Understanding Transformer-based Vision Models

through Inversion

Jan Rathjens 1∗, Shirin Reyhanian 1∗, David Kappel 1,2†, Laurenz Wiskott 1†

1Institute for Neural Computation (INI), Faculty of Computer Science, Ruhr University Bochum, Germany

2Center for Cognitive Interaction Technology (CITEC), Faculty of Technology, Bielefeld University, Germany

{jan.rathjens, laurenz.wiskott}@rub.de, {shirin.reyhanian, david.kappel}@ini.rub.de

Abstract

Understanding the mechanisms underlying deep neural networks remains a fundamental

challenge in machine learning and computer vision. One promising, yet only preliminarily

explored approach, is feature inversion, which attempts to reconstruct images from interme-

diate representations using trained inverse neural networks. In this study, we revisit feature

inversion, introducing a novel, modular variation that enables signiﬁcantly more eﬃcient

application of the technique. We demonstrate how our method can be systematically ap-

plied to the large-scale transformer-based vision models, Detection Transformer and Vision

Transformer, and how reconstructed images can be qualitatively interpreted in a meaning-

ful way. We further quantitatively evaluate our method, thereby uncovering underlying

mechanisms of representing image features that emerge in the two transformer architec-

tures. Our analysis reveals key insights into how these models encode contextual shape and

image details, how their layers correlate, and their robustness against color perturbations.

These ﬁndings contribute to a deeper understanding of transformer-based vision models

and their internal representations. The code for reproducing our experiments is available at

https://github.com/wiskott-lab/inverse-tvm.

1 Introduction

In recent years, the focus in the ﬁeld of computer vision has shifted from convolutional neural networks

(CNNs) to transformer-based vision models (TVMs) (Dosovitskiy et al.,2020;Li et al.,2023a;Carion et al.,

2020;Zhu et al.,2021;Zhang et al.,2022). Despite their impressive performance, the internal mechanisms

that enable these networks to solve complex tasks remain largely opaque. This opaqueness prevents an

interpretation and a clear understanding of how predictions are made within these networks (Zhang and

Zhu,2018;Fan et al.,2021;Li et al.,2022b). Enhancing network interpretability, i.e., understanding the

mechanisms underlying the functionality of a particular deep neural network (DNN), is crucial for ensuring

safety, optimizing performance, and identifying potential weaknesses.

Feature inversion using inverse networks, introduced by Dosovitskiy and Brox (Dosovitskiy and Brox,2016),

is an early technique to interpret the processing capabilities of DNNs for vision. Building on a substantial

body of work on generating images from intermediate representations (Erhan et al.,2009;Zeiler and Fergus,

2014;Mahendran and Vedaldi,2014;Springenberg et al.,2015), their method involved training an inverse

network for each layer of the CNN AlexNet Krizhevsky et al. (2012) to reconstruct input images from

intermediate representations. By analyzing these reconstructed images and their distinct characteristics

from various layers, they gained insights into the underlying mechanisms of the architecture.

While feature inversion was successfully applied to AlexNet, it has not seen widespread adoption in the

context of modern DNNs for vision. We attribute this limited use to two main factors. Firstly, training

∗Assert joint ﬁrst authorship.

†Assert joint last authorship.

arXiv:2412.06534v4 [cs.CV] 13 Aug 2025

individual inverse networks for each layer of a DNN is computationally demanding, particularly for the large

CNNs and TVMs of today. Secondly, the potential of using feature inversion as a tool for analyzing and

interpreting neural networks was only preliminarily explored by Dosovitskiy and Brox (Dosovitskiy and Brox,

2016), leaving much of the of the capabilities of the method underutilized.

In this work, we revisit feature inversion and apply it to two widely used TVMs (see Figure 1for an illustra-

tion): Detection Transformer (DETR) (Carion et al.,2020) and Vision Transformer (ViT) (Dosovitskiy et al.,

2020), which serve as standalone models as well as backbones in state-of-the-art vision systems (e.g., Li et al.,

2022a;Oquab et al.,2024;Ravi et al.,2024). We begin by introducing a novel feature inversion approach

that builds on the classical idea of training layer-wise inverse networks but adopts a modular strategy that

inverts only speciﬁc components of the model. This design enables a substantially more eﬃcient application

of feature inversion to large-scale deep networks.

enc

...

enc-1

bb-1

...

bb enc

DETR

ViT

...

Figure 1: Illustration of our approach. Left: We invert components of transformer-based vision models,

such as the backbone and encoder. Right: Using these inverted components, we reconstruct images from

diﬀerent processing stages to analyze DETR and ViT. Here, we recolor a yellow bus to blue to examine color

processing in the two architectures.

We empirically validate our method on DETR and ViT, and demonstrate how reconstructed images from

diﬀerent layers can be interpreted in a systematic and meaningful way (see Figure 1for an illustration).

We introduce several novel analysis techniques for feature inversion and quantitatively evaluate a range of

hypotheses about internal representations. Our analyses uncover key properties of DETR and ViT, as well

as fundamental architectural diﬀerences. Among our ﬁndings are contrasts in the preservation of contextual

shape and image detail, inter-layer representational correlations, and robustness to color perturbations.

Notably, despite their similar architecture, the two models exhibit distinct strategies for visual abstraction:

DETR gradually transforms object shapes and colors into more prototypical representations at higher layers,

while ViT retains ﬁne-grained visual detail throughout all layers. We summarize our core contributions as

follows:

•We introduce a novel highly eﬃcient feature inversion method based on modular, independently

trained inverse components, which we empirically test and validate.

•We demonstrate how reconstructed images can be systematically used to interpret internal processing

mechanisms, introducing new analysis techniques such as targeted embedding manipulation.

•We identify shared properties across DETR and ViT, including gradual representation changes across

layers, thereby extending prior ﬁndings on ViT to the DETR architecture.

•We reveal fundamental diﬀerences between DETR and ViT, particularly in terms of image detail

preservation, abstraction behavior, and robustness to color perturbations.

2 Related work

In computer vision, feature inversion is a technique that reconstructs an input image from its intermediate fea-

ture representations, enabling direct inspection of the information a DNN preserves, discards, or transforms

at diﬀerent processing stages. It serves as a general tool for studying information ﬂow and representation

dynamics of DNNs.

