Title: Brain-like Flexible Visual Inference by Harnessing Feedback Feedforward Alignment
Venue: NeurIPS 2023
Accepted: yes
Keywords: Visual inference

Bio-plausible learning algorithm

Feedback connections

Visual imagery

Occlusions

Noise
Abstract: In natural vision, feedback connections support versatile visual inference capabilities such as making sense of the occluded or noisy bottom-up sensory information or mediating pure top-down processes such as imagination. However, the mechanisms by which the feedback pathway learns to give rise to these capabilities flexibly are not clear. We propose that top-down effects emerge through alignment between feedforward and feedback pathways, each optimizing its own objectives. To achieve this co-optimization, we introduce Feedback-Feedforward Alignment (FFA), a learning algorithm that leverages feedback and feedforward pathways as mutual credit assignment computational graphs, enabling alignment. In our study, we demonstrate the effectiveness of FFA in co-optimizing classification and reconstruction tasks on widely used MNIST and CIFAR10 datasets. Notably, the alignment mechanism in FFA endows feedback connections with emergent visual inference functions, including denoising, resolving occlusions, hallucination, and imagination. Moreover, FFA offers bio-plausibility compared to traditional backpropagation (BP) methods in implementation. By repurposing the computational graph of credit assignment into a goal-driven feedback pathway, FFA alleviates weight transport problems encountered in BP, enhancing the bio-plausibility of the learning algorithm. Our study presents FFA as a promising proof-of-concept for the mechanisms underlying how feedback connections in the visual cortex support flexible visual functions. This work also contributes to the broader field of visual inference underlying perceptual phenomena and has implications for developing more biologically inspired learning algorithms.

Brain-like Flexible Visual Inference by Harnessing Feedback-Feedforward Alignment

Abstract

In natural vision, feedback connections support versatile visual inference capabilities such as making sense of the occluded or noisy bottom-up sensory information or mediating pure top-down processes such as imagination. However, the mechanisms by which the feedback pathway learns to give rise to these capabilities flexibly are not clear. We propose that top-down effects emerge through alignment between feedforward and feedback pathways, each optimizing its own objectives. To achieve this co-optimization, we introduce Feedback-Feedforward Alignment (FFA), a learning algorithm that leverages feedback and feedforward pathways as mutual credit assignment computational graphs, enabling alignment. In our study, we demonstrate the effectiveness of FFA in co-optimizing classification and reconstruction tasks on widely used MNIST and CIFAR10 datasets. Notably, the alignment mechanism in FFA endows feedback connections with emergent visual inference functions, including denoising, resolving occlusions, hallucination, and imagination. Moreover, FFA offers bio-plausibility compared to traditional backpropagation (BP) methods in implementation. By repurposing the computational graph of credit assignment into a goal-driven feedback pathway, FFA alleviates weight transport problems encountered in BP, enhancing the bio-plausibility of the learning algorithm. Our study presents FFA as a promising proof-of-concept for the mechanisms underlying how feedback connections in the visual cortex support flexible visual functions. This work also contributes to the broader field of visual inference underlying perceptual phenomena and has implications for developing more biologically inspired learning algorithms.

1 Introduction

Humans possess remarkable abilities to infer the properties of objects even in the presence of occlusion or noise. They can mentally imagine objects and reconstruct their complete forms, even when only partial information is available, regardless of whether they have ever seen the complete form before. The process of visual inference on noisy or uncertain stimuli requires additional time, implying cognitive processes that go beyond a simple feedforward pass on visual input and suggest the involvement of additional mechanisms such as feedback and recurrence (Kar et al., 2019; Kietzmann et al., 2019; Gilbert and Sigman, 2007; Debes and Dragoi, 2023; Kreiman and Serre, 2020). Despite the abundant evidence on the involvement of feedback connections in various cognitive processes, understanding the precise mechanisms through which they flexibly give rise to the ability to infer or generate perceptual experiences is not clear.

While hierarchical feedforward models of the ventral visual cortex based on deep learning of discriminative losses have achieved remarkable success in computer vision tasks (Yamins et al., 2014; Khaligh-Razavi and Kriegeskorte, 2014; Lindsay, 2021), alternative frameworks, such as predictive processing models, offer a distinct perspective on visual processing. Predictive processing models propose that the brain generates fine-grained predictions about incoming sensory inputs and compare them with actual sensory signals to minimize prediction errors (Rao and Ballard, 1999; Friston, 2009; Clark, 2013). These models emphasize the role of feedback connections in the visual cortex, with higher-level areas sending top-down predictions to lower-level areas to guide perception (Wen et al., 2018; Choksi et al., 2021; Whittington and Bogacz, 2017; Millidge et al., 2020). Unlike deep learning models that learn from large-scale datasets, predictive processing models prioritize the role of prior knowledge and expectations in shaping perception as originally emphasized as far back as Helmholtz (Helmholtz et al., 1909). While predictive processing models emphasize the active role of top-down predictions and prior knowledge in shaping visual perception, they lag behind feedforward models in mechanistic specificity and thus direct neurophysiological evidence (Walsh et al., 2020; Clark, 2013; Keller and Mrsic-Flogel, 2018). Moreover, most large-scale implementation of predictive coding or, in general, recurrence relies on back-propagation-through-time (BPTT) to train the recurrence and feedback connections (Choksi et al., 2021; Tscshantz et al., 2023; Spoerer et al., 2017), which suffers from many issues regarding bio-plausible implementation (Lillicrap and Santoro, 2019a). Another main constraint on the space of models is the learning algorithm to train the model. Classical error backpropagation (BP) has been a workhorse algorithm for training discriminative, feedforward deep neural networks, particularly for visual object recognition (Rumelhart et al., 1986; Krizhevsky et al., 2012). Despite its immense success in training the state-of-the-art, BP has been criticized on a number of implementational issues, some of which also call into question its bio-plausibility for the brain: weight symmetry requires weight transport to the feedback network (Grossberg, 1987), the feedback network is not used during runtime inference, and feedforward discrimination performance is not robust to noise (Goodfellow et al., 2015; Akrout, 2019). Beyond these issues, BP is an infinitesimally local estimate of the gradient, and other higher-order methods for computing the gradient could accelerate learning. As pointed out by (Bengio, 2014), the inverse of the weight matrix, rather than the transpose, may provide a valid path for credit assignment, learning a linear extrapolation of the underlying landscape (Bengio, 2014). However, attempts to match BP by learning the inverse weights instead of the transpose in a stage-wise fashion, also called target propagation (TP), have yielded limited practical success for reasons that are not entirely clear (Lee et al., 2014; Bartunov et al., 2018) - potentially related to the difficulty of learning an inverse function using noisy gradients as opposed to the relative ease of taking a transpose, a noiseless procedure (Kunin et al., 2020).

