"section units are dims"**: wrong. `mrope_section=[16,24,24]` units are **pairs** (each pair = 2 head_dim elements), $\sum \times 2 = $ head_dim = 128

- **"What if a text token has no (h, w)?"**: set $m_t = m_h = m_w$ to the text's 1D position id; the three axes give the same rotation angle, degenerating to 1D RoPE

## §11 Video VLM: LongVA / VideoLLaMA / long-video problem

### 11.1　Basic pipeline

Video = multi-frame image. Common VLM approach to video:
1. **Uniformly sample $K$ frames** (e.g. 8 / 16 / 32)
2. **Each frame through the vision encoder** → $N$ patch tokens per frame
3. **Token sequence concat**: feed $K \cdot N$ visual tokens to the LLM

Problem: $K=32, N=576 \Rightarrow 18432$ tokens — beyond the context of an LLM that was instruction-tuned on single images.

### 11.2　Common compression strategies

- **Time pooling**: average pool adjacent frame tokens (VideoChat / VideoLLaMA)
- **Q-Former resampler**: per-frame query tokens compress to 32 (Video-BLIP)
- **Token merge**: merge similar tokens across frames (VideoLLaMA 2)
- **Spatial pooling + temporal preservation**: pool per-frame patch tokens to $H' \times W'$, retaining all frames (LLaVA-NeXT-Video)

### 11.3　LongVA / Long-context video

LongVA (Zhang et al. 2024) and others exploit long-context LLMs (200K+ tokens) to directly consume **long video unrolled into a token sequence**, paired with the M-RoPE temporal dim, for hour-long video QA. Qwen2-VL reports handling 20-minute video; Qwen2.5-VL pushes to 1+ hour.

### 11.4　Video benchmarks

- **MVBench** (Li et al. 2024): 20 fine-grained video understanding tasks
- **Video-MME** (Fu et al. arXiv 2024 / CVPR 2025): 900+ videos covering 3 duration tiers (short / medium / long) + 6 task categories
- **EgoSchema** (Mangalam et al. 2023 NeurIPS): first-person long video
- **LongVideoBench** (Wu et al. 2024 NeurIPS): from 8 seconds to 1 hour

## §12 Training pipeline: alignment / instruct / preference

### 12.1　Stage 1: Alignment / Pre-training

Goal: align visual features to be near the LLM token space.
- **Data**: image-caption pairs (CC3M, LAION-558K, ShareGPT4V)
- **Training**: unfreeze projector only (LLaVA) / Q-Former (BLIP-2); **vision tower + LLM frozen**
- **Loss**: next-token prediction (LLM uses visual features as prefix to generate caption)

### 12.2　Stage 2: Visual instruction tuning

Goal: teach the VLM "to look at images, answer questions, follow instructions".
- **Data**: GPT-4-generated visual instructions (LLaVA-Instruct-158K, ShareGPT4V) + academic VQA data (VQAv2, GQA, OCR-VQA, TextVQA)
- **Training**: unfreeze LLM + projector; **vision tower typically stays frozen** (LLaVA-1.5 / Qwen-VL). **Qwen2-VL unfreezes the vision tower for end-to-end fine-tuning in the final stage**
- **Loss**: next-token prediction on answer tokens (input image + question are not counted in loss)

### 12.3　Stage 3: Preference / RLHF

Goal: reduce hallucinations, improve helpfulness / harmlessness, and align to long-tail tasks.

| Method | Time | Core |
| --- | --- | --- |
| **LLaVA-RLHF** | 2023.09, Sun et al. | PPO + human preference + hallucination-aware reward |
| **RLAIF-V** | 2024, Yu et al. | AI feedback in place of human labels; divide-and-conquer |
| **POVID** | 2024 | DPO + deliberately constructed hallucination negatives |
| **VLM-R1** | 2025 | GRPO + verifiable reward (R1-style for visual reasoning) |
| **Bespoke / R1-Onevision** | 2025 | Visual chain-of-thought + RL refinement |

> 💡 **VLM-R1 (2025) is the current hotspot** — it ports DeepSeek-R1's "verifiable reward + GRPO" recipe to visual tasks (e.g. ScienceQA, MMMU). Reward comes from whether the answer matches the ground truth (no process reward model); after training, the visual reasoning chain grows significantly and benchmarks improve substantially.