A seminal work by Mahendran and Vedaldi (2014) framed inversion as an optimization problem in the image

space, generating images whose features matched those of a target layer in CNNs. However, this approach was

computationally expensive, and generated images varied with diﬀerent image space regularizers. Additionally,

although visually appealing, the mean squared errors (MSE) between the reconstructed and ground truth

images were relatively high.

Dosovitskiy and Brox (2016) advanced feature inversion by training dedicated inverse networks for each layer

of a CNN, achieving substantially higher-quality reconstructions, as reﬂected by lower MSE compared to

ground-truth images. Applied to AlexNet (Krizhevsky et al.,2012), this approach showed that both color

and spatial information are preserved across the network hierarchy. However, the method remained com-

putationally expensive, as it required training a separate network for each layer, which becomes demanding

for larger architectures. Nonetheless, their primary focus was on comparing inversion strategies rather than

fully leveraging feature inversion as a tool for network interpretability.

Feature inversion should not be confused with activation maximization studies (Erhan et al.,2009;Zeiler

and Fergus,2014;Springenberg et al.,2015;Nguyen et al.,2016;Olah et al.,2017), a technique for image

synthesis from intermediate network states. While feature inversion reconstructs the original input from

intermediate representations to reveal the information preserved at each stage, activation maximization

instead synthesizes inputs that maximally activate speciﬁc network units, such as neurons, channels, or

entire layers. The resulting images typically show simple, low-level structures (e.g., edges) for early layers

and more complex, high-level patterns for deeper layers.

In the broader scope of model interpretation, a variety of techniques have been developed to clarify how

internal representations evolve and contribute to downstream predictions. Saliency and attribution methods,

such as gradient-based saliency maps (Simonyan et al.,2014), class activation mapping (Selvaraju et al.,

2017), and layer-wise relevance propagation (Bach et al.,2015) typically produce heatmaps that spatially

highlight which part of an input image most inﬂuences the prediction of the model, often via gradient

backpropagation or pixel-level relevance propagation. While insightful for localizing decision-critical regions,

these methods do not reveal the actual visual content encoded within intermediate representations.

Perturbation-based analyses, such as occlusion sensitivity (Zeiler and Fergus,2014) and adversarial at-

tacks (Goodfellow et al.,2015), assess input relevance and model robustness by measuring prediction changes

under controlled modiﬁcations such as masking out image regions to produce spatial relevance maps akin to

saliency methods, or adding subtle adversarial noise to identify worst-case vulnerabilities. These methods

are valuable to quantify sensitivity and robustness to input perturbations but oﬀer little insight into the

underlying information-processing pipeline.

Representational Similarity Analysis (RSA) methods such as singular vector canonical correlation analy-

sis (Raghu et al.,2017), and Centered Kernel Alignment (CKA) (Kornblith et al.,2019) compare encoding

spaces and quantify alignment between diﬀerent layers or models to identify how representations evolve,

providing both global and sample-speciﬁc similarity metrics but without directly visualizing the preserved

spatial or semantic content.

Loss landscape analyses (Li et al.,2018;Garipov et al.,2018;Keskar et al.,2017) examine the geometry of the

optimization surface in parameter space, revealing aspects like sharpness, ﬂatness, and mode connectivity,

to study generalization capacity and learning dynamics, yet oﬀer little intuitive insight into the layer-wise

encoding of speciﬁc inputs.

Interpretability research on TVMs, and ViT in particular, has typically employed one or more of the afore-

mentioned broader techniques rather than feature inversion, with a primary focus on attention-based analy-

ses, representation probing, and robustness evaluations. For instance, attribution methods such as attention

rollout (Abnar and Zuidema,2020) and relevance propagation through attention layers (Chefer et al.,2021)

trace decision pathways across tokens by aggregating and propagating attention weights through successive

layers, producing attention maps that aim to highlight the most inﬂuential regions or tokens for the pre-

diction of the model. Other attribution studies assess the importance of attention heads via pruning and

leave-one-out ablations, evaluating prediction changes to quantify the contribution of each head (Li et al.,

2023b). Perturbation-based studies analyze robustness against occlusion, patch permutation, and adversarial

noises (Naseer et al.,2021), as well as analyzing loss landscape (Park and Kim,2022;Paul and Chen,2022).

Findings of these works indicate that ViT gradually reﬁnes its representations throughout its layers, depends

less on high-frequency features than CNNs, maintains spatial information throughout its architecture, and

is particularly robust against image perturbations compared to CNNs.

RSA studies using CKA (Raghu et al.,2021) quantify alignment or separability of features across layers,

also indicate that ViT has more uniform and similar representations across layers than CNNs, driven by

early global information aggregation. Complementary studies (e.g., Ghiasi et al. (2022)) use activation

maximization to generate synthetic patterns that most strongly activate speciﬁc ViT neurons, observing

a layer-wise shift from local textures to object-level features. However, these approaches mostly highlight

decision-critical regions or quantifying token/feature importance, rather than directly visualizing the full

spatial and semantic content retained at intermediate stages.

In contrast to ViT, interpretability studies on TVMs for object detection, like DETR, remain limited (Chefer

et al.,2021), partly because highly entangled features common for object detection are diﬃcult to interpret

with current methods. Instead, rather than analyzing existing models, recent works focus on architectural

changes to improve interpretability by design, e.g., by incorporating feature disentanglement techniques or

introducing new modules designed to learn prototypical features, thereby making subsequent interpretation

more tractable (Yu et al.,2024;Paul et al.,2024;Rath-Manakidis et al.,2024).

To the best of our knowledge, feature inversion has not been systematically applied to to TVMs for inter-

pretability and inverting the operations of self-attention and cross-attention layers has been considered a

challenging task (Fantozzi and Naldi,2024;Bibal et al.,2022), as these mechanisms dynamically aggregate

information across all tokens, entangling spatial and semantic features in a non-local manner. Our work

addresses this gap by reintroducing feature inversion as a scalable, semantically grounded interpretability

tool for large-scale TVMs.

We apply feature inversion to the two TVMs DETR (Carion et al.,2020), designed for object detection, and

ViT (Dosovitskiy et al.,2020), designed for image classiﬁcation. DETR comprises a convolutional backbone,

a transformer encoder-decoder, and a multi-layer perceptron (MLP) prediction head. On the other hand,

ViT features a linear projection layer (serving as its backbone) followed by a transformer encoder and a

MLP head. In both architectures, images are represented as sequences of tokens within their encoders,

maintaining a one-to-one correspondence with their spatial locations, making them well-suited for feature

inversion. We additionally advance the feature inversion approach by training modular inverse components

locally, eliminating the need to train separate networks for each layer. This advancement greatly improves

eﬃciency and scalability, enabling the application of it to large-scale architectures.