Here, we simultaneously learn feedforward and feedback functions that are mutual global inverses of each other such that each path can perform credit assignment for the other during the training pass. We term this Feedback-Feedforward Alignment (FFA) since the discriminator (encoder) contributes the gradients for the reconstructor (decoder) and vice versa. We show that rather than trading against each other as in typical, single-objective settings, co-optimizing discrimination and reconstruction objectives can lead to a mutualistic symbiotic interaction.

Next, we explore the potential of the gradient path as a model of feedback connections. We are inspired by the structural similarity of the credit assignment computational graph and the feedforward pass, which parallels the anatomically reciprocated feedforward and feedback connections in the primate visual cortex (Markov et al., 2013, 2014). Importantly we hypothesized an objective function for feedback connections motivated by the High-resolution buffer hypothesis by (Lee and Mumford, 2003) regarding the primary visual cortex (V1), arguing that V1 is uniquely situated to act as a high-resolution buffer to synthesize images through generative processes. We hypothesized that by co-tuning feedforward and feedback connections to optimize two different but dependent objective functions, we could explain the properties of flexible visual inference of visual detail under occlusion, denoising, dreaming, and mental imagery.

The contributions of this study are as follows:

Based on the role of feedback connections in the brain, we propose a novel strategy to train neural networks to co-optimize for two objective functions.

We leverage the credit assignment computational graph as feedback connections during learning and inference.

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We suggest and verify that training feedforward and feedback connections for discrimination and reconstruction respectively, induces noise robustness.

We show that FFA can flexibly support an array of versatile visual inferences such as resolving occlusion, hallucination, and visual imagery.

2 Related Work

2.1 Models of visual perception and inference in the brain

In going beyond purely feedforward models, there is a large hypothesis space of recurrent neural network models (RNNs), and training inference into an RNN via backpropagation through time raises severe questions about bio-plausibility of the learning algorithm as well as architecture (Lillicrap and Santoro, 2019b). Prior work on RNNs for visual classification whether through complex architecture search (Nayebi et al., 2022) or through imposing theoretically motivated lateral recurrent connections (Tang et al., 2014, 2018) has shown benefits for the classification loss but was not geared to improve our understanding of how feedback or recurrence supports visual inference. On the other hand, there is increasing evidence supporting distinct phases of processing pertaining to perception and inference which parallels the notion of bottom-up versus top-down processing. Recent studies suggest that feedforward and feedback signaling operate through distinct "channels," enabling feedback signals to influence the forward processing without directly affecting the forward-propagated activity, including feedback interaction being more dominant during spontaneous, putatively internally generated activity periods (Semedo et al., 2022; Kreiman and Serre, 2020). Thus, implementing recursion

through feedforward and feedback-dominated phases, as we suggest in FFA, has an anatomical and physiological basis.

Algorithm 1 Training a simple three-layer network by FFA

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Internally generated perceptual experiences, such as hallucinations, dreams, and mental imagery evoke vivid experiences that mimic the perception of real-world stimuli. Neuroimaging studies demonstrate an overlap in neural activation between internally generated experiences and perception suggesting a shared neural substrate for generating and processing sensory information (Ganis et al., 2004; Pearson, 2019; Pearson et al., 2008; Abid et al., 2016; Dijkstra et al., 2017). While studies have provided insights into the brain regions involved in these phenomena, the neural mechanisms and computations underlying hallucination and imagery remain a topic of ongoing research and debate. One challenge is that hallucinations and imagery are subjective experiences that are difficult to objectively measure and study (Pearson et al., 2008). Additionally, the neural correlates of these experiences can vary across individuals and different types of hallucinations (Suzuki et al., 2017, 2023). Thus, computational modeling of how comparable phenomena can emerge in neural networks, without explicitly training for complex non-bio-plausible generative objective functions (Goodfellow et al., 2014), would help elucidate the neural mechanisms that may underpin these internally-generated perceptions.