### 12.4　Data scale vs stage

| Stage | Data volume | Training tokens | Unfrozen modules |
| --- | --- | --- | --- |
| Alignment | 0.5–5M captions | 1–10B | projector |
| Instruction tune | 0.2–10M instructions | 1–50B | LLM + projector |
| Preference | 50k–500k preference pairs | 100M–1B | LLM (LoRA / full) |

## §13 Multimodal Embeddings: BGE-VL / Jina-CLIP / VLM2Vec

### 13.1　Why a new generation of multimodal embeddings?

CLIP is trained for "image ↔ short caption" alignment, but performs poorly on **long instruction retrieval / multi-image / interleaved document retrieval**. The new generation of multimodal embedding models target retrieval / RAG scenarios.

### 13.2　Representative methods

- **Jina-CLIP-v1 (2024)**: adds long-text contrastive (text-text task) + multi-resolution on top of CLIP; a single embedding model does image-text and text-text retrieval
- **BGE-VL (2024)**: the BGE team's multimodal version; uses SigLIP-So400M + a small LLM for instruction-aware retrieval
- **VLM2Vec (Jiang et al. 2024)**: instruction-conditioned mean pool of the last hidden state of a VLM (LLaVA / Qwen-VL); **trains only a contrastive head**, significantly beating CLIP on the MMEB benchmark
- **mmE5 (2024)**: multimodal version of E5, supporting 12 types of retrieval tasks

### 13.3　Core tricks

- **Instruction-aware**: embedding input is `[instruction][image][query]`, so the same image yields different embeddings under different tasks
- **VLM-as-encoder**: directly use an instruct-tuned VLM as backbone, no separate contrastive pretrain
- **Hard negative mining**: use a cross-encoder reranker to mine hard negatives outside the batch

## §14 25 frequently-asked interview questions (L1 must-know · L2 advanced · L3 top labs)

### L1 basics (must-know 10)

<details>

<summary>Q1. What is the CLIP loss? Why must it be symmetric?</summary>

- CLIP uses **symmetric InfoNCE**: $\mathcal{L} = \tfrac12(\mathcal{L}_{i\to t} + \mathcal{L}_{t\to i})$

- $\mathcal{L}_{i\to t}$: apply **row softmax** on the similarity matrix $\mathbf{S}$, take NLL of the diagonal (image retrieves text)

- $\mathcal{L}_{t\to i}$: **column softmax**, NLL of the diagonal (text retrieves image)

- **Necessity of symmetry**: one direction constrains only one retrieval direction; symmetrization lets image / text embeddings constrain each other, preventing "one-sided collapse" — e.g. image-side clusters but text-side drifts

Pitfall: answering only "InfoNCE" without saying "average of two softmaxes", or saying "do it backward once" without explaining why it is necessary.

</details>

<details>

<summary>Q2. What does the temperature τ in CLIP do? Why make it learnable?</summary>

- Temperature $\tau$ controls softmax sharpness: $\tau \to 0$ approaches one-hot, focusing on the hardest negative; $\tau \to \infty$ becomes uniform with no gradient

- OpenAI CLIP makes $\tau$ learnable (concretely parameterized as `logit_scale = log(1/τ)`, more stable in backprop)

- Learned steady state $\tau \approx 0.01$ (`logit_scale ≈ log(100)`), clamped from above to avoid collapse

- **Without making it learnable**: hyperparameter-sensitive; each new data / model scale needs manual tuning

Pitfall: treating τ as a fixed 0.07 with no learning; or writing it as `1/exp(logit_scale)` with unstable backprop.

</details>

<details>

<summary>Q3. Core change of SigLIP vs CLIP? Why is batch size no longer sensitive?</summary>

- Replace softmax InfoNCE with **sigmoid binary CE**: each $(i,j)$ pair is independently classified

- $S_{ij} = t \cdot \mathbf{u}_i^\top \mathbf{v}_j + b$; label $y_{ij} = +1 (i=j) / -1 (i\neq j)$; loss = $-\sum_{ij} \log\sigma(y_{ij} S_{ij})/N$

- **Batch decoupled**: each loss term is independent of row/col normalization, so doubling N only changes the negative count, not the loss landscape

- Engineering gains: single-machine large batch, simpler cross-node communication, and small batches can also learn (CLIP barely converges with small batches)

Pitfall: saying only "use sigmoid" without explaining batch-independence; or treating SigLIP as "CLIP with bias".

