File size: 7,809 Bytes
d4bcd5c
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
"""
SPLIT: Salience-guided Partitioning towards Local coverage for Importance-aware
Token dropping.  Faithful, training-free reimplementation of Algorithm 1 from
SPLIT-VLM (ICML 2026, OpenReview Elm4TdaXi0).

Given the per-layer ViT hidden states of the vision patch tokens and the final
patch-token embeddings, SPLIT selects a subset of `budget` tokens by:
  1. temporal-shift importance   I(x) = mean_l ||h_l - h_{l-1}|| / ||h_l||   (Eq.5-6)
  2. adaptive region budget       B_k = B/K + B * I(X_k)/sum_j I(X_j)          (Eq.7)
  3. diversity-score selection     D(i) = lambda*std_j(S_ij) - mean_j(S_ij)     (Eq.8-10)
     select top-B_k tokens by D within each region.

All operations are batch-size-1 (one image) and vectorised in torch.
"""
from __future__ import annotations
import math
import torch


def temporal_shift_importance(hidden_states, layers=None):
    """
    hidden_states: list/tuple of length L+1, each [N, d]  (patch tokens only,
                   CLS already removed), h[0] = embeddings, h[l] = after layer l.
    layers: iterable of layer indices l>=1 to use (default: all).
    returns I: [N] importance per token (Eq. 6).
    """
    L = len(hidden_states) - 1
    if layers is None:
        layers = range(1, L + 1)
    layers = [l for l in layers if 1 <= l <= L]
    acc = None
    for l in layers:
        h = hidden_states[l]
        hprev = hidden_states[l - 1]
        num = torch.linalg.vector_norm(h - hprev, dim=-1)          # ||h_l - h_{l-1}||
        den = torch.linalg.vector_norm(h, dim=-1).clamp_min(1e-6)  # ||h_l||
        delta = num / den
        acc = delta if acc is None else acc + delta
    return acc / len(layers)


def region_ids_grid(num_tokens, grid_hw, region_grid):
    """
    Map each patch token to a region id for a square grid of patches.
    grid_hw = (H, W) patch grid (e.g. 24,24); region_grid = (rh, rw) e.g. (4,4)=16 regions.
    returns LongTensor [N] with region id in [0, rh*rw).
    """
    H, W = grid_hw
    rh, rw = region_grid
    assert H * W == num_tokens, f"{H}*{W} != {num_tokens}"
    idx = torch.arange(num_tokens)
    row = idx // W
    col = idx % W
    # region row/col via proportional binning (handles non-divisible grids)
    r_row = (row * rh // H).clamp(max=rh - 1)
    r_col = (col * rw // W).clamp(max=rw - 1)
    return (r_row * rw + r_col).long()


def allocate_region_budgets(importance, region_ids, K, budget):
    """
    Eq. 7 hybrid allocation, then integer rounding that sums exactly to `budget`
    and never exceeds region population.
    importance: [N]; region_ids: [N]; K regions; budget total tokens to keep.
    returns dict region_id -> int budget.
    """
    device = importance.device
    reg_imp = torch.zeros(K, device=device)
    reg_cnt = torch.zeros(K, device=device)
    reg_imp.scatter_add_(0, region_ids, importance)
    reg_cnt.scatter_add_(0, region_ids, torch.ones_like(importance))
    # region-level importance = mean token importance within region
    mean_imp = torch.where(reg_cnt > 0, reg_imp / reg_cnt.clamp_min(1), torch.zeros_like(reg_imp))
    total_imp = mean_imp.sum().clamp_min(1e-9)
    # B_k = B/K + B * I(X_k)/sum_j I(X_j)   (Eq. 7).  As written this sums to 2*B
    # (both terms individually sum to B), so we renormalise the hybrid allocation
    # to distribute exactly the total budget B (i.e. a 50/50 uniform+importance mix).
    b_float = budget / K + budget * (mean_imp / total_imp)
    # zero out empty regions
    b_float = torch.where(reg_cnt > 0, b_float, torch.zeros_like(b_float))
    b_float = b_float * (budget / b_float.sum().clamp_min(1e-9))
    # cap by population (redistribute happens via largest-remainder below)
    b_float = torch.minimum(b_float, reg_cnt)
    # round preserving the exact total via largest-remainder
    floor = torch.floor(b_float)
    rem = b_float - floor
    alloc = floor.clone()
    deficit = int(round(budget - float(alloc.sum().item())))
    if deficit > 0:
        # give +1 to regions with largest remainder that still have capacity
        cap = (reg_cnt - alloc)
        order = torch.argsort(rem * (cap > 0), descending=True)
        i = 0
        while deficit > 0 and i < len(order):
            k = order[i].item()
            if cap[k] > 0:
                alloc[k] += 1
                cap[k] -= 1
                deficit -= 1
            i += 1
            if i >= len(order) and deficit > 0:
                # loop again over any region with capacity
                cap = (reg_cnt - alloc)
                order = torch.argsort(cap, descending=True)
                i = 0
                if float(cap.max()) <= 0:
                    break
    elif deficit < 0:
        order = torch.argsort(rem)  # smallest remainder first -> remove
        i = 0
        while deficit < 0 and i < len(order):
            k = order[i].item()
            if alloc[k] > 0:
                alloc[k] -= 1
                deficit += 1
            i += 1
    return {k: int(alloc[k].item()) for k in range(K)}


