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Deep Learning/Recurrent Networks

Lukas Eisenmann, Zahra Monfared, Niclas Göring, Daniel Durstewitz

Recurrent neural networks (RNNs) are popular machine learning tools for modeling and forecasting sequential data and for inferring dynamical systems (DS) from observed time series. Concepts from DS theory (DST) have variously been used to further our understanding of both, how trained RNNs solve complex tasks, and the training process itself. Bifurcations are particularly important phenomena in DS, including RNNs, that refer to topological (qualitative) changes in a system's dynamical behavior as one or more of its parameters are varied. Knowing the bifurcation structure of an RNN will thus allow to deduce many of its computational and dynamical properties, like its sensitivity to parameter variations or its behavior during training. In particular, bifurcations may account for sudden loss jumps observed in RNN training that could severely impede the training process. Here we first mathematically prove for a particular class of ReLU-based RNNs that certain bifurcations are indeed associated with loss gradients tending toward infinity or zero. We then introduce a novel heuristic algorithm for detecting all fixed points and $k$-cycles in ReLU-based RNNs and their existence and stability regions, hence bifurcation manifolds in parameter space. In contrast to previous numerical algorithms for finding fixed points and common continuation methods, our algorithm provides $\textit{exact}$ results and returns fixed points and cycles up to high orders with surprisingly good scaling behavior. We exemplify the algorithm on the analysis of the training process of RNNs, and find that the recently introduced technique of generalized teacher forcing completely avoids certain types of bifurcations in training. Thus, besides facilitating the DST analysis of trained RNNs, our algorithm provides a powerful instrument for analyzing the training process itself.

Deep Learning/Recurrent Networks

Sean McLeish, Long Tran-Thanh

Scope of Reproducibility:In this report, we aim to validate the claims of Bansal et al. These are that the recurrent architecture presented, with skip connections and a progressive loss function, prevent the original problem being forgotten or corrupted during processing allowing for the recurrent module to be applied indefinitely and that this architecture avoids the overthinking trap. We use both code released by the authors and newly developed to recreate many results presented in the paper. Additionally, we present analysis of the newly introduced alpha hyperparameter and investigate interesting perturbation behaviour of prefix sums models. Further, we conduct a hyperparameter search and provide an analysis of the Asymptotic Alignment scores of the models presented.Methodology:We use the PyTorch code released by the authors to replicate accuracy experiments. We then, independently, develop our own PyTorchFI to replicate perturbation experiments presented by Bansal et al. Overall, providing a replication of all results shown in the main body of the paper. We then extend these results, providing an analysis of the alpha hyperparameter, analysis of perturbation recovery, Asymptotic Alignment scores and a hyperparameter search. We used both a Nvidia RTX 2080Ti GPU and sets of three NVIDIA Quadro RTX6000 GPUs, taking a total of 982.2 GPU hours to create all results presented in the main body of this report.Results:We verify the authors' claims by replicating the experiments presented by Bansal et al. All of our experiments show identical results to the ones presented in the paper, apart from perturbation testing for which we provide an additional in depth analysis. We also provide an analysis of the new alpha hyperparameter and a hyperparameter search.What was easy:The code provided by Bansal et al gave clear instructions on how to use it, along with pretrained models being available for all problems.What was difficult:Chess models required a considerable amount of time to train, putting a drain on resources. Also, code for reproducing perturbation results was not available so this had to developed from scratch.Communication with original authors:We had good communication with the original authors, both emailing and meeting online.