2.2 Bio-plausible training

Our work also falls within the class of bio-plausible extensions of the original BP algorithm that try to avoid the weight transport problem (Grossberg, 1987). In an effort to mitigate the weight transport problem, (Lillicrap et al., 2016) developed an algorithm known as Feedback Alignment (FA). This algorithm employs random and fixed feedback connections to propagate errors, initiating a line of research that explored different variations of random, yet fixed, feedback connections for credit assignment (Nøkland, 2016; Crafton et al., 2019; Liao et al., 2015). Another line of work uses a strategy that still aims for BP-like symmetric weights while circumventing weight transport by designing a training objective for the feedback path that encourages symmetry (Akrout et al., 2019). For example, augmenting a reconstruction loss with weight decay will constrain solutions to the transpose in the linear setting (Kunin et al., 2019, 2020). However, our method differs in two key ways. First, those methods required invoking a separate gradient pass to train the feedback weights whereas we accomplish the training of feedback with the same feedforward network, thus adding no other hidden paths. Second, those methods explicitly seek symmetry whereas we do not constrain the stage-wise feedback weights, only their end-to-end goal. Our algorithm resembles the stage-wise reconstruction in target propagation (TP) which could also result in end-to-end propagation of latent representations back to inputs if noise at each local propagation step is sufficiently small (Bengio, 2014; Lee et al., 2014). Unlike the layerwise implementation of TP, our training approach is end-to-end, and we do not use any BP training on the penultimate layer of the discriminator.

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3 Feedback-Feedforward Alignment

During the training, BP uses a computational graph to backpropagate the error to the hidden layers (Figure 1). This computational graph is a linear neural network that is the transpose of the forward neural network and is constantly updated every time the forward weights are updated. FA and in general the family of the random feedback gradient path such as DFA, use random values and do not update the backward weights during the training. FFA in essence runs two FA algorithms to train the forward pass and backward pass alternatively. The FFA diagram in Figure 1 highlights its two distinguishing features: feedback (decoder) has an end-to-end goal and co-opting of the forward discriminator path (encoder) to train this decoder. A pseudo-code for a simple three-layer neural network to clarify the parameter updates in FFA is in algorithm 1.

Below, we compare how FFA operates on MNIST across two architectures (fully connected and convolutional) and on CIFAR10 using a ResNet architecture by directly reconstructing from the ten-dimensional discriminator output. For details on the architecture please refer to Supplementary material 8.1. For each architecture, we compare FFA to BP and feedback alignment (FA) (Lillicrap et al., 2016) training of a single objective (feedforward discrimination or an autoencoder loss) resulting in 5 control models: FFA, BP, FA, BP-AE, and FA-AE. The purpose of these controls was to verify that the properties of gradient descent on a single loss at the output does not trivially invoke reconstruction of input for example in BP-trained discriminative networks.

3.1 FFA achieves the co-optimization of discrimination and reconstruction

We highlight performance results on a convolutional architecture but also report results on a fully connected architecture. Convolutional architectures are potentially of greater interest because they are used for scaling up algorithms to larger datasets. Furthermore, convolutional architectures tend to expose greater performance gaps between BP and FA (Bartunov et al., 2018). FFA-trained networks achieved digit discrimination performance on par with FA but slightly below BP (Figure 2). However, on MNIST, reconstruction performance is exceedingly high. Critically, we were also interested in

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seeing if FFA could co-train, using only the discriminator weights for credit assignment, a digit reconstruction path. We found that FFA produced reconstruction on par with a BP-trained autoencoder for convolutional architectures while slightly lagging the autoencoder standard for reconstruction on fully connected architectures. Thus, within the same network, FFA co-optimizes two objectives at levels approaching the high individual standards set by a BP-trained discriminator and a BPtrained reconstructor (see Figure 2 and Figure Suppl. 7). In FFA, like FA, the feedforward and feedback weights aligned over training (Lillicrap et al., 2016), but only in FFA, alignment is useful for reconstruction, presumably because both paths are free to align to each other which breaks the random feedback constraint of FA. In examining discrimination versus reconstruction performance, these can be mutually exclusive. For example, single objective networks tend to improve along one axis or the other. In contrast, FFA-trained networks moved toward the top-right corner of the plot indicating co-optimization along both axes (Figure 2, scatter plot). As shown in Figure 2B for CIFAR10, FFA and FA both struggle to keep up with BP, so for the rest of the paper regarding inference, we focus on MNIST.

3.2 FFA induces robustness to image noise and adversarial attacks

Although in FFA training, we did not use any noise augmentation, as we show in this section, the network trained under FFA developed robustness to noise and adversarial attacks relative to the BP control. Previous works showed that BP networks are vulnerable to noise and highlighted that FA-trained networks are surprisingly robust (Goodfellow et al., 2015; Akrout, 2019). When pixel noise was used to degrade input characters, we found that FFA was more robust than BP conferring some of the same robustness seen in FA (Figure 2C). This advantage of FFA and FA over BP was also true for gradient-based white-box adversarial attacks (Figure Suppl. 9).

4 Flexible visual inference through recursion

While FFA is not explicitly a recurrent network, by coupling the feedforward and feedback pathways through mutual learning of dual, complementary losses, it may indirectly encourage compatibility in their inference processes. That is, we can run the network in a closed loop, passing ˆ x from the decoder back in as input to the encoder (replacing x ) (see Figure 1). In this section, we explore the capabilities of FFA in dealing with missing information (noise or occlusion) and in generation (visual imagery, hallucinations, or dreams). It is worth noting that FFA was not trained to perform any of these tasks and was only trained for discrimination and reconstruction of clean images, conditioned on this discrimination. The inference algorithm we use in this section relies on two main components:

iterations

iterations

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Occluded

recursion and noisiness of inference in each recursion. The algorithm was developed in (Kadkhodaie and Simoncelli, 2021) for denoising autoencoders based on Empirical Bayes Theorem (Miyasawa, 1961). Although FFA is not trained as a denoiser autoencoder (no noisy input was used during training), we hypothesized that since it exhibits robustness to noise properties, then the theory applies here and the algorithm can be adapted to draw effective inferences from the representation learned by FFA. We especially focused on the effect of the noisiness of inference to inform the computational role of noisy responses in actual biological neurons, as the utility of noisy responses remains largely unknown despite extensive active research (Echeveste and Lengyel, 2018; Findling and Wyart, 2021; McDonnell and Ward, 2011).