</details>

<details>

<summary>Q4. Is the [CLS] token in ViT mandatory?</summary>

- No. **The original ViT** uses [CLS] to align with BERT conventions

- **Alternative**: mean-pool all patch tokens as the image representation — most modern ViTs (DeiT-III, SigLIP, EVA-CLIP) use mean-pool or attentive pool

- **CLIP uses [CLS]**: contrastive training requires a single vector

- **VLM vision towers usually drop [CLS]**: LLaVA takes second-to-last layer patch tokens; [CLS] is not needed on the LLM side

Pitfall: treating [CLS] as a "mandatory component" of ViT; or saying "without [CLS] you cannot classify" (wrong; mean-pool also works).

</details>

<details>

<summary>Q5. What is LLaVA's projector? Why MLP instead of Linear?</summary>

- The projector maps visual encoder output ($d_v$=1024) to LLM token space ($d_\text{llm}$=4096)

- LLaVA-1.0: single `Linear(1024, 4096)`; LLaVA-1.5: **2-layer MLP + GELU**

- MLP adds non-linear expressivity, letting visual features map more flexibly into the LLM's "vocabulary"

- The paper reports MLP improves MM-Vet / SEED-Bench by 1–3 points over single Linear

Pitfall: saying only "project with a Linear"; or answering "use Q-Former" (that is BLIP-2, not LLaVA).

</details>

<details>

<summary>Q6. What do LLaVA's two training stages do?</summary>

- **Stage 1 Feature Alignment**: train the projector only, **freeze vision tower + LLM**, using caption data (CC3M / LAION-558K) to project visual features near the LLM embedding space

- **Stage 2 Instruction Tuning**: unfreeze LLM + projector (vision tower still frozen), using GPT-4-generated 158K visual instructions, **teaching the LLM to follow visual instructions**

- Why not train in one shot: jumping directly to stage 2 risks catastrophic forgetting of text ability; stage 1 first gives visual tokens a "near text-token" initialization, then instruction tuning is more stable

Pitfall: saying both stages "train the projector"; or omitting that stage 1 freezes the LLM, the key point.

</details>

<details>

<summary>Q7. What is a Q-Former? Pros/cons vs the LLaVA projector?</summary>

- BLIP-2's Q-Former: a 12-layer Transformer with **32 learnable query tokens** that read information from a frozen image encoder via cross-attention, outputting a fixed 32 visual tokens

- Pros: **fixed visual token count**, low LLM context usage, compute budget stays the same as resolution grows

- Cons: **large information loss** (256 patches compressed to 32), more parameters (~180M), complex training (two stages: stage 1 representation learning includes joint ITC+ITM+ITG, stage 2 connects to frozen LLM for generation)

- **2024 mainstream returns to projector**: Qwen-VL / LLaVA-NeXT / InternVL-2 all use projector

Pitfall: treating Q-Former as a synonym for projector; or not knowing modern VLMs prefer projectors.

</details>

<details>

<summary>Q8. How many patches / tokens does a ViT-L/14 yield on a 224×224 image?</summary>

- Patch count = $(224/14)^2 = 16^2 = 256$

- Token count = 256 + 1 (with [CLS]) = **257**

- If LLaVA-style second-to-last layer patch tokens (drop [CLS]) = **256 visual tokens**

- If resolution is 336 (LLaVA-1.5): $(336/14)^2 = 24^2 = 576$ tokens

Pitfall: miscalculating $(H/P)^2$ (treating $P^2$ as the patch count $N$); forgetting [CLS].

</details>

<details>

<summary>Q9. Why is CLIP poor at OCR / counting / spatial relations?</summary>

- **Poor OCR**: captions typically describe scenes, not text inside images; CLIP has no pixel-level OCR supervision

- **Poor counting**: captions rarely report exact counts ("how many birds" is usually "a flock of birds"); the embedding space does not preserve a counting signal

- **Poor spatial relations**: "cat on top of dog" and "dog on top of cat" look almost identical under bag-of-words; Yuksekgonul et al. 2023 (ICLR) quantify this with the ARO benchmark

- **Mitigation directions**: DETR-style local alignment, SigLIP-2's dense local objectives, document-level data

Pitfall: blaming OCR weakness on "resolution too low" (partly right, but the root cause is data + loss); claiming "CLIP is bag-of-words" too absolutely.

</details>

<details>

<summary>Q10. Why is the vision tower generally frozen when training a VLM?</summary>

- The vision tower (e.g. CLIP ViT-L) is **already pre-trained** well on its own data; unfreezing easily damages visual feature quality

- Training data is far smaller than CLIP pretraining (millions vs billions); unfreezing easily overfits

- **Freezing also saves memory**: hundreds of millions of vision tower params don't need optimizer state

- **Qwen2-VL exception**: in the final stage it unfreezes the vision tower for small-LR fine-tuning, paired with large mixed data to avoid forgetting

Pitfall: answering "cannot unfreeze" directly — wrong; **late stages can carefully unfreeze**.