Deep Learning/Recurrent Networks

Rainer Engelken

Training recurrent neural networks (RNNs) remains a challenge due to the instability of gradients across long time horizons, which can lead to exploding and vanishing gradients. Recent research has linked these problems to the values of Lyapunov exponents for the forward-dynamics, which describe the growth or shrinkage of infinitesimal perturbations. Here, we propose gradient flossing, a novel approach to tackling gradient instability by pushing Lyapunov exponents of the forward dynamics toward zero during learning. We achieve this by regularizing Lyapunov exponents through backpropagation using differentiable linear algebra. This enables us to "floss" the gradients, stabilizing them and thus improving network training. We show that gradient flossing controls not only the gradient norm but also the condition number of the long-term Jacobian, facilitating multidimensional error feedback propagation. We find that applying gradient flossing before training enhances both the success rate and convergence speed for tasks involving long time horizons.For challenging tasks, we show that gradient flossing during training can further increase the time horizon that can be bridged by backpropagation through time. Moreover, we demonstrate the effectiveness of our approach on various RNN architectures and tasks of variable temporal complexity. Additionally, we provide a simple implementation of our gradient flossing algorithm that can be used in practice. Our results indicate that gradient flossing via regularizing Lyapunov exponents can significantly enhance the effectiveness of RNN training and mitigate the exploding and vanishing gradients problem.

Deep Learning/Recurrent Networks

Haggai Agmon, Yoram Burak

The storage of continuous variables in working memory is hypothesized to be sustained in the brain by the dynamics of recurrent neural networks (RNNs) whose steady states form continuous manifolds. In some cases, it is thought that the synaptic connectivity supports multiple attractor manifolds, each mapped to a different context or task. For example, in hippocampal area CA3, positions in distinct environments are represented by distinct sets of population activity patterns, each forming a continuum. It has been argued that the embedding of multiple continuous attractors in a single RNN inevitably causes detrimental interference: quenched noise in the synaptic connectivity disrupts the continuity of each attractor, replacing it by a discrete set of steady states that can be conceptualized as lying on local minima of an abstract energy landscape. Consequently, population activity patterns exhibit systematic drifts towards one of these discrete minima, thereby degrading the stored memory over time. Here we show that it is possible to dramatically attenuate these detrimental interference effects by adjusting the synaptic weights. Synaptic weight adjustment are derived from a loss function that quantifies the roughness of the energy landscape along each of the embedded attractor manifolds. By minimizing this loss function, the stability of states can be dramatically improved, without compromising the capacity.

Deep Learning/Recurrent Networks

Jimmy Smith, Shalini De Mello, Jan Kautz, Scott Linderman, Wonmin Byeon

Effectively modeling long spatiotemporal sequences is challenging due to the need to model complex spatial correlations and long-range temporal dependencies simultaneously. ConvLSTMs attempt to address this by updating tensor-valued states with recurrent neural networks, but their sequential computation makes them slow to train. In contrast, Transformers can process an entire spatiotemporal sequence, compressed into tokens, in parallel. However, the cost of attention scales quadratically in length, limiting their scalability to longer sequences. Here, we address the challenges of prior methods and introduce convolutional state space models (ConvSSM) that combine the tensor modeling ideas of ConvLSTM with the long sequence modeling approaches of state space methods such as S4 and S5. First, we demonstrate how parallel scans can be applied to convolutional recurrences to achieve subquadratic parallelization and fast autoregressive generation. We then establish an equivalence between the dynamics of ConvSSMs and SSMs, which motivates parameterization and initialization strategies for modeling long-range dependencies. The result is ConvS5, an efficient ConvSSM variant for long-range spatiotemporal modeling. ConvS5 significantly outperforms Transformers and ConvLSTM on a long horizon Moving-MNIST experiment while training $3\times$ faster than ConvLSTM and generating samples $400\times$ faster than Transformers. In addition, ConvS5 matches or exceeds the performance of state-of-the-art methods on challenging DMLab, Minecraft and Habitat prediction benchmarks and enables new directions for modeling long spatiotemporal sequences.

Deep Learning/Recurrent Networks

Talia Konkle, George Alvarez

Given the rich visual information available in each glance, humans can internally direct their visual attention to enhance goal-relevant information---a capacity often absent in standard vision models. Here we introduce cognitively and biologically-inspired long-range modulatory pathways to enable `cognitive steering’ in vision models. First, we show that models equipped with these feedback pathways naturally show improved image recognition, adversarial robustness, and increased brain alignment, relative to baseline models. Further, these feedback projections from the final layer of the vision backbone provide a meaningful steering interface, where goals can be specified as vectors in the output space. We show that there are effective ways to steer the model that dramatically improve recognition of categories in composite images of multiple categories, succeeding where baseline feed-forward models without flexible steering fail. And, our multiplicative modulatory motif prevents rampant hallucination of the top-down goal category, dissociating what the model is looking for, from what it is looking at. Thus, these long-range modulatory pathways enable new behavioral capacities for goal-directed visual encoding, offering a flexible communication interface between cognitive and visual systems.