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As a first step toward future recurrent processing within FFA, we simply ran the network in a closed loop, passing ˆ x from the decoder back in as input to the encoder (replacing x ) (see Figure 1) and found that both discrimination and reconstruction performance is sustained over iterations similar to an autoencoder whereas BP and FA discriminators change over multiple closed-loop iterations - when their feedback path from training was used for generative inference in runtime - and thus would require a dynamic decoder to recover any performance (Figure 3).

4.2 Resolving occlusions

We occlude parts of an input image by a blank square and run the network inference. The assumption here is that the occluded image was briefly presented and during the inference, the original image is not accessible throughout inference. Figure 4 shows examples of completion of the pattern using FFA. Even though for high noise inference more iterations were needed, the generated samples do not reflect any superiority compared to low noise inference which took fewer iterations to converge.

4.3 Hallucination

Visual hallucinations refer to the experience of perceiving objects or events even when there is no corresponding sensory stimulation that would typically give rise to such perceptions. As mentioned above, the spontaneous activity in V1 is linked to the vividness of hallucinated patterns. Here, we let the FFA-trained network run through the inference algorithm starting from Gaussian noise at the input and adding noise in each iteration. As shown in Figure 5, when in the high noise regime ( β = 0 . 2 ), the quality of hallucinated digits is better compared to the low noise regime ( β = 0 . 99 , for the definition of β see Section 8.5). Given that the noise in the inference algorithm controls the convergence rate (Kadkhodaie and Simoncelli, 2021), these results suggest that the computational role of spontaneous activity in generating stronger hallucinated percepts may be the refinement of the hallucinated patterns.

4.4 Mental imagery

Visual mental imagery refers to the ability to create mental representations or pictures of visual information in the absence of actual sensory input (Pearson et al., 2015; Colombo, 2012). A key distinction between mental imagery and hallucinations is that mental imagery involves voluntarily creating mental images through imagination, while hallucinations are involuntary sensory perceptions. To implement the voluntary, top-down activation of a percept (e.g. '9'), we add the average activation pattern of the category in the latent layer to each recursion in the inference algorithm. Presumably, the brain has a recollection of the category which can be read out from memory during mental imagery. Figure 6 shows that as noise in the inference goes higher, so does the quality of the imagined digits.

5 Limitations

We acknowledge several limitations of the Feedback-Feedforward Alignment (FFA) framework in its current form. One key limitation is the difficulty of scaling FFA to larger datasets such as ImageNet. While we observed gaps in performance compared to classical backpropagation (BP) on CIFAR10, we found little difference compared to the Feedback Alignment (FA) baseline in discrimination performance on smaller datasets such as CIFAR10. However, it is yet possible that FFA could be more suitable at large scale for specific architectures, such as transformers, where layer sizes do not decrease towards the output layer. Scaling up FFA requires further theoretical and empirical exploration. Another limitation is related to the assessment of the generated inferences. Currently, the evaluation relies primarily on visual inspection. Although we included classifier accuracy reports for denoising, it assumes that perception arises solely from top activations and that bottom hierarchy activation (such as V1) does not directly contribute to perception. Enhancing the evaluation methodology to incorporate more objective measures and quantitative assessments of generated inferences would strengthen the framework. Furthermore, while FFA demonstrates a balance between discrimination performance, efficient learning, and robust recurrent inference, it is important to acknowledge that FFA may not fully capture all aspects of the biological brain. The

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framework represents a step towards understanding the brain's mechanisms but may still fall short in faithfully replicating the intricacies of neural processing such as the precise dynamics of neural responses or differences in tuning among feedforward and feedback neural subtypes, though it takes a step toward those directions. Overall, these limitations highlight the need for further research and development to address the scalability of FFA, refine evaluation methodologies, and gain deeper insights into the biological plausibility of the framework. Overcoming these limitations will pave the way for more effective and robust alternatives to BP, advancing the understanding and application of neural network training algorithms to neurobiology.

6 Conclusions

In moving beyond classical error backpropagation training of a single-objective, feedforward network, we have presented a feedforward-feedback algorithm that trains neural networks to achieve mutualistic optimization of dual objectives. Co-optimization provides attendant advantages: avoids weight transport, increases robustness to noise and adversarial attack, and gives feedback its own runtime function that allows closed-loop inference. Through our experiments, we demonstrated that the network trained using the FFA approach supports various visual inference tasks.

7 Broader Impacts

This work has broader impacts that include advancing our understanding of human perception, enhancing the robustness and performance of neural networks, helping to identify the emergence of closed-loop inference in larger networks for real-time applications, and potential implications for clinical research of mental disorders. By studying the neural mechanisms underlying visual perception, this research contributes to our understanding of natural and artificial vision.

Acknowledgments

T.T. is supported by NIH 1K99EY035357-01. This work was supported by NIH RF1DA056397, NSF 1707398, Gatsby Charitable Foundation GAT3708, NIH R34 (NS116739), Klingenstein-Simons fellowship, Sloan Foundation fellowship and Grossman-Kavli Scholar Award, as well as a NVIDIA GPU grant, and was performed using the Columbia Zuckerman Axon GPU cluster.

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Lillicrap, T. P. and Santoro, A. (2019a). Backpropagation through time and the brain. Curr. Opin. Neurobiol. , 55:82-89.