We leverage our novel modular feature inversion approach as a systematic interpretability framework, and

instead of inferring importance from gradients, perturbations, or similarity metrics, we directly reconstruct

images from intermediate representations, providing human-interpretable depictions of what each stage en-

codes. This enables both qualitative inspection of visual richness, abstraction level, and spatial ﬁdelity, as

well as quantitative analysis, e.g., reconstruction error comparison, across stages and models. Furthermore,

using targeted perturbations into feature space, we enable step-by-step analysis of the model’s information

processing pipeline and robustness. Moreover, the framework serves as a diagnostic tool for detection failures,

oﬀering a detailed view into intermediate representations when prediction errors occur.

3 Methods

3.1 Feature inversion

Feature inversion attempts to reconstruct input images from intermediate representations within a neural

network to gain insights into and interpret the processing mechanisms of the network. To formalize the

method, let N:X0→ XLbe a neural network with parameters θ, mapping from an image space X0to an

output space XL. Assume that Nconsists of nprocessing stages of interest indexed by P:= (1, . . . , n), a

subset of the layers of the network. We denote the representation of an image at input stage as x0∈ X0and

its representation at stage j∈ P as xj:= N0:j(x0;θ0:j), where Ni:j:Xi→ Xjrepresents the component of

the network spanning layers ito jwith parameters θi:j⊆θ.

Furthermore, we deﬁne the approximate inverse of component Ni:jas the neural network N−1

j:i:Xj→ Xi

with parameters ϕj:i. The reconstruction of xifrom processing stage j∈ P is given by ˆ

xj:i:= N−1

j:i(xj).

When i= 0, we refer to the reconstruction as image reconstruction and layer reconstruction otherwise.

Feature inversion for the network interpretability approach by Dosovitskiy and Brox (2016) follows two

steps. First, separate inverse components N−1

j:0 are trained for each j∈ P by minimizing the expected mean

squared error (MSE) between image reconstructions ˆ

xj:0 and their corresponding input images x0. Then, the

inverse components are used to generate reconstructed images from the various processing stages, enabling

an interpretation of the processing mechanisms of the forward network.

Intuitively, feature inversion relies on the principle that inverse components reconstruct an image by generat-

ing an average over plausible images corresponding to a given representation xj. As a network processes an

input, it abstracts information and omits details at various stages. If the inverse components are suﬃciently

powerful, the reconstructed image will reﬂect these abstractions and omissions at the pixel level. Analyz-

ing these pixel-level transformations allows for an assessment of what information is retained, omitted, or

abstracted at diﬀerent processing stages, thereby enhancing the interpretability of the network.

3.2 Modular feature inversion

We modify the classic approach to feature inversion in a key aspect. Instead of training inverse components

to map from Xjto X0directly, we train local inverse components, learning N−1

j:j−1for all j∈ P. Formally,

given a training set of images, we optimize the expected MSE for an inverse component over parameters

ϕj:j−1:

LMSE(ϕj:j−1) := E∥xj− N −1

j:j−1(xj)∥2

2(1)

With the modular approach, we then obtain image reconstructions by sequentially applying the trained

inverse components from any processing stage b∈ P:

x0:j:= (N−1

1:0 ◦ · · · ◦ N −1

j:j−1)(xj)(2)

Our modular approach oﬀers various advantages. Biasing the inverse solution space of inverse components

by independently training inverse components maintains greater symmetry between the processing stages of

the forward and backward path. Additionally, computational eﬃciency is greatly improved, as fewer, smaller

components are required compared to training separate inverse components attempting to inverse the entire

forward path for each stage.

This eﬃciency can be illustrated by comparing the total number of trainable parameters in the full-path

approach of Dosovitskiy and Brox (2016) versus our modular approach: Let Nbe a DNN with pparameters

and nprocessing stages of interest, for simplicity, each with p/n parameters. In the full-path approach, n

inverse models are trained, each inverting an increasingly larger network portion. Assuming each inverse

network roughly mirrors its forward path, the total parameter count for all inverse networks is Pn

i=1 i·p

np+p

2, scaling linearly with n. In contrast, for the same N, our modular method uses nmodular inverse

components of size p/n, totaling pparameters, constant in pand independent of n.

3.3 Application to DETR and ViT

We applied modular feature inversion to the two TVMs, DETR and ViT (see Figure 2for an illustration of

our approach on DETR). The procedure for ViT follows the same methodology. Speciﬁcally, we analyzed

pretrained DETR-R50 and ViT-B/16 as they are a reasonable compromise between performance and size.

For DETR, we identiﬁed four processing stages of interest P:= (1,2,3,4) while for ViT, we considered

two stages P:= (1,2). These correspond to the representations after processing by the backbone (bb),

encoder (enc), decoder (dec), and prediction head (pred). Note that ViT does not consist of a decoder,

and we excluded the prediction head of ViT from our analysis, as it operates on a single token, discarding

the remaining encoder sequence. In contrast, the prediction head of DETR processes the entire decoder

sequence.

bb-1

enc dec

enc-1 dec-1

pred

pred-1

...

... ...

Figure 2: Modular feature inversion of DETR. The top half illustrates the main components of DETR,

with blue arrows indicating the forward path of an input image through the architecture. The bottom half

shows our modular inversion approach, where each component is inverted individually. Red arrows trace the

backward path from predictions through the inverse components, enabling image reconstruction from any

processing stage. Green double-arrows indicate correspondence between representations, i.e., representations

output by a respective forward component can be used as input to the corresponding inverse component

during inference or as a supervision signal during training.

To improve readability, we will henceforth write bb instead of N0:1,bb-1 instead of N−1

1:0 , and xbb instead of x1,

with analogous notation for other components, e.g., enc for N1:2. When referring to an image reconstruction

from a speciﬁc processing stage, such as the encoder, we write ˆ

xenc:0.

Our inverse components were designed to mirror their respective forward components. For DETR, we

implemented a deconvolutional network as bb−1, resembling an inversion of DETR’s backbone (ResNet-50

(He et al.,2016)). We set enc−1to be structurally equivalent to enc, but with swapped inputs and outputs.