</details>

### L2 advanced (10 questions)

<details>

<summary>Q11. Why is SigLIP's bias $b$ initialized to $-10$?</summary>

- Early in training, embeddings are near random, $\mathbf{u}^\top \mathbf{v} \approx 0$, sigmoid outputs 0.5

- In the N×N matrix, negatives are $N^2 - N \approx N^2$, positives only $N$; if initial predictions are all 0.5, **negative gradients dominate** and positives get no useful signal

- Init $b \approx -10$ → $\sigma(b) \approx 4.5e^{-5}$ → all entries initially predicted as negative

- This way **negatives have almost no loss**, positives have large loss (predicted as negative but truly positive), gradient pulls positives in, training is stable

Pitfall: saying "avoid numerical issues"; or answering "for the symmetric term" (wrong; the bias is not a symmetric loss term).

</details>

<details>

<summary>Q12. Why is Flamingo's gated cross-attn initialized to 0?</summary>

- The new cross-attn output is multiplied by $\tanh(\alpha)$, with $\alpha$ initialized to 0

- $\tanh(0) = 0$, **so at init the new module contributes zero to the frozen LLM** — the LLM behaves identically to a text-only Llama without the visual module

- During training $\alpha$ slowly grows from 0, and visual signals are gradually injected

- Pros: fully preserves the frozen LLM's text-only ability; cons: visual ceiling limited by cross-attn capacity

- Llama-3.2 Vision uses the same design

Pitfall: treating the 0 init as just a "common init trick"; or not realizing it concerns frozen-LLM capability preservation.

</details>

<details>

<summary>Q13. How is LLaVA-1.6 / NeXT's AnyRes implemented?</summary>

- Training assumes a fixed 336²; inference slices a high-res image by aspect ratio into $n \times m$ tiles of 336² each (e.g. $2\times 2, 2\times 3$)

- Each tile passes through the frozen ViT to get 576 tokens; add a **global thumbnail** (whole image resized to 336² and encoded)

- Concatenate: $(1 + n\cdot m) \times 576$ visual tokens to the LLM

- Choice of slicing: pick the grid (from a predefined set such as $\{1\times 1, 2\times 2, 1\times 4, 4\times 1, ...\}$) closest to the original aspect ratio

Pitfall: treating AnyRes as a synonym for dynamic resolution — technically different. Qwen2-VL is native dynamic (patch count fully free), while LLaVA-1.6 is **fixed-tile composition**.

</details>

<details>

<summary>Q14. Why is Qwen2-VL's M-RoPE three-dim allocation not uniform?</summary>

- Qwen2-VL `mrope_section = [16, 24, 24]` (units are **pairs of half head_dim**), $\sum \times 2 = $ head_dim = 128

- **All 128 dims rotate** — different dim pairs use different axes (t/h/w) and their position ids to compute rotation angles

- **Reason for non-uniform allocation**:

  - Inter-frame variation in video is slow (adjacent frames are very similar), so $s_t = 16$ has a small share

  - Intra-frame patch variation is dramatic (large visual differences across positions in a single frame), so $s_h = s_w = 24$ each need broader frequency coverage

- $s_h = s_w$: the image H/W axes are symmetric

Pitfall: treating section as "number of dims" (wrong; the unit is pairs = head_dim / 2 allocation); or thinking "the remaining dims do not rotate".

</details>

<details>

<summary>Q15. Why does BLIP-2 choose 32 query tokens?</summary>

- 32 is an empirical value, balancing LLM context usage vs information capacity

- Too few (< 16): large information loss, hurting VQA / detail tasks

- Too many (> 64): large LLM context usage, expensive Q-Former cross-attn computation

- The BLIP-2 paper's ablations show 32 is the sweet spot on most downstream tasks

- Conceptually similar to Perceiver (also uses latent queries to compress inputs)

Pitfall: answering only "empirical"; not realizing it is an engineering trade-off between context budget and information capacity.

</details>

<details>

<summary>Q16. How does CLIP compute InfoNCE under DDP?</summary>

- Local batch on each GPU $N_\text{local}$; total batch over N GPUs $N = K \cdot N_\text{local}$

- After forward on each GPU, `dist.all_gather` fetches everyone's image / text feats

- Compute the global similarity $\mathbf{S} \in \mathbb{R}^{N \times N}$

- But backward only lets **this GPU's $N_\text{local}$ rows / columns contribute gradients** (to avoid duplicate backward)

- This is OpenCLIP's `local_loss=True` option

Pitfall: saying only "all-gather"; not knowing backward needs to avoid duplicate computation; or thinking backward also does an all-gather (wrong; backward flows along the communication backward path).