Deep Learning/Recurrent Networks

Joseph Costello, Hisham Temmar, Luis Cubillos, Matthew Mender, Dylan Wallace, Matt Willsey, Parag Patil, Cynthia Chestek

Brain-machine interfaces (BMIs) can restore motor function to people with paralysis but are currently limited by the accuracy of real-time decoding algorithms. Recurrent neural networks (RNNs) using modern training techniques have shown promise in accurately predicting movements from neural signals but have yet to be rigorously evaluated against other decoding algorithms in a closed-loop setting. Here we compared RNNs to other neural network architectures in real-time, continuous decoding of finger movements using intracortical signals from nonhuman primates. Across one and two finger online tasks, LSTMs (a type of RNN) outperformed convolutional and transformer-based neural networks, averaging 18% higher throughput than the convolution network. On simplified tasks with a reduced movement set, RNN decoders were allowed to memorize movement patterns and matched able-bodied control. Performance gradually dropped as the number of distinct movements increased but did not go below fully continuous decoder performance. Finally, in a two-finger task where one degree-of-freedom had poor input signals, we recovered functional control using RNNs trained to act both like a movement classifier and continuous decoder. Our results suggest that RNNs can enable functional real-time BMI control by learning and generating accurate movement patterns.

Deep Learning/Recurrent Networks

Guan Wang, Yuhao Sun, Sijie Cheng, Sen Song

Recurrent spiking neural networks (RSNNs) hold great potential for advancing artificial general intelligence, as they draw inspiration from the biological nervous system and show promise in modeling complex dynamics.However, the widely-used surrogate gradient-based training methods for RSNNs are inherently inaccurate and unfriendly to neuromorphic hardware.To address these limitations, we propose the evolving connectivity (EC) framework, an inference-only method for training RSNNs.The EC framework reformulates weight-tuning as a search into parameterized connection probability distributions, and employs Natural Evolution Strategies (NES) for optimizing these distributions.Our EC framework circumvents the need for gradients and features hardware-friendly characteristics, including sparse boolean connections and high scalability.We evaluate EC on a series of standard robotic locomotion tasks, where it achieves comparable performance with deep neural networks and outperforms gradient-trained RSNNs, even solving the complex 17-DoF humanoid task.Additionally, the EC framework demonstrates a two to three fold speedup in efficiency compared to directly evolving parameters.By providing a performant and hardware-friendly alternative, the EC framework lays the groundwork for further energy-efficient applications of RSNNs and advances the development of neuromorphic devices.Our code is publicly available at https://github.com/imoneoi/EvolvingConnectivity.

Deep Learning/Recurrent Networks

Niranjan Damera Venkata, Chiranjib Bhattacharyya

Deep neural networks (DNNs) have recently emerged as a powerful paradigm for solving Markovian optimal stopping problems. However, a ready extension of DNN-based methods to non-Markovian settings requires significant state and parameter space expansion, manifesting the curse of dimensionality. Further, efficient state-space transformations permitting Markovian approximations, such as those afforded by recurrent neural networks (RNNs), are either structurally infeasible or are confounded by the curse of non-Markovianity. Considering these issues, we introduce, for the first time, an optimal stopping policy gradient algorithm (OSPG) that can leverage RNNs effectively in non-Markovian settings by implicitly optimizing value functions without recursion, mitigating the curse of non-Markovianity. The OSPG algorithm is derived from an inference procedure on a novel Bayesian network representation of discrete-time non-Markovian optimal stopping trajectories and, as a consequence, yields an offline policy gradient algorithm that eliminates expensive Monte Carlo policy rollouts.