Similarly, we deﬁned dec−1as structurally equivalent to dec, but initialized its input as blank tokens that

self-attend to each other and cross-attend to xdec. For pred−1, we used a simple MLP that takes the

concatenation of bounding box and the full distribution of class logits as input.

For ViT, we employed a local small deconvolutional network as bb−1. Although bb in ViT is a simple,

local invertible linear transformation, its analytical inverse proved to be ill-conditioned, making it highly

sensitive to layer reconstruction errors between xbb and ˆ

xenc:bb. For enc−1we used a structurally equivalent

component to enc, but reversed the direction of information ﬂow. The details of our components are provided

in our code repository1.

We trained all inverse components on the COCO 2017 (Fleet et al.,2014) training dataset and evaluated

image reconstructions on the corresponding test set. We trained at least three instances for each inverse

component variant and interchanged them during analysis to ensure that ﬁndings are not attributable to

random variation.

1https://github.com/wiskott-lab/inverse-tvm

4 Results

4.1 Assessing modular approach

After training the inverse components for DETR and ViT, we ﬁrst tested the feasibility of our modular

feature inversion approach. To this end, we began by evaluating reconstructed images of arbitrary examples

generated with our method from the various processing stages of the two architectures.

Figure 3presents exemplary image reconstructions. Early-stage image reconstructions from both DETR

and ViT maintain the overall scene layout and coarse object structure. However, ViT preserved ﬁne-grained

details more accurately, while DETR reconstructions show early signs of blurring even at the backbone stage.

These diﬀerences become more pronounced in deeper stages, where DETR reconstructions progressively lose

structural detail, introduce color shifts, and abstract away background elements, suggesting a systematic

abstraction process. In contrast, ViT reconstructions remain comparatively faithful across stages.

Figure 3: Image reconstructions from processing stages. Column 1 shows the original input images. Columns

2-5 and 6-7 show reconstructions from diﬀerent processing stages of DETR and ViT, respectively.

We quantiﬁed these discrepancies between image reconstructions in DETR and ViT in Figure 4(left), using

the average MSE across diﬀerent processing stages. As expected, reconstruction error increases at later

stages in both models; however, ViT maintains signiﬁcantly lower MSE than DETR throughout, consistent

with our ﬁrst assessment of reconstructed images. Notably, in DETR, the MSE from the decoder stage

onward exceeds the baseline error of comparing each image to the dataset mean (a grayish, structureless

reference image). While this could superﬁcially suggest that representations from the decoder stage onward

are less informative than a simple average image, visual inspection of the corresponding reconstructions in

Figure 3reveals the contrary: Despite the higher reconstruction error, these outputs preserve structured,

object-speciﬁc content, indicating that the underlying representations encode nontrivial scene information.

This observation suggests a desirable property of our modular approach to feature inversion: Despite the

potential for error accumulation across sequential inverse modules, the approach enables reconstructions that

retain stage-speciﬁc transformations without collapsing into a globally averaged output, even when applied

Figure 4: Left: Average reconstruction error across processing stages for DETR and ViT on the COCO

validation dataset. "mean" denotes the average reconstruction error between validation images and the

mean image of the dataset. Center: Reconstruction loss (MSE) at the decoder stage versus object detection

performance (AP) for DETR, evaluated across diﬀerent values of λ. The label "modular" indicates the

performance of our modular feature inversion approach without ﬁne-tuning. Right: Reconstruction loss

(MSE) at the encoder stage versus classiﬁcation accuracy (Acc) for ViT across varying λ.

sequentially across deep model stages. This hypothesis prompted a more systematic evaluation of the validity

of our modular feature inversion framework presented in Section 4.2.

4.2 Validating modular approach

We validated our modular approach to feature inversion by comparing the image reconstructions obtained

with our method to those generated using the classic feature inversion approach. For classic feature inversion,

we selected a processing stage of interest for DETR and ViT, speciﬁcally, xdec for DETR and xenc for ViT,

and trained networks to reconstruct input images directly, following the classic approach to feature inversion.

That is, we trained inverse networks to determine the optimal parameters ϕdec:0 for DETR and ϕenc:0 for

ViT.

As an additional control experiment , we also ﬁne-tuned the forward weights of both models by incorporating

an image reconstruction loss. This allowed us to assess whether the loss of detail in reconstructions was due to

limitations in the forward components rather than ineﬀective inverse components. Speciﬁcally, we combined

the reconstruction loss with the objectives of the respective architectures, LOBJ, following the approach

of Rathjens and Wiskott (2024):

L(θ∪ϕj:0) = λLMSE(θ) + (1 −λ)LOBJ(θ) + LMSE(ϕj:0)(3)

We trained four model variants with λ∈ {0.0,0.1,0.9,1.0}, setting jto dec for DETR and enc for ViT.

Notably, λ= 0.0corresponds to the classic feature inversion approach, where the forward weights θare

not inﬂuenced by the reconstructions loss, while the other λ-values correspond to ﬁne-tuned versions of

our models. For ViT, we used the ImageNet-1K dataset (Krizhevsky et al.,2012), as ViT is designed for

classiﬁcation, not object detection, making the COCO object detection dataset less suitable for ﬁne-tuning..

Figure 5presents the image reconstructions obtained with ﬁne-tuned inverse models alongside those gener-

ated using our modular approach and the classic feature inversion approach. Across all examples, a consistent

pattern emerges: for high λvalues, the reconstructions maintain high ﬁdelity, capturing image details accu-

rately. As λdecreases, reconstruction quality deteriorates. This eﬀect is particularly pronounced in DETR,

especially in the last two columns, where blur is high. In contrast, ViT exhibits this eﬀect to a lesser degree.

Interestingly, for DETR, clear diﬀerences emerge between the last two columns: The reconstructions in the

λ= 0 column, which represent the classic feature inversion approach, exhibit a grayish tone, whereas those

in the modular approach column display more saturated colors.

We quantitatively analyzed this pattern in Figure 4, which displays the mean squared error (MSE) alongside

average precision (AP) for DETR (center plot) and MSE alongside accuracy for ViT (right plot). The

results align with the qualitative assessment of the reconstructed images: As λdecreases, reconstruction

error increases. Moreover, as λdecreases, the object detection and classiﬁcation performances of DETR

and ViT improve, highlighting a trade-oﬀ between reconstruction quality and the tasks of the architectures.

Unsurprisingly, the MSE is lower for the classic feature inversion approach than for our modular approach.