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8 Supplementary

8.1 Model architectures

For the experiment on a fully connected architecture, we used a 4-layer network with [1024, 256,256,10] neurons in each layer and ReLU non-linearity between layers. For the experiment on a convolutional architecture, we used a modified version of ResNet (He et al., 2015), where the last convolutional layer has the same number of channels as classes, and an adaptive average pooling operator is used to read out of each channel (see below). Since the last layer doesn't have any learnable parameters, the penultimate layer can be as large as desired which works fine for FFA. The convolutional architecture consists of 11 convolutional layers with 658,900 trainable parameters in total. For autoencoder controls (trained under BP or FA), we additionally trained a linear decoder on the activations of the penultimate layer to assess the linear separability of the representation learned by autoencoders.

Code is available at: https://github.com/toosi/Feedback_Feedforward_Alignment

8.2 More control networks: autoencoders

MNIST

CIFAR10

8.3 Alignment between feedback and feedforward

A) MNIST

B) CIFAR10

8.4 Robustness assessment

We added Gaussian noise with zero mean and varied the variance σ 2 = [0 . 0 , 0 . 2 , 0 . 4 , 0 . 8 , 1 . 0] to assess the robustness of models to input noise. We also performed a widely used white box adversarial attack Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2015). FGSM can be summarized by

where σ is the magnitude of the perturbation, J is the loss function and y ∗ is the label of x . While in BP this perturbation is computed through transposed forward parameters, for FFA and FA, we used their gradient pass parameters which are learned feedback and random feedback, respectively. We used a range of ϵ to cover the interval between 0 to 1.

8.5 Visual inference algorithm

We adapt the sampling algorithm developed in (Kadkhodaie and Simoncelli, 2021) to implement the visual inference in FFA-trained networks. β parameter which varies between 0 and 1 controls the proportion of injected noise ( β = 1 indicates no noise). The injected noise together with the gradient step size controls the number of iterations for convergence.

Algorithm 2 The core visual inference algorithm

(adapted with minimal modification from Kadkhodaie and Simoncelli (2021)))

parameters:

σ 0 , σ L , h 0 , β

initialization:

t = 1 , draw x 0 ∼ N (0 . 5 , σ 2 0 I )