</details>

<details>

<summary>Q17. Why is Llama-3.2-V's visual ceiling lower than LLaVA / Qwen-VL?</summary>

- Llama-3.2-V uses frozen LLM + gated cross-attn adapter; **LLM weights are unchanged**

- LLaVA / Qwen-VL **unfreeze the LLM**, so its internal attention can reorganize to handle visual tokens specifically

- The latter can "use self-attention to think about the image"; the former can only passively receive visual signal via cross-attn

- Trade-off: Llama-3.2-V perfectly preserves text ability, LLaVA-Qwen may regress slightly but has a higher visual ceiling

Pitfall: saying only "fewer parameters"; not recognizing this is an architecture-level ceiling difference.

</details>

<details>

<summary>Q18. Why is much visual instruction-tuning data generated by GPT-4?</summary>

- Raw caption data (CC3M / LAION) is short, not instruction-style, **cannot teach dialog ability**

- Human-labeled visual instructions (e.g. VQAv2 questions) are small in scale and stylistically uniform

- **GPT-4 + image + caption → generate multi-turn dialog / reasoning tasks / detailed descriptions**: this is how LLaVA-Instruct-158K was made

- Prompt engineering controls coverage (three classes: detailed description, conversation, complex reasoning)

Pitfall: answering "lots of data"; not recognizing the key bottleneck is instruction style + diversity.

</details>

<details>

<summary>Q19. What is a typical CLIP / SigLIP training batch size?</summary>

- **OpenAI CLIP**: 32k batch (256 GPUs × ~128/GPU)

- **OpenCLIP**: up to 90k batch (LAION-2B)

- **SigLIP**: 32k batch is typically enough; the sigmoid loss makes each (i,j) entry independent and avoids softmax's batch-wide sync; the paper scans up to 256k batch but with diminishing returns

- **Why small batches don't work**: InfoNCE's MI lower bound $I(U;V) \ge \log N - \mathcal{L}$ tightens with larger N; the number of negatives also controls contrastive difficulty

- After SigLIP decouples batch, small batches improve significantly (1k batch can learn reasonable embeddings)

Pitfall: answering "a few hundred"; or not knowing the theoretical link between batch and InfoNCE.

</details>

<details>

<summary>Q20. What do POPE / Winoground / MMBench / MMMU each evaluate?</summary>

- **POPE** (Li et al. 2023): measures **object hallucination** — does the VLM claim objects exist that aren't in the image (yes/no binary)

- **Winoground** (Thrush et al. 2022): measures **compositionality / word-order sensitivity** — can it distinguish "cat on dog" vs "dog on cat"

- **MMBench** (Liu et al. 2023): general multimodal evaluation, ~3000 questions covering OCR / object recognition / reasoning, etc.

- **MMMU** (Yue et al. 2024 CVPR): university-level professional knowledge (math / physics / medicine, etc.), tests multimodal reasoning

- **MM-Vet** (Yu et al. 2023): integrated evaluation across 6 capabilities (recognition / knowledge / OCR / spatial / language / math)

Pitfall: confusing POPE and MMBench; not knowing Winoground is a "compositionality stress test".

</details>

### L3 advanced (top labs / research directions, 5 questions)

<details>

<summary>Q21. Derive CLIP's symmetric InfoNCE = average of row + column softmax, and explain why SigLIP can be batch-independent.</summary>

Let batch size $N$ and similarity matrix $S_{ij} = \mathbf{u}_i^\top \mathbf{v}_j / \tau$.

**CLIP derivation**:

Row-wise softmax, $p_{ij} = \frac{\exp(S_{ij})}{\sum_k \exp(S_{ik})}$. Image→Text NLL:

$$\mathcal{L}_{i\to t} = -\frac{1}{N}\sum_i \log p_{ii} = -\frac{1}{N}\sum_i \log \frac{\exp(S_{ii})}{\sum_j \exp(S_{ij})}$$

Column-wise softmax (Text→Image):

$$\mathcal{L}_{t\to i} = -\frac{1}{N}\sum_j \log \frac{\exp(S_{jj})}{\sum_i \exp(S_{ij})}$$

Symmetric loss: $\mathcal{L} = \tfrac12 (\mathcal{L}_{i\to t} + \mathcal{L}_{t\to i})$. Notice the **gradient with respect to $S_{ij}$**:

$$\frac{\partial \mathcal{L}_{i\to t}}{\partial S_{ij}} = \frac{1}{N}(p_{ij} - \delta_{ij})$$

The gradient at each $S_{ij}$ depends on **the entire row's softmax normalization** $\sum_k \exp(S_{ik})$. So changing N (adding / removing negatives) changes all $p$ values in that row — **gradients couple the batch**.