Figure 5: Reconstructions with ﬁne-tuned models. Columns 2–4 show reconstructions from models ﬁne-

tuned with diﬀerent λvalues. Column 1 displays input images, and column 6 shows reconstructions using

our modular feature inversion approach. Top: Images from the DETR dec processing stage. Bottom: Images

from the ViT enc processing stage.

As a side note, despite this trade-oﬀ, our ﬁne-tuned ViT for λset to 0.0, 0.1, and even 0.9, achieved

slightly higher validation accuracy on ImageNet-1K than the released ViT-B/16 model (used in our modular

approach).

We interpret these ﬁndings as follows. Firstly, incorporating reconstruction-driven information into the

forward path enhances reconstruction quality but degrades the performance of the architectures, in line with

previous work (Rathjens and Wiskott,2024). This trade-oﬀ suggests that blur in reconstructions is not a

result of ineﬀective inverse components but rather a consequence of how information is processed in the

forward model. Importantly, this implies that poor reconstructions are not detrimental to interpretability;

on the contrary, they highlight which information is omitted or abstracted at diﬀerent stages of the model.

Secondly, our modular approach to feature inversion enhances reconstruction properties for interpretability.

While the classic approach has a better reconstruction performance in terms of MSE, it does so by shifting

colors toward a grayish tone, reﬂecting the average color of the COCO dataset, particularly evident for

DETR. This shift occurs because the inverse network in the classic approach can exploit global dataset-wide

color statistics as they are not trained locally. In contrast, the modular approach better preserves stage-

speciﬁc information, though the MSE between input and reconstructed images may increase, particularly

when reconstructed from deeper representations.

4.3 Analyzing color

Having established the feasibility and validity of our modular inversion framework, we turned to its primary

purpose, i.e., interpreting intermediate representations in DETR and ViT.

Building on our initial observations suggesting substantial diﬀerences in color processing between DETR and

ViT, we conducted a systematic analysis to explore these diﬀerences in more detail. Precisely, we recolored

speciﬁc objects in input images and evaluated the inﬂuence of these modiﬁcations on image reconstructions

from the various processing stages. For recoloring, we used the segmentation annotations from the COCO

dataset to apply six diﬀerent color ﬁlters in the HSV color space to various object categories. Speciﬁcally,

we adjusted the hue of speciﬁed objects to red, green, blue, shifted the hue values by 120 or 240 degrees, or

converted all image pixels to grayscale. Figure 6illustrates recolored images alongside their corresponding

reconstructions for several examples. Each row presents an example from a diﬀerent object category with a

distinct color ﬁlter applied. Each column presents a reconstruction from a diﬀerent processing stage.

green

input bb

DETR

enc dec

ViT

bb enc

240120

bluegrayscale

Figure 6: Eﬀects of color perturbations. Rows show images where speciﬁc object categories were color-

perturbed (from top to bottom: stop sign colored green, bear with colors rotated by 240°, apple with colors

rotated by 120°, bus colored blue, giraﬀe converted to grayscale). Columns 2-4 and 5-6 show reconstructions

from diﬀerent processing stages of DETR and ViT, respectively.

For DETR, we observe that color perturbations are preserved in image reconstructions from the backbone

representations for all objects and ﬁlters but gradually fade or disappear almost entirely in image reconstruc-

tions from the encoder representations. In ˆ

xdec:0 practically no color perturbation remains. Instead, colors

shift toward prototypical representations (red for the stop sign and bus, brown for the bear, red or yellow for

the apples, and yellow for the giraﬀe) even when color information was deleted (see giraﬀe). In contrast, we

do not observe a similar eﬀect in ViT, as color perturbations remain visible in image reconstructions from

all processing stages.

We quantiﬁed the response to color perturbations by computing the average pairwise MSE between image

reconstructions of diﬀerently perturbed images from each processing stage. Speciﬁcally, given an image x0,

we applied each color ﬁlter separately, generating six perturbed versions. We calculated the average pairwise

MSE between these perturbed images at the input stage. Similarly, for the backbone stage, we computed

the average pairwise MSE between the six corresponding reconstructed images ˆ

xbb:0, following the same

approach for the encoder and decoder stages. The left plot in Figure 7presents these MSE values, averaged

across all categories and images in the dataset.

input bb enc dec

MSE (x 10 3)

DETR

ViT

- r g b 120 240 gs

DETR

ViT

Figure 7: Quantiﬁcation of color perturbations. Left: Average pairwise MSE between image reconstructions

of diﬀerently perturbed versions of an image, comparing inputs and reconstructions across processing stages.

Shaded area indicates 95% conﬁdence intervals over the COCO test set. Right: DETR’s and ViT’s sensitivity

to color perturbations (none, red, green, blue, 120°shift, 240°shift, grayscale) in relation to the performance

of their objectives.

For DETR, we observe that the average pairwise MSE decreases progressively from x0to ˆ

xenc:0, indicating

increasing similarity. However, at the decoder stage, the MSE returns to input levels. This observation aligns

with our qualitative analysis, conﬁrming that reconstructions tend to converge to the same or similar colors

as they progress through the DETR architecture. The increase in average pairwise MSE at the decoder

stage is likely not due to color divergence but rather distortions in object shapes. For ViT, the preservation

of color perturbations throughout the architecture is reﬂected in an almost constant pairwise MSE across

processing stages.

The greater loss of color information in DETR compared to ViT suggests that DETR is more robust to

color changes than ViT. We tested this hypothesis by evaluating the performance of each architecture on

recolored images (see right plot Figure 7). Speciﬁcally, we recolored entire images from the ImageNet dataset

and measured classiﬁcation performance for ViT, as segmentation data was not available. To ensure a fair

comparison, we also applied full-image recoloring for DETR. The results show that accuracy of ViT drops

compared to the default setting, whereas DETR remains unaﬀected.

4.4 Analyzing structure

Our initial assessment of reconstructed images indicated that DETR progressively alters the image structure

across its processing stages, whereas ViT tends to preserve it. To investigate this phenomenon in greater

depth, we again reconstructed images from various stages of both architectures, this time focusing on the

analysis of structural changes. Given the particularly interesting behavior observed in DETR, we employed

two variants for its pred−1: a standard pred−1

FD, which receives xpred with full distribution of class logits

as input, and an additional pred−1

OH, which takes a one-hot encoded variant of xpred. The latter retains

only the highest-conﬁdence class per detected object, discarding information about the uncertainty in class

predictions. Bounding boxes are retained in both variants. We hypothesized that the full distribution of class

conﬁdences, beyond just the top prediction, encodes meaningful visual cues. The one-hot variant allowed us

to evaluate more prototypical reconstructions of certain objects, without the model being able to exploit the

uncertainty information and low-conﬁdence class associations during the reconstruction process.