F

: trained feedforward

B : trained feedback

end

8.6 Visual occlusion

High Noise

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors present a novel artificial neural network architecture which they relate to visual processing in the brain. In particular, the authors avoid the weight transport problem by proposing that feedback weights can be learned by optimising them to reconstruct the original input (autoencoder). The authors test the model on image datasets and show that the network can both discriminate and reconstruct the original image, as well as replicating biological visual phenomena with respect to resolving occlusions, hallucinations and imagination.\n\nSTRENGTHS:\n- the paper is generally well written\n- The proposed model architecture/learning rules are interesting and creative\n\nWEAKNESSES:\n- there is a distinct lack of specificity in the formal model description. Its illustration and algorithm is helpful, but I think the clarity of its exact computations would significantly benefit from equations\n- The authors do not address analytical aspects of their model. What types of solution should one expect in weight space compared to discrimination/auto-encoder only models? What is the extent of alignment compared to fixed random weights (feedback alignment). The authors write that \"co-optimizing discrimination and reconstruction objectives can lead to a mutualistic symbiotic interaction\", would it be possible to quantify this? Relately, are there any necessary conditions for this architecture to work, or where it'll break? for example, feedback alignment struggles with harder tasks, should one expect this with FFA?\n- The functional benefit of FFA is not very clear to me. For example, backprop still outperforms models even with noise on harder CIFAR task (fig 2), and why are several iterations necessary for discrimination if performance gets worse anyway (fig 3)? Is it not simpler just to train with backprop using two loss functions (discrimination and reconstruction), or is the idea that that's less bio-plausible?\n- I'm a little confused about the bio-plausibility of FFA: If I understand correctly, the forward weights W_f affect the activity in the post-synaptic neuron and this activity propagates forward, but the same activity doesn't propogate it the feedback pathway? How is this possible biologically?\n\nQUESTIONS:\n- are there no other computational models of top-down architectures to compare to? The authors cite works in experimental neuroscience which support top-down feedback during visual processing, do other explicit implementations not exist? e.g. are bidirectional variational autoencoders not related? (e.g. Kingma et al. Neurips 2016)\n- in the fig 1 inference box, should it not be delta_{t-1} >= delta*? Same for Algorithm 1. I'm not sure the figure caption text '* shows the desired value' is the right language, isn't delta* rather an imposed upper bound which we want to fall below?\n- Fig 1 caption last sentence: add full stop\n- line 99: \"Prior work on RNNs..was not geared to improve our understanding of how feedback or recurrence supports inference of visual details\": Could the authors clarify what is meant by 'visual details'?\n- For discrimination performance figures percentage signs should be added\n- Fig 2B: 'customised' is unclear. Are these fully connected feedforward nets?\n- line 132: 'Unlike the original TP, we do not constrain the intermediate stages'. What constraints are the authors referring to?\n- line 137: FA is used before it has been defined as feedback alignment\n- line 156: 'on MNIST, discrimination performance is exceedingly high'. What is meant here?\n- line 162: 'In FFA, like FA, the feedforward and feedback weights aligned over training'. Could the authors show this?\n- I advise the authors to use consistent references to supplementary figures (cf. line 162 vs 178). Moreover, remove the space between the figure number and subpanel (e.g. Figure 2C in line 177)\n- line 182: z has not been defined. Is this the random sample as in algorithm 1?\n- Figure 4: the meaning of the left-to-right in this selection of images is unclear. Is each x position a different iteration? which iteration? the difference between high/low noise also appears very small. The authors argue that low noise \"took fewer iterations to converge\" but I do not find it very clear from the figure (except the second shown iteration for the 5 example). Similarly, in Figure 6 the authors state that \"Figure 6 shows that as noise in the inference goes higher, so does the quality of the imagined digits\": this appears true for the 3 digit but not 5. Is there a way to quantify the quality over all digits?\n- In section 8.1 the model architecturers are not very readable. A schematic on even textual description would be easier to intepret. \n- Equation in section 8.3: is it not supposed to be epsilon in the equation, not sigma\n\nLIMITATIONS:\nThe authors do address some limitations, though as I say above I think it should also be highlighted in the paper the lack of theoretical study/support", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-06-29"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis article proposes and exploits a bio-plausible mechanism inspired from the Feedback Alignement : the Feedfback-Feedforward Alignement (FFA). Through a series of experiments (classification, robustness, denoising, generation…) the authors demonstrate that the FFA could be used for various applications.\n\nSTRENGTHS:\nI have found this paper original, as it proposes a solution that solves the weight transport problem in biology without imposing additional constraints such as weight symmetry. I have also found interesting the versatility of the FFA as well as recursion-like inference.\n\nWEAKNESSES:\nDespite the very interesting topic and idea, I was not convinced by the experimental parts (see more details below). The main point of this article is the  bio-plausibility of the method: this is a good motivation, but not a result in itself. I would have expected more results in line with biology/psychophysics (see Major Concern 2 ), to show that the proposed algorithms is a good model of the human cognition. Overall the article presents a series of experiments that lacks comparison with 1) similar model in machine learning (see Major Concern 1) and 2) biological data.\n\nMajor Concerns:\n1) The literature review is weak, especially in the field of machine learning. Plenty of algorithms have already been proposed to model human cognition using feedforward and feedback connections. Some of these works should have served as a benchmark in the proposed experiments. Here are more details:\n[1] proposed a deep-learning friendly implementation of the predictive coding algorithms (using backdrop). They are demonstrating that the prediction accuracy gets refined through time. It seems that the model you proposed has lowered accuracy through time (see Fig 3 A : the red curve tends to decrease whatever the noise). How do you explain that ? what’s the point of degrading performance through time ?\n[2] proposes a similar network to [1] but more in line with bio-plausible training. It shows refined denoising abilities thought time. How do you compare the FFA with those models ?\n[3], [4] have developed VAE-models based on predictive coding. Those are showing nice ‘hallucination’ and denoisiing abilities as well as good classification accuracy in challenging environment (noisy image…). Such models might serve as a good baseline to compare with.\n[5], [6] have published numerous articles to show that backprogation could be approximated (in a biology-friendly way) using the predictive coding model. The authors don’t even mention those works !\n[7] : have proposed a predictive coding model doing discrimination and classification in the same time. Such a network would have served as a good comparison for the FFA\n\n2) The main interest of the FFA seems to be its bio-plausibility, but the authors keep evaluating it as a machine learning model rather than a biological model. Most of the experiments the authors are showcasing actually show the weaknesses of the model rather than its advantage. Here are some exemples : \n* Fig 1 shows that FFA is not as good as a classical Autoencoder to reconstruct, and not as good as a BP feedforward model to classify… The only argument in favor of a FFA is that it could do both in the same time… but with lower performance… this is not very appealing (even more when we look at the CIFAR10 curve).