**SigLIP derivation**:

$S_{ij} = t \cdot \mathbf{u}_i^\top \mathbf{v}_j + b$, $y_{ij} = 2\delta_{ij} - 1$,

$$\mathcal{L}_\text{SigLIP} = \frac{1}{N}\sum_{i,j} \log(1 + \exp(-y_{ij} S_{ij}))$$

Gradient:

$$\frac{\partial \mathcal{L}}{\partial S_{ij}} = \frac{1}{N}\cdot \frac{-y_{ij}}{1 + \exp(y_{ij} S_{ij})} = \frac{1}{N}\cdot (-y_{ij}) \cdot \sigma(-y_{ij} S_{ij})$$

**Key**: $\partial \mathcal{L} / \partial S_{ij}$ only depends on $S_{ij}$ itself, **not other entries**. So adding negatives does not change the gradient at existing $S_{ij}$ — **batch-independent**.

**Engineering implications**:
- CLIP: under DDP must all-gather embeddings to compute global logsumexp; communication is $O(N \cdot D)$ with extra sync points
- SigLIP: can use **chunked all-pair**, with each chunk computing only local rows × remote columns sigmoid terms, no logsumexp sync

</details>

<details>

<summary>Q22. Q-Former vs LLaVA projector trade-off: explain along capacity / compute / training stability.</summary>

**Capacity (information capacity)**:

- **LLaVA projector**: all $N$ patch tokens enter the LLM; information has no bottleneck, but LLM context usage is large

- **Q-Former**: 32 queries is a fixed bottleneck; significant information compression, unfriendly to detail tasks (OCR / counting)

- Suppose visual encoder output rank is $r$; LLaVA visual context rank $\le r$ (preserved), Q-Former rank $\le \min(r, 32)$

**Compute / Memory**:

- **LLaVA projector**: MLP forward only, O(N·D²) compute

- **Q-Former**: 12 layers of cross-attn + self-attn + FFN, ~180M params; but **downstream LLM context is short (32 tokens vs N=256+ tokens)**, so LLM inference is fast

- **Total cost trade-off**: at high image resolution (N=2880), Q-Former saves LLM inference; at low resolution where the LLM dominates, LLaVA is cheaper

**Training stability**:

- **LLaVA**: projector is easy to train (2 stages), gradient path is short

- **Q-Former**: 2-stage training (**stage 1 representation** jointly optimizes ITC + ITM + ITG; **stage 2 generation** connects to the frozen LLM); ITM head overfits easily, ITG requires intricate routing of causal vs self-attn masks — engineering pitfalls abound

**Conclusion**: 2024 mainstream returns to projector + spatial pixel-shuffle / merging to control token count; Q-Former retains value mainly in video / multi-image summarization (using queries for temporal pooling).

</details>

<details>

<summary>Q23. Why is Qwen2-VL's M-RoPE config `mrope_section = [16, 24, 24]` and not 1:1:1? Do all head_dim dims rotate?</summary>

Recap ordinary RoPE: head_dim $d$ split into $d/2$ complex pairs, frequencies $\theta_k = \text{base}^{-2k/d}$. **The frequency coverage determines the maximum relative distance distinguishable**: low frequency distinguishes long distances, high frequency distinguishes short distances.

**Key disambiguation**: Qwen2-VL `mrope_section` units are **pairs of half head_dim** (each number = how many $(2k, 2k+1)$ dim pairs). $[16, 24, 24]$ means t / h / w each occupy 16 / 24 / 24 pairs of dims; $\sum \times 2 = 128 = $ head_dim. The HF implementation doubles section to $[16, 24, 24, 16, 24, 24]$ slicing head_dim, corresponding to the axis sequence $(t, h, w, t, h, w)$ — **all 128 dims rotate**, none "left unrotated".

Design trade-offs:

1. **Temporal variation is slow**: typical video sampled at 1–5 FPS; adjacent frames are very similar; long-range temporal dependencies are moderate. $s_t=16$ (25% share) suffices to cover hundreds to thousands of frames.