Deep Learning/Recurrent Networks

Jishnu Ray Chowdhury, Cornelia Caragea

Binary Balanced Tree Recursive Neural Networks (BBT-RvNNs) enforce sequence composition according to a preset balanced binary tree structure. Thus, their non-linear recursion depth (which is the tree depth) is just $\log_2 n$ ($n$ being the sequence length). Such logarithmic scaling makes BBT-RvNNs efficient and scalable on long sequence tasks such as Long Range Arena (LRA). However, such computational efficiency comes at a cost because BBT-RvNNs cannot solve simple arithmetic tasks like ListOps. On the flip side, RvNN models (e.g., Beam Tree RvNN) that do succeed on ListOps (and other structure-sensitive tasks like formal logical inference) are generally several times more expensive (in time and space) than even Recurrent Neural Networks. In this paper, we introduce a novel framework --- Recursion in Recursion (RIR) to strike a balance between the two sides - getting some of the benefits from both worlds. In RIR, we use a form of two-level nested recursion - where the outer recursion is a $k$-ary balanced tree model with another recursive model (inner recursion) implementing its cell function. For the inner recursion, we choose Beam Tree RvNNs. To adjust Beam Tree RvNNs within RIR we also propose a novel strategy of beam alignment. Overall, this entails that the total recursive depth in RIR is upper-bounded by $k \log_k n$. Our best RIR-based model is the first model that demonstrates high ($\geq 90\%$) length-generalization performance on ListOps while at the same time being scalable enough to be trainable on long sequence inputs from LRA (it can reduce the memory usage of the original Beam Tree RvNN by hundreds of times). Moreover, in terms of accuracy in the LRA language tasks, it performs competitively with Structured State Space Models (SSMs) without any special initialization - outperforming Transformers by a large margin. On the other hand, while SSMs can marginally outperform RIR on LRA, they (SSMs) fail to length-generalize on ListOps. Our code is available at: https://github.com/JRC1995/BeamRecursionFamily/

Deep Learning/Recurrent Networks

Jishnu Ray Chowdhury, Cornelia Caragea

Beam Tree Recursive Neural Network (BT-RvNN) was recently proposed as an extension of Gumbel Tree RvNN and it was shown to achieve state-of-the-art length generalization performance in ListOps while maintaining comparable performance on other tasks. However, although better than previous approaches in terms of memory usage, BT-RvNN can be still exorbitantly expensive. In this paper, we identify the main bottleneck in BT-RvNN's memory usage to be the entanglement of the scorer function and the recursive cell function. We propose strategies to remove this bottleneck and further simplify its memory usage. Overall, our strategies not only reduce the memory usage of BT-RvNN by $10-16$ times but also create a new state-of-the-art in ListOps while maintaining similar performance in other tasks. In addition, we also propose a strategy to utilize the induced latent-tree node representations produced by BT-RvNN to turn BT-RvNN from a sentence encoder of the form $f:\mathbb{R}^{n \times d} \rightarrow \mathbb{R}^{d}$ into a token contextualizer of the form $f:\mathbb{R}^{n \times d} \rightarrow \mathbb{R}^{n \times d}$. Thus, our proposals not only open up a path for further scalability of RvNNs but also standardize a way to use BT-RvNNs as another building block in the deep learning toolkit that can be easily stacked or interfaced with other popular models such as Transformers and Structured State Space models. Our code is available at the link: https://github.com/JRC1995/BeamRecursionFamily.

Deep Learning/Recurrent Networks

Nicolas Zucchet, Robert Meier, Simon Schug, Asier Mujika, Joao Sacramento

Online learning holds the promise of enabling efficient long-term credit assignment in recurrent neural networks. However, current algorithms fall short of offline backpropagation by either not being scalable or failing to learn long-range dependencies. Here we present a high-performance online learning algorithm that merely doubles the memory and computational requirements of a single inference pass. We achieve this by leveraging independent recurrent modules in multi-layer networks, an architectural motif that has recently been shown to be particularly powerful. Experiments on synthetic memory problems and on the challenging long-range arena benchmark suite reveal that our algorithm performs competitively, establishing a new standard for what can be achieved through online learning. This ability to learn long-range dependencies offers a new perspective on learning in the brain and opens a promising avenue in neuromorphic computing.