Figure 8displays exemplary image reconstructions. For DETR, we observed that low-level structural infor-

mation is generally well-preserved in reconstructions from xbb. Notably, at the later stages starting from

dec, objects undergo signiﬁcant alterations, including changes in size, shape, structure and orientation (e.g.,

the person in the ﬁrst row appears taller with a lowered hand, the sunﬂowers in the third row shift into a

generic green plant, and the horse in the fourth row is reoriented to face right), the addition of contextual

elements (left person in the second row appears to be wearing a suit in reconstructions from dec and pred,

inferred from the presence of a tie), or complete omissions of objects (e.g. the bollards in the second row, or

the photo frame on the wall in the third row are completely abstracted out). Furthermore, we observe some

artifacts, e.g., in the reconstructions from predOH in the fourth row, a dark object appears near the horse

that seems to be another person, which is not present in earlier stages. These transformations appeared

repeatedly across diverse samples and object classes, suggesting that the model learns structured abstraction

behaviors that are consistent within each class.

Figure 8: Structural transformations analysis in DETR and ViT

In contrast, ViT reconstructions show little structural change across stages. Object shape, spatial conﬁgu-

ration, and contextual elements are consistently preserved, suggesting that ViT retains low-level visual and

semantic information without applying the same degree of abstraction observed in DETR.

We interpret these observations as follows. In higher processing stages, DETR tends to omit image details

that are not relevant to object detection, such as objects that are not explicitly recognized (e.g., the omission

of bollards and photo frame, compared to detected objects indicated by bounding boxes in the input images).

Instead of preserving raw image details, DETR represents objects in a prototypical manner, discarding

information deemed irrelevant for recognition, such as pose and shape variations or orientation changes (e.g.,

the altered posture of the person or the transformed sunﬂowers). Additionally, DETR appears to learn priors

about object co-occurrences and typical scene compositions. It may modify contextual elements to enhance

object recognizability, as seen in the addition of a suit coat to emphasize the tie. Using only top-scoring

classes for reconstructions can also lead to semantically relevant hallucinations, like a person appearing near

a horse, emphasizing the role of model conﬁdence in activating the co-occurrence of related objects. On the

other hand, ViT does not appear to undergo these abstractions, as image details remain largely preserved

throughout its architecture.

4.5 Analyzing spatial correlations

Throughout our experiments, we observed that ViT preserves image details more eﬀectively across processing

stages than DETR, suggesting a stronger spatial correspondence between the input image and its token

representations. To further examine this spatial correlation, we replaced 20% of randomly selected tokens

at two processing stages with identical uniform noise added to the respective positional embeddings, and

analyzed the resulting image reconstructions. Speciﬁcally, we manipulated xbb and generated reconstructions

N−1

bb:0(xbb)and N−1

enc:0(Nbb:enc(xbb)), which we refer to as bbman and encman+. Additionally, we manipulated

xenc to generate reconstruction N−1

enc:0(xenc)which we refer to as encman. Note that positional information

of tokens from the encoder stage of ViT cannot be preserved, as explicit positional encodings are no longer

present at that processing stage.

Our reasoning for the experimental setup was as follows: If the manipulation of tokens result in visible

distortions at their corresponding spatial locations, while the rest of the image remains unchanged, it would

indicate that the reconstruction process relies primarily on local features. Such behavior suggests a low level

of abstraction, where image information is not distributed across all tokens. Conversely, if the manipulated

tokens do not produce localized distortions but instead aﬀect the entire reconstruction, it implies that the

image information is distributed across tokens, pointing to a higher level of abstraction and reduced spatial

locality.

To enable a more isolated analysis of enc, we introduced a local inverse backbone variant for DETR. In this

conﬁguration, each image patch is reconstructed solely from the token corresponding to its spatial location,

without incorporating global features. This design decouples the global integration of image details across

tokens performed by the encoder from that of the backbone.

Figure 9shows results for two example images for both architectures. For the DETR setup with the standard

bb−1, token manipulation leads to slightly increased blurring and color shifts in the reconstructions across

all processing stages. However, the reconstructions do not reveal which tokens were manipulated, as the

noisy tokens were consistently ﬁlled in with plausible content.

input

default

bb enc bbman

manipulated

encman encman+

DETR

DETR - local bb 1

ViT

Figure 9: Image reconstructions from default (unmanipulated) and manipulated representations with DETR,

a DETR variant with a local inverse backbone, and ViT. Tokens were replaced with the same random uniform

noise at diﬀerent processing stages before reconstruction. For encman+, embeddings were manipulated at the

backbone stage, processed through enc, and then used for reconstruction.

With the local inverse backbone variant for DETR, overall reconstruction quality deteriorates signiﬁcantly,

as expected. Unlike the standard inverse backbone, reconstructed images with the local version enable a

more accurate identiﬁcation of the manipulated tokens. Since the local bb−1reconstructs each image patch

using only a single token, and all manipulated tokens are replaced with identical noise, the corresponding

patches appear visually identical, as visible in the bbman setup.

In the encman setup, manipulated tokens can still be identiﬁed, as their corresponding reconstructed patches

diﬀer from those based on unmanipulated tokens. However, these diﬀerences are less pronounced, suggesting

that manipulated tokens integrate some contextual information from surrounding tokens. In the encman+

condition, patches reconstructed from manipulated tokens are nearly indistinguishable from others, as the

noisy tokens blend seamlessly into the overall image.

The appearance of reconstructed images from manipulated representations in DETR stands in sharp contrast

to those obtained from ViT. For ViT, manipulated tokens manifest as visible noise within their corresponding

patches, while unmanipulated patches remain unaﬀected.

The diﬀerences in image reconstructions from manipulated representations strongly support the hypothesized

distinction in information processing between the two architectures. While both the DETR backbone and

encoder distribute image details associated with a given location across multiple tokens, ViT components

preserve a spatial correspondence between tokens and image locations. As a result, the inverse components in

ViT do not require global integration to reconstruct the image, an eﬀect particularly evident in the encman+

setup, where the manipulated tokens remain clearly identiﬁable despite being processed through multiple

stages.