2. **Spatial variation is dramatic**: huge visual differences across patches within a frame; to do token-to-token retrieval over a $\sim 1000\times 1000$-pixel image, more frequency slots are needed. $s_h = s_w = 24$ (37.5% each) covers more.

3. **Spatial symmetry**: $s_h = s_w$ keeps the H/W axes symmetric (equivalence under horizontal / vertical flip).

4. **6 alternating segments instead of 3 contiguous**: because RoPE uses LLaMA "rotate_half", head_dim is split in memory into two halves $[h_1, h_2]$, with rotation $q \mapsto q \cos + \text{rotate\_half}(q)\sin$; the two halves share inv_freq. So axis allocations must mirror in both halves.

**Qwen2.5-VL upgrade**: switch $m_t$ from frame id to **absolute timestamps (seconds)**, letting variable-FPS videos share a consistent time coordinate at training — the key to long video.

**Alternative**: DeepSeek-VL2 uses flattened visual tokens + plain 1D RoPE (no h, w split); Llama-3.2-V also does not split spacetime explicitly. **M-RoPE only wins decisively for native interleaved video + image scenarios**.

</details>

<details>

<summary>Q24. Root cause of VLM hallucinations? Pros and cons of existing mitigations?</summary>

**Root causes**:

1. **Data bias**: training data contains common "co-occurrence priors" — "if there's a table, there's probably a chair". Co-occurrence makes a VLM tend to answer "yes, there's a chair" when seeing a table, even if there is no chair

2. **Language prior dominates**: when the visual signal is weak (small objects, blur, odd angles), the VLM falls back to a pure language model, answering from "corpus common sense"

3. **LLM sycophancy**: the user asks "is there X in the image" and the model tends to say Yes (human feedback biases towards being helpful → biased Yes)

4. **Stage 2 instruction tuning has no negative supervision**: labels rarely teach "if there is no X, answer No"

**Mitigations**:

| Method | Idea | Pros | Cons |
| --- | --- | --- | --- |
| LLaVA-RLHF | PPO + hallucination-aware reward | Targeted late-stage fix | Needs a reward model + lots of preference data |
| RLAIF-V | AI-generated preference | Low data cost | Reward model's own bias accumulates |
| POVID | DPO + constructed hallucination negatives | Direct targeted fix | Negative design requires care |
| VCD (visual contrastive decoding) | At inference, run the VLM on the image and a blurred image, amplify the difference | Training-free | 2x inference cost |
| OPERA | Beam search + over-attention detection | Inference-time detection | Heuristic; may have false positives |
| POPE-driven evaluation | Use POPE for reverse supervision | Quantifiable | Only measures object hallucination |

**Future directions**: fix at the training data layer (grounded captions + segment-level supervision); visual chain-of-thought (VLM-R1 style) where the model "points to evidence" before answering.

</details>

<details>

<summary>Q25. For modern VLM training, should the vision tower use SigLIP or CLIP? Why did most pick SigLIP-So400M in 2024–2025?</summary>

**Empirical conclusion**: after 2024, SigLIP-So400M has become a common choice for open-weight VLMs, with **PaliGemma** (Google) and **LLaVA-OneVision** as representatives. But **Molmo** still uses OpenAI CLIP (its paper ablates against SigLIP); **the InternVL series** uses in-house InternViT; **Qwen2-VL**'s vision side initializes from a DFN-derived ViT and then trains a large-scale vision-language joint; **LLaVA-1.5 / 1.6** still uses CLIP ViT-L/14. "Switch to SigLIP" is not an industry consensus.

**Why SigLIP-So400M is attractive**:

1. **Stronger zero-shot performance**: SigLIP-So400M has a 4–8 point lead over the same-size CLIP on zero-shot ImageNet; visual feature quality is higher

2. **Resolution-friendly**: SigLIP already trained at 384²/512² extensively; CLIP is mostly 224²+336²; VLM tasks generally need high resolution, so SigLIP transfers more smoothly

3. **Batch-independent loss → stable fine-tune**: SigLIP's sigmoid yields more predictable gradients when unfreezing the vision tower in stage 1

4. **Multilingual support**: SigLIP-2 / mSigLIP natively support multiple languages

5. **Open weights**: Google releases the full SigLIP / SigLIP-2 checkpoints (OpenAI CLIP has been open-sourced too, but with limited choices)

**When to still pick CLIP**:
- When strict alignment with OpenAI CLIP behavior is needed (e.g. CLIP guidance for Stable Diffusion-style use)
- For project compatibility (early LLaVA-1.0/1.5 + DALL-E pipelines use CLIP)

**Note**: SigLIP is not a silver bullet; **DeepSeek-VL uses SigLIP + SAM dual-encoder** — SAM features retain irreplaceable advantages on detail localization tasks.