\n* Fig 1c shows that FFA is not as good as FA for classification of noisy MNIST and not as good as the BP model for classifying noisy images..\n* Fig 3 shows that the more you let the iterative process going, the more the performance degrade… Then what’s the point oh having an iterative inference process ?\n\n\nI would suggest the authors to modify the way they are evaluating the model. For example why not testing if the FFA is sensitive to perceptual illusion (as in [8]), are why not comparing the number of iterative inference steps with the human reaction time ? Those comparison would tend to show that the FFA is a good model of human cognition.\n\n\n[1] : Wen, Haiguang, et al. \"Deep predictive coding network for object recognition.\" International conference on machine learning. PMLR, 2018.\\\n[2] : Choksi, Bhavin, et al. \"Predify: Augmenting deep neural networks with brain-inspired predictive coding dynamics.\" Advances in Neural Information Processing Systems 34 (2021): 14069-14083.\\\n[3] Marino, Joseph. \"Predictive coding, variational autoencoders, and biological connections.\" Neural Computation 34.1 (2022): 1-44.\\\n[4] Boutin, Victor, et al. \"Iterative VAE as a predictive brain model for out-of-distribution generalization.\" arXiv preprint arXiv:2012.00557 (2020).\\\n[5] Whittington, James CR, and Rafal Bogacz. \"An approximation of the error backpropagation algorithm in a predictive coding network with local hebbian synaptic plasticity.\" Neural computation 29.5 (2017): 1229-1262.\\\n[6] Millidge, Beren, Alexander Tschantz, and Christopher L. Buckley. \"Predictive coding approximates backprop along arbitrary computation graphs.\" Neural Computation 34.6 (2022): 1329-1368.\\\n[7] Tschantz, Alexander, et al. \"Hybrid predictive coding: Inferring, fast and slow.\" arXiv preprint arXiv:2204.02169 (2022).\\\n[8] : Pang, Zhaoyang, et al. \"Predictive coding feedback results in perceived illusory contours in a recurrent neural network.\" Neural Networks 144 (2021): 164-175.\n\nQUESTIONS:\n1) Could you detail a bit more the implementation of the FA and FFA algorithms. You are showing the losses in Figure 1, but it does not tell us how the FFA algorithm is trained. It would suggest to strongly clarify the paper to include a ‘pseudo code’ to explain the training procedure ? \n2) The legend of the Figure 4 is not clear enough ! What are the rows 3 and 4 ? Is that the type of noise you apply ? The reconstruction ? \n3) In Figure 5 : What is the difference between the low noise and the high noise setting ? Perceptually speaking, the noise seems to be so high in both cases that it is very hard to make the difference between both. \n4) Have you controlled for the number of parameters of all compared networks ? \n\nMinor Typo : \nL 53 : critiqued —> criticized\n\nLIMITATIONS:\nThe authors have correctly discussed the limitation part. I considered that small black and white dataset is a limitation ONLY if you compare yourself with machine learning models (which is what the authors are doing). On my opinion, this is not a limitation anymore if you leverage those ’simple’ datasets to model and probe the human cognition.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 2, "DATE": "2023-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper presents a new neural network architecture called Feedback Alignment (FFA) that demonstrates the effectiveness of co-optimizing classification and reconstruction tasks on MNIST and CIFAR10 datasets. FFA uses a goal-driven feedback pathway to alleviate weight transport problems encountered in traditional backpropagation (BP) methods, enhancing the bio-plausibility of the learning algorithm. The alignment mechanism in FFA endows feedback connections with emergent visual inference functions, including denoising, resolving occlusions, hallucination, and imagination. The study presents FFA as a promising proof-of-concept for the mechanisms underlying how feedback connections in the visual cortex support flexible visual functions and contributes to the broader field of visual inference underlying perceptual phenomena.\n\nSTRENGTHS:\nS1. This paper proposes a novel strategy to train neural networks to co-optimize for two objective functions based on the role of feedback connections in the brain, and leverages the credit assignment computational graph as feedback connections during learning and inference\nS2. FFA for discrimination and reconstruction respectively induces noise robustness, and can flexibly support an array of versatile visual inferences such as resolving occlusion\nS3. This paper is well written overall.\n\nWEAKNESSES:\nW1. Although the paper claims that FFA is bio-plausible, the discrimination and reconstruction in biological system are not processed through feedforward and feedback pathways.\nW2. The datasets for test are way too simple and small.\nW3. They reason for choosing discrimination and reconstruction as the tasks is not clear, as the visual system has multiple abilities.\n\nQUESTIONS:\nSee the weaknesses stated above and also the following questions.\nQ1. Please explain why FFA is bio-plausible more clearly.\nQ2. Please broaden the datasets to validate the superior performance of FFA.\nQ3. Some details should be added, such as how the noises are added, why choose discrimination and reconstruction as the training tasks.\n\nLIMITATIONS:\nWhile the idea is interesting, more explanations of the choices and experimental details should be added.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-05"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper explores the intriguing subject of integrating feedback connections into neural networks during both learning and inference stages, drawing inspiration from the brain. This study has the potential to significantly advance artificial intelligence (AI). Feedback connections are a topic of interest in both theoretical and experimental neuroscience, and establishing a link between neuroscience and AI research could mark a major advancement in both fields. Therefore, the motivation behind this study is commendable.\n\nHowever, despite its compelling premise, the paper has issues with the presentation of the algorithm, its novelty, and the explanation for its superior performance over standard auto-encoders. Specifically, Figure 1 and the corresponding explanation in the main body of the text are brief and do not provide clear insight into how their system operates. Figure 1C suggests that the feedforward weights are trained using Feedback Alignment (FA) and not Backpropagation (BP) at any stage or layer of the network, yet this point is not explicitly clarified.\n\nThe authors also neglected to specify whether noise was introduced into the hidden layers to replicate the inherent noise in neurons, despite stating that no noise was added to augment the data during training. Additionally, during the inference stage, the reconstruction is updated and passed as an input in the forward pass, going through multiple iterations. However, the paper does not provide guidelines on how and when this iterative process should cease to deliver a final inference result.\n\nIn Figure 3A, there is a noticeable degradation in performance and reconstruction as a function of iterations. This degradation is less pronounced than with the FA-autoencoder or BP-autoencoder, but its presence is still problematic.\n\nA significant point of confusion is the authors' claim that training their architecture with FA versus BP in both forward and feedback processes would lead to better generalization. This claim is not sufficiently explained in the paper. The scalability of the proposed method is another major concern. Like other FA training methods, the presented approach appears incapable of scaling to more complex problems, such as ImageNET, which is a significant limitation. Considering that there is no explanation provided for why their algorithm is more robust to noise in simpler problems like MNIST, the lack of scalability is a particular concern.\n\nFurthermore, the claim of adversarial robustness is not adequately substantiated, as it should include a more comprehensive set of white box attacks. Since 2015, numerous studies have shown that networks improving robustness to the Fast Gradient Sign Method (FGSM) are not necessarily robust against stronger attacks, such as boundary-based optimization methods.