The lower level of abstraction in ViTs suggests that, in the forward pass, greater emphasis is placed on

attention from the class token to image tokens rather than self-attention among image tokens. To test

hypothesis, we disabled self-attention in enc retaining only the cross-attention from the class token to image

tokens, and ﬁne-tuned the architecture on ImageNet-1K. Remarkably, this modiﬁed model still achieved

approximately 69% top-1 accuracy, only seven percentage points lower than the 76% accuracy of ViT-B/16

with enabled self-attention, supporting our hypothesis.

4.6 Analyzing detection errors in DETR

Our method also enables a visual inspection of detection errors by examining the reconstructed images to

ﬁnd out how DETR encodes, or fails to encode, objects across stages. As illustrated in Figure 10, objects

that are ultimately not detected (e.g., the bicycle in the second row or the potted plants in the third row)

are gradually suppressed across the processing stages. Although clearly visible in the input, these elements

begin to fade in the reconstructions from bb and enc, and leave no trace in the reconstructions from dec or

pred. This gradual disappearance suggests that the model deems them irrelevant and ﬁlters them out during

object query formation or matching.

In contrast, false positives often exhibit the opposite behavior: Reconstructions from later stages reveal a

shift toward features associated with incorrect classes (e.g., the second ﬁre hydrant in the ﬁrst row or the

second stop sign in the fourth row). This suggests that, if DETR misinterprets certain features or contextual

cues, it constructs coherent features and consolidates them into prototypical object representations.

These observations provide a visual trail of where detection errors arise by revealing the stages in the pro-

cessing pipeline where critical information is lost or misrepresented. This stage-wise visual access to internal

representations makes reconstruction-based analysis a valuable diagnostic tool for interpreting the inner

workings of DETR, highlighting where in the architecture corrective reﬁnements might be most eﬀective.

4.7 Analyzing intermediate layers

Until now, we have applied feature inversion only to representations from selected processing stages, thereby

excluding layers not explicitly chosen for our analysis. However, unlike in CNNs, transformer-based vision

models oﬀer a unique analytical opportunity: The intermediate representations within both the encoder and

decoder maintain a consistent shape across layers. This property allows intermediate encoder representations

to be passed through the inverse backbone and inverse encoder, and intermediate decoder representations

through the inverse decoder, even though these components were not trained for this purpose. Leveraging this

Figure 10: Image reconstructions from various processing stages of DETR. Analysing detection errors using

reconstructions of various stages. The ﬁrst and second columns depict input images along with ground truth

labels and predictions of DETR, respectively.

unique property, we explored whether our inverse components could reconstruct images from intermediate

encoder and decoder representations, despite the mismatch in training context. Speciﬁcally, we analyzed

intermediate representations from the encoder and decoder of DETR, as well as from the encoder of ViT.

Figure 11 provides illustrative examples.

Predictably, for intermediate representations of both architectures, we obtained best reconstruction perfor-

mances for the representations the inverse components were trained on: xbb for bb−1,xenc for enc−1and,

for DETR, xdec for dec−1. The quality of reconstructions gradually decreases as we move farther away from

the representations the inverse components were trained on, a pattern particularly evident for the input to

dec−1since decoder tokens initially hold values that are independent of the input image.

Despite of this degradation, image features are generally preserved across intermediate layers, especially

when feeding intermediate encoder representations into enc−1. For DETR, most variations in bb−1and

enc−1appear as color shifts, whereas reconstructions from dec−1exhibit greater stability in color than in

shape. For ViT, reconstructions from enc−1preserve both shape and color, while bb−1display strong tiling

eﬀects, likely due to the local operations of the inverse backbone. Nevertheless, both color and shape remain

discernible.The overall stability of reconstructions across layers is noteworthy, as inverse modules might be

expected to produce only noisy outputs when applied to intermediate embeddings they have not been trained

on.

From these observations, we draw three key conclusions. Firstly, the diﬀerence in feature preservation

between DETR and ViT further highlights their distinct approaches to information abstraction, as DETR

progressively alters colors throughout its hierarchy. Secondly, intermediate embeddings in transformer-based

vision models evolve gradually across layers, as suggested by Raghu et al. for ViTs (Raghu et al.,2021) and

by Liu et al. for LLMs (Liu et al.,2023). Finally, feature inversion is particularly well-suited for TVMs, as

inverse components can be applied across multiple layers, eliminating the need to train a separate inverse

component for each layer.

enc

bb 1

enc

DETR

enc 1

input

dec

123456

dec 1

enc

from component

bb 1

into inverse component

input

enc

ViT

246

intermediate layer

8 10 12

enc 1

Figure 11: Image reconstructions from intermediate encoder and decoder layers. The left y-axis labels

indicate the component from which we extracted the respective intermediate representation. The x-axis

labels denote the speciﬁc intermediate layer corresponding to the intermediate representation. The right

y-axis labels indicate into which inverse component we fed the intermediate representation.

5 Discussion

In this work, we set out to apply an eﬃcient variant of the classic feature inversion approach from Dosovitskiy

and Brox (2016) to study the intermediate representations of the TVMs DETR and ViT. We began by

formulating a modular version of feature inversion that signiﬁcantly improves eﬃciency by replacing large

global inverse networks with lightweight, local inverse components, thereby substantially reducing the number

of trainable parameters.

After a brief glimpse into image reconstructions obtained with our novel variant from DETR and ViT, we

ﬁrst validated its feasibility for network interpretability on both architectures. To this end, we qualitatively

and quantitatively compared our approach to classical feature inversion on ViT and DETR, and variants

of the two architectures ﬁne-tuned with a combination of reconstruction loss and architecture speciﬁc ob-

jectives. We found that reconstructed images obtained with modular feature inversion are reﬂective of the

processing mechanisms of both architectures. Additionally, despite potential error accumulation through

repeated application of inverse components, the method opposes trivial image reconstructions, rendering our

modular approach not only more eﬃcient than classic feature inversion but also better suited for network

interpretability.

Building on this foundation, we commenced with a systematic interpretability study of DETR and ViT,

beginning with an investigation of how color information is processed. We observed that DETR progres-

sively shifts object colors toward prototypical representations, while ViT preserves original color information

throughout. Consistent with these ﬁndings, DETR shows strong robustness to color perturbations, whereas

the classiﬁcation performance of ViT degrades, challenging previous claims (Naseer et al.,2021;Paul and

Chen,2022) that ViT is remarkably resilient to image perturbations.