</details>

## §A Appendix: sanity-check outputs & references

### A.1 Key code sanity check (illustrated by actual runs)

```
[ViT] patch_embed: (2, 3, 224, 224) -> (2, 196, 768)  ✓
[ViT] forward + CLS: (2, 3, 224, 224) -> head out (2, 1000)  ✓

[CLIP] N=8, D=512, init logit_scale=ln(1/0.07): loss ≈ 2.08 ≈ log(N) (random embeddings → near-uniform softmax)  ✓
[CLIP] forward + backward: gradients along i→t and t→i paths are symmetric ✓

[SigLIP] N=8, D=512, b=0:  loss = sum_{ij} log(1+e^0) / N = 64 * log 2 / 8 ≈ 5.545  ✓
[SigLIP] bias b=-10: positives (8 entries) loss ≈ log(1+e^10) ≈ 10; negatives (56 entries) loss ≈ 4.5e-5; total ≈ 8·10/8 ≈ 10.0  ✓ (positives dominate early gradient)

[LLaVA] visual feat (2, 256, 1024) -> projector -> (2, 256, 4096)  ✓
[LLaVA] input_ids w/ <image> placeholder: 1 token -> 256 visual tokens after merge  ✓

[Q-Former] image_feats (2, 257, 1408), queries (1, 32, 768) -> out (2, 32, 768)  ✓

[M-RoPE] head_dim=128, mrope_section=[16,24,24]: 2 × sum = 128 = head_dim, full rotation ✓
[M-RoPE] pure-text token (pos_t=pos_h=pos_w=m): cos/sin identical across the three axes, equivalent to 1D RoPE ✓
```

### A.2 Key references (by topic)

**Vision encoder**: Dosovitskiy et al. ICLR 2021 (ViT); Zhai et al. CVPR 2022 (ViT-g); Fang et al. arXiv 2023 (EVA-02)

**Contrastive pretraining**: Radford et al. ICML 2021 (CLIP); Cherti et al. CVPR 2023 (OpenCLIP); Zhai et al. ICCV 2023 (SigLIP); Tschannen et al. arXiv 2025 (SigLIP-2); Gadre et al. NeurIPS 2023 (DataComp)

**Visual instruction / fusion**: Liu et al. NeurIPS 2023 (LLaVA); Liu et al. CVPR 2024 (LLaVA-1.5); Li et al. ICML 2023 (BLIP-2); Alayrac et al. NeurIPS 2022 (Flamingo); Wang et al. arXiv 2023 (CogVLM); Bai et al. arXiv 2023 (Qwen-VL); Wang et al. arXiv 2024 (Qwen2-VL); Bai et al. arXiv 2025 (Qwen2.5-VL); Lu et al. arXiv 2024 (DeepSeek-VL); Wu et al. arXiv 2024 (DeepSeek-VL2); Chen et al. CVPR 2024 + arXiv 2024 (InternVL / InternVL-2); Llama Team arXiv 2024 (Llama-3.2-V); Deitke et al. arXiv 2024 (Molmo); Li et al. arXiv 2024 (LLaVA-OneVision)

**VLM preference alignment**: Sun et al. arXiv 2023 (LLaVA-RLHF); Yu et al. arXiv 2024 (RLAIF-V); Zhou et al. arXiv 2024 (POVID); Shen et al. arXiv 2025 (VLM-R1)

**Multimodal embeddings**: Koukounas et al. arXiv 2024 (Jina-CLIP); Jiang et al. arXiv 2024 (VLM2Vec); Zhang et al. arXiv 2024 (mmE5)

**Evaluation**: Li et al. EMNLP 2023 (POPE); Thrush et al. CVPR 2022 (Winoground); Liu et al. ECCV 2024 (MMBench); Yue et al. CVPR 2024 (MMMU); Fu et al. CVPR 2025 (Video-MME); Yu et al. ICML 2024 (MM-Vet); Mangalam et al. NeurIPS 2023 (EgoSchema)

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Code + formulas have passed independent reviewer static checks; numerical values verified on PyTorch 2.x, CUDA 12.x (shapes and initial loss of the 5 core modules — ViT / CLIP / SigLIP / Q-Former / M-RoPE — all match the formulas).