def diversity_scores(token_embeds, lam=0.5, chunk=None):
    """
    Eq. 8-10.  token_embeds: [N, d].  D(i) = lam*sigma_i - mu_i, where S is the
    cosine self-similarity matrix.  Returns D: [N].
    """
    x = torch.nn.functional.normalize(token_embeds.float(), dim=-1)
    N = x.shape[0]
    # S = x x^T  (N x N); compute mu, sigma row-wise (optionally chunked for memory)
    if chunk is None or N <= chunk:
        S = x @ x.t()
        mu = S.mean(dim=1)
        sigma = S.std(dim=1, unbiased=False)
    else:
        mu = torch.empty(N, device=x.device)
        sigma = torch.empty(N, device=x.device)
        for s in range(0, N, chunk):
            e = min(s + chunk, N)
            Sc = x[s:e] @ x.t()
            mu[s:e] = Sc.mean(dim=1)
            sigma[s:e] = Sc.std(dim=1, unbiased=False)
    return lam * sigma - mu


def split_select(hidden_states, token_embeds, budget,
                 grid_hw=(24, 24), region_grid=(4, 4), layers=None, lam=0.5):
    """
    Full SPLIT selection. Returns sorted LongTensor of kept token indices (len=budget).
    hidden_states: per-layer ViT hidden states for the N patch tokens (CLS removed).
    token_embeds:  [N, d] final patch embeddings used for diversity.
    """
    N = token_embeds.shape[0]
    if budget >= N:
        return torch.arange(N, device=token_embeds.device)
    K = region_grid[0] * region_grid[1]
    device = token_embeds.device
    imp = temporal_shift_importance(hidden_states, layers).to(device)      # [N]
    rid = region_ids_grid(N, grid_hw, region_grid).to(device)             # [N]
    budgets = allocate_region_budgets(imp, rid, K, budget)
    D = diversity_scores(token_embeds, lam=lam)                            # [N]
    keep = []
    for k in range(K):
        bk = budgets[k]
        if bk <= 0:
            continue
        mask = (rid == k).nonzero(as_tuple=True)[0]
        if mask.numel() == 0:
            continue
        dk = D[mask]
        topk = torch.topk(dk, min(bk, mask.numel())).indices
        keep.append(mask[topk])
    keep = torch.cat(keep) if keep else torch.arange(min(budget, N), device=device)
    return torch.sort(keep).values


# ---- baselines for comparison (Claim 3 control) ----
def random_select(N, budget, generator=None, device="cpu"):
    if budget >= N:
        return torch.arange(N, device=device)
    perm = torch.randperm(N, generator=generator)[:budget]
    return torch.sort(perm).values.to(device)


def attention_select(cls_attn, budget):
    """FastV/HiRED-style: keep top-`budget` tokens by CLS->patch attention.
    cls_attn: [N] attention from CLS to each patch (already averaged over heads)."""
    N = cls_attn.shape[0]
    if budget >= N:
        return torch.arange(N, device=cls_attn.device)
    idx = torch.topk(cls_attn, budget).indices
    return torch.sort(idx).values