We continued our interpretability study with a focused analysis of how image structure is processed in the

two architectures. We found that DETR abstracts object structure and context, modifying shapes and

poses, omitting irrelevant but adding contextually relevant features, reﬂecting a shift toward prototypical

representations that likely simplify object detection in later stages. In contrast, ViT retains object geometry

and spatial layout with minimal distortion, pointing to a lower level of abstraction and a stronger preservation

of visual detail.

We then turned towards analyzing spatial correlations between intermediate representations and input im-

ages. Using a novel analysis method in the context of feature inversion, speciﬁcally, injecting noise into

intermediate representations, we found that ViT encodes spatial information in a localized manner. At the

same time, DETR diﬀuses spatial information more globally. The spatial correspondence in ViT questions

the importance of self-attention within the architecture, particularly given that we achieved reasonable clas-

siﬁcation accuracy in a ViT with disabled self-attention. Notably, Jaegle et al. (2021) have shown that

a transformer-based model can achieve competitive accuracy on ImageNet-1k using only cross-attention.

However, in their model, self-attention was still applied to register tokens, and its computational complexity

exceeded that of ViT.

After brieﬂy showing how DETR reconstructions vary with detection errors, we concluded our analysis by

leveraging a key property of transformer architectures, namely, the constant shape of intermediate repre-

sentations across encoder and decoder layers. The consistency allowed us to feed these representations into

inverse components optimized for reconstruction from diﬀerent layers. We found that both DETR and ViT

reﬁne their representations gradually across layers, a pattern consistent with prior ViT studies (Raghu et al.,

2021) and now extended to DETR, suggesting that gradual reﬁnement is a general characteristic of TVMs.

This property also enhances the eﬃciency of feature inversion in such models.

On the whole, we found both shared and divergent properties between DETR and ViT. For instance, both

models exhibit gradually evolving representations across layers, yet diﬀer in their treatment of color and

structural image information. While similarities can likely be attributed to the transformer-based nature of

both models, the diﬀerences raise important questions for future research, and we outline several hypotheses

regarding their origin.

One potential factor is the diﬀerence in training data. The ViT we analyzed was trained on the large-scale

JFT-300M dataset, which contains around 18,000 classes (Sun et al.,2017), while the DETR we analyzed

was trained on COCO (Fleet et al.,2014), which includes approximately 90 object categories. The greater

visual diversity in JFT-300M may require ViT to preserve ﬁner image details, whereas DETR, trained on

a smaller and more constrained set of categories, may aﬀord more abstraction. Future work could examine

how the training dataset inﬂuences feature inversion results, for example, by retraining both architectures

on the same dataset.

Another hypothesis relates to the diﬀerence in training objectives. DETR is trained for object detection,

which involves identifying and localizing multiple objects per image. In contrast, ViT is trained for image-

level classiﬁcation, where only a single object needs to be identiﬁed without localization. Classiﬁcation,

therefore, may place less demand on the model to transform input features extensively. In contrast, object

detection requires more abstract and context-aware representations to support both recognition and spatial

localization. Future research could explore this hypothesis by training the architectures with swapped

objectives and analyzing the impact on feature inversion outcomes.

Lastly, architectural diﬀerences, particularly in the backbone, may also contribute to the observed diﬀerences

in image reconstructions. DETR uses a CNN as its backbone, which is known to produce progressively

more abstract representations (Mahendran and Vedaldi,2014), whereas ViT employs an invertible linear

embedding that preserves all input information. Consequently, the inputs to the transformer encoders in

DETR and ViT diﬀer substantially from the outset, potentially leading to distinct representational dynamics

throughout the network. Future work could explore the role of the backbone by systematically swapping the

backbones of the two architectures and analyzing their eﬀect on image reconstructions.

From a methodological perspective, we have shown that modular feature inversion is both more eﬃcient and

more naturally aligned with the architecture of TVMs than the classical approach. These properties make it

well-suited for analyzing modern iterations of TVMs such as DINOv2 (Oquab et al.,2024) or SAM (Kirillov

et al.,2023). Furthermore, since our approach is not limited to TVMs and we expect it to oﬀer advantages

for a broad range of DNNs, it may also prove valuable for analyzing modern CNN-based models such as

ConvNeXt V2 (Woo et al.,2023) or YOLOv8 (Ultralytics).

One particularly intriguing property of our method is that, despite yielding higher image reconstruction error

than classical feature inversion, images are better suited for network interpretability. While we can attribute

this eﬀect to the closer mirroring of the forward processing path obtained with modular feature inversion

compared to the classical approach, its extent remains unclear. Future research could explore this further by

systematically varying the number of inverse components and examining the impact on both reconstruction

quality and interpretability.

In this line of research, future work could also address a fundamental limitation of feature inversion: Even

with the modular approach, it remains challenging to conclusively attribute speciﬁc properties in recon-

structed images to individual processing stages. Drawing reliable conclusions typically requires additional

quantitative analysis. However, increasing the number of inverse components may oﬀer ﬁner-grained insights

and help localize speciﬁc representational eﬀects to particular layers.

Our method may have broader applications beyond network interpretability. In the case of DETR, we

observed that undetected objects often vanish in reconstructed images, while misclassiﬁed objects tend to

appear signiﬁcantly altered. These ﬁndings point to a promising direction for applying modular feature

inversion to error detection: By comparing reconstructed images to their inputs, discrepancies may serve as

indicators of detection failures.

Drawing a parallel to computational neuroscience, prior work has shown that generative models of episodic

memory require the integration of both discriminative and generative processes (Fayyaz et al.,2022). Future

models could build on this idea by unifying a TVM and its inverse within a single architecture. Like-

wise, TVMs may be well-suited for biologically plausible learning systems, as they naturally support local

reconstruction losses (Kappel et al.,2023).

In summary, we proposed a modular feature inversion framework for TVMs that enables scalable, component-

wise interpretability with minimal training overhead. Applied to DETR and ViT, it revealed shared and

distinct representational dynamics in abstraction, spatial encoding, and robustness. Beyond interpretabil-

ity, the approach shows promise for error detection and biologically inspired learning, positioning modular

inversion as a practical tool for probing modern vision models and guiding future discriminative-generative

integration.

Acknowledgments

This work was supported by grants from the German Research Foundation (DFG), project number 397530566

– FOR 2812, P5.

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