\n\nIn summary, while the paper delves into an intriguing research area and is well-motivated, it lacks clarity regarding the proposed algorithm and its novelty compared to standard autoencoders. Additional concerns include the paper's omission of details about potential noise introduced in hidden layers, and the lack of a clear process for terminating the iterative inference stage. Additionally, the authors' assertion of better generalization through FA versus BP is not clearly explained. Issues of scalability and incomplete testing for adversarial robustness also cast doubt on the practicality and comprehensive effectiveness of the proposed method. If these issues are clearly addressed in a revision, this paper could contribute significantly to AI research.\"\n\nSTRENGTHS:\nImportant problem \nInteresting idea to train both forward and feedback weights with FA\n\nWEAKNESSES:\nNeed more clarity \nMore explanation why training with FA works better for generalization than BP\nLack scalability to more complex problems \nNeeds stronger white box attacks to substantiate claims about robustness to adversarial attacks\n\nQUESTIONS:\nExplain the algorithm much better and compare to previous work like auto-encoders. Provide theoretical or intuitive explanation why training this particular architecture with FA is better than BP. Was not clear if noise is introduced in the hidden layers.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-08"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes a bio-inspired computer vision algorithm for classification that includes feedback and aims to use alignment rather than backprop for training the models of feedforward and feedback.\n\nSTRENGTHS:\nThe paper provides a novel idea for including feedback (or recurrence) in visual classification that would be interesting for neuroscientists to investigate further.\nThe emerging noise robustness is a big strength for this model and confirms a lot of neuro theories about feedback.\n\nWEAKNESSES:\nThe explanation of the methods is severely inadequate. The training phase is not well explained. I usually prefer to have a visual explanation over equations but in this case I believe that the learning phase, the equations for the learning process should be included as well especially given that there are variables and paramters that are included without explanation of how they contribute to the process in figure 1. The supplements also shows two separate networks for feedforward and feedback and the alignment process should be included.\n\nThe literature review is also not proper and misses many important publications in the field, for example:\n- Spoerer et al 2017: Recurrent Convolutional Neural Networks: A Better Model of Biological Object Recognition\n- Abdelhack and Kamitani 2018 Sharpening of hierarchical visual feature representations of blurred images\n- Huang et al. 2019 Brain-inspired Robust Vision using Convolutional Neural Networks with Feedback\n\nThe first analysis shows performance on both CIFAR and MNIST while all the subsequent analyses are only including MNIST. This makes me wonder if the performance on CIFAR is not as impressive as it was not included even in supplementary materials. I think the reader would appreciate full transparency on this.\n\nIt was unclear why training on Imagenet would not be feasible. Is it a computing problem or other?\n\nMinor: p 5 line 156 typo: discrimination -> reconstruction\n\nQUESTIONS:\nAre the codes going to be released?\n\nLIMITATIONS:\nNA", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-17"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors propose a mechanism for biologically plausible learning in visual circuits that can endow the system with additional epiphenomenal capabilities that resemble phenomena humans are known to exhibit. The mechanism resembles feedback alignment, where the weight transport problem is resolved by substituting different feedback weights in the backward pass instead of the transpose of the forward weights. In contrast to previous approaches that dynamically train the backward weights to achieve symmetry through local learning, the authors suggest concurrently training the feedback weights to reconstruct the system's visual inputs based exclusively on activations in the final latent layer. They then show that these feedback weights can be used for a wide variety of additional tasks (similar to Kadkhodaie & Simoncelli 2021), including image generation, conditional image generation based on a weakly clamped latent layer, and denoising.\n\nSTRENGTHS:\nThe concept for the paper is a very strong one: it is a major failing of the 'feedforward paradigm' of visual cortex modeling that it cannot account for capabilities and phenomena the visual system is known to exhibit, including mental imagery, hallucination, and to some extent de-occlusion (e.g. filling in the visual blind spot caused by the optic nerve). That a network can be shown to accomplish this through exclusively through a reasonably local learning algorithm (a feedback alignment variant) is very impressive. Furthermore, the notion that the feedback pathway could have additional functional utility beyond exclusively providing credit assignment signals for learning is a much-needed perspective for the biologically plausible plasticity field, especially the subfield that is primarily focused on variants of the feedback alignment algorithm.\n\nWEAKNESSES:\nOn the theory of learning side of things, the paper falls short in several ways.\n\nFirst and foremost, the authors do not actually explain their learning algorithm in the detail that would be required to reproduce it. The authors should provide detailed math explaining the actual steps required to implement the proposed rule at each layer of their system, as well as potentially pseudocode. This is required for me to increase my confidence and maintain my score--what I imagine the authors to be doing based on my own understanding of the feedback alignment algorithm is a perfectly viable approach, but it's not possible to confirm this based on the text itself. For reproducibility purposes, the authors should also commit to providing a github link to their code implementation of the model.\n\nSecond, (as with the original FA paper) it is not obvious why the authors' approach works at all. It is possible to draw some loose similarities between the proposed algorithm and target propagation, but the authors provide no mathematics that explain why the proposed algorithm should actually produce learning. Given that the empirical performance results begin to drop off steeply for CIFAR10 (and presumably fail entirely for imagenet), the convergence properties of this algorithm deserve serious attention.\n\nFurthermore, the authors do not perform any form of direct comparison to alternative biologically plausible algorithms that would be expected to show similar results. In particular, both the predictive coding (PC) approach and the Wake-Sleep algorithm should show similar effects, and energy-based models like the Boltzmann machine, PC, and even Hopfield networks have a long history of demonstrating pattern completion effects and image generation on simple datasets like binarized MNIST. The paper would benefit immensely from a discussion of the experimentally testable predictions that are specific to this model and not to other approaches, as well as a discussion of the factors that make this method conform to known experimental data more than these methods.\n\nLastly, the inpainting effects produced in this paper are qualitatively worse than those observed in Kadkhodaie & Simoncelli 2021. The paper would benefit from an empirical comparison to the model actually used in this paper, or at least a discussion of the similarities & differences, as well as why we should expect worse results here.\n\nQUESTIONS:\nDo multilayer perceptron networks trained on these tasks show qualitatively similar inpainting and generation? The authors say that the MLP results are present, but I've been unable to find them in the text or supplemental. Networks that do not have within-layer weight sharing are of more interest from the perspective of biological plausibility, and while I believe that an MLP should produce similar results, it would be good to have visual confirmation.\n\nCould you discuss the biological plausibility of BatchNorm, which appears to be used in all tested network architectures? Have similar results been obtained in the absence of BatchNorm?\n\nLIMITATIONS:\nYes, the authors do adequately discuss the limitations of their work.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-18"}