Topological Neural Discrete Representation Learning à la Kohonen

Unsupervised learning of discrete representations from continuous ones in neural networks (NNs) is the cornerstone of several applications today. Vector Quantisation (VQ) has become a popular method to achieve such representations, in particular in the context of generative models such as Variational Auto-Encoders (VAEs). For example, the exponential moving average-based VQ (EMA-VQ) algorithm is often used. Here we study an alternative VQ algorithm based on the learning rule of Kohonen Self-Organising Maps (KSOMs; 1982) of which EMA-VQ is a special case. In fact, KSOM is a classic VQ algorithm which is known to offer two potential benefits over the latter: empirically, KSOM is known to perform faster VQ, and discrete representations learned by KSOM form a topological structure on the grid whose nodes are the discrete symbols, resulting in an artificial version of the topographic map in the brain. We revisit these properties by using KSOM in VQ-VAEs for image processing. In particular, our experiments show that, while the speed-up compared to well-configured EMA-VQ is only observable at the beginning of training, KSOM is generally much more robust than EMA-VQ, e.g., w.r.t. the choice of initialisation schemes. Our code is public.

Learning to Control Rapidly Changing Synaptic Connections: An Alternative Type of Memory in Sequence Processing Artificial Neural Networks

Short-term memory in standard, general-purpose, sequence-processing recurrent neural networks (RNNs) is stored as activations of nodes or "neurons." Generalising feedforward NNs to such RNNs is mathematically straightforward and natural, and even historical: already in 1943, McCulloch and Pitts proposed this as a surrogate to "synaptic modifications" (in effect, generalising the Lenz-Ising model, the first non-sequence processing RNN architecture of the 1920s). A lesser known alternative approach to storing short-term memory in "synaptic connections" -- by parameterising and controlling the dynamics of a context-sensitive time-varying weight matrix through another NN -- yields another "natural" type of short-term memory in sequence processing NNs: the Fast Weight Programmers (FWPs) of the early 1990s. FWPs have seen a recent revival as generic sequence processors, achieving competitive performance across various tasks. They are formally closely related to the now popular Transformers. Here we present them in the context of artificial NNs as an abstraction of biological NNs -- a perspective that has not been stressed enough in previous FWP work. We first review aspects of FWPs for pedagogical purposes, then discuss connections to related works motivated by insights from neuroscience.

CTL++: Evaluating Generalization on Never-Seen Compositional Patterns of Known Functions, and Compatibility of Neural Representations

Well-designed diagnostic tasks have played a key role in studying the failure of neural nets (NNs) to generalize systematically. Famous examples include SCAN and Compositional Table Lookup (CTL). Here we introduce CTL++, a new diagnostic dataset based on compositions of unary symbolic functions. While the original CTL is used to test length generalization or productivity, CTL++ is designed to test systematicity of NNs, that is, their capability to generalize to unseen compositions of known functions. CTL++ splits functions into groups and tests performance on group elements composed in a way not seen during training. We show that recent CTL-solving Transformer variants fail on CTL++. The simplicity of the task design allows for fine-grained control of task difficulty, as well as many insightful analyses. For example, we measure how much overlap between groups is needed by tested NNs for learning to compose. We also visualize how learned symbol representations in outputs of functions from different groups are compatible in case of success but not in case of failure. These results provide insights into failure cases reported on more complex compositions in the natural language domain. Our code is public.

Images as Weight Matrices: Sequential Image Generation Through Synaptic Learning Rules

Work on fast weight programmers has demonstrated the effectiveness of key/value outer product-based learning rules for sequentially generating a weight matrix (WM) of a neural net (NN) by another NN or itself. However, the weight generation steps are typically not visually interpretable by humans, because the contents stored in the WM of an NN are not. Here we apply the same principle to generate natural images. The resulting fast weight painters (FPAs) learn to execute sequences of delta learning rules to sequentially generate images as sums of outer products of self-invented keys and values, one rank at a time, as if each image was a WM of an NN. We train our FPAs in the generative adversarial networks framework, and evaluate on various image datasets. We show how these generic learning rules can generate images with respectable visual quality without any explicit inductive bias for images. While the performance largely lags behind the one of specialised state-of-the-art image generators, our approach allows for visualising how synaptic learning rules iteratively produce complex connection patterns, yielding human-interpretable meaningful images. Finally, we also show that an additional convolutional U-Net (now popular in diffusion models) at the output of an FPA can learn one-step "denoising" of FPA-generated images to enhance their quality. Our code is public.

Neural Differential Equations for Learning to Program Neural Nets Through Continuous Learning Rules

Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have also been used to derive theoretical results for NN learning rules, e.g., the famous connection between Oja's rule and principal component analysis. Such rules are typically expressed as additive iterative update processes which have straightforward ODE counterparts. Here we introduce a novel combination of learning rules and Neural ODEs to build continuous-time sequence processing nets that learn to manipulate short-term memory in rapidly changing synaptic connections of other nets. This yields continuous-time counterparts of Fast Weight Programmers and linear Transformers. Our novel models outperform the best existing Neural Controlled Differential Equation based models on various time series classification tasks, while also addressing their scalability limitations. Our code is public.

Unsupervised Learning of Temporal Abstractions with Slot-based Transformers

The discovery of reusable sub-routines simplifies decision-making and planning in complex reinforcement learning problems. Previous approaches propose to learn such temporal abstractions in a purely unsupervised fashion through observing state-action trajectories gathered from executing a policy. However, a current limitation is that they process each trajectory in an entirely sequential manner, which prevents them from revising earlier decisions about sub-routine boundary points in light of new incoming information. In this work we propose SloTTAr, a fully parallel approach that integrates sequence processing Transformers with a Slot Attention module and adaptive computation for learning about the number of such sub-routines in an unsupervised fashion. We demonstrate how SloTTAr is capable of outperforming strong baselines in terms of boundary point discovery, even for sequences containing variable amounts of sub-routines, while being up to 7x faster to train on existing benchmarks.

The Dual Form of Neural Networks Revisited: Connecting Test Time Predictions to Training Patterns via Spotlights of Attention

Linear layers in neural networks (NNs) trained by gradient descent can be expressed as a key-value memory system which stores all training datapoints and the initial weights, and produces outputs using unnormalised dot attention over the entire training experience. While this has been technically known since the '60s, no prior work has effectively studied the operations of NNs in such a form, presumably due to prohibitive time and space complexities and impractical model sizes, all of them growing linearly with the number of training patterns which may get very large. However, this dual formulation offers a possibility of directly visualizing how an NN makes use of training patterns at test time, by examining the corresponding attention weights. We conduct experiments on small scale supervised image classification tasks in single-task, multi-task, and continual learning settings, as well as language modelling, and discuss potentials and limits of this view for better understanding and interpreting how NNs exploit training patterns. Our code is public.

A Modern Self-Referential Weight Matrix That Learns to Modify Itself

The weight matrix (WM) of a neural network (NN) is its program. The programs of many traditional NNs are learned through gradient descent in some error function, then remain fixed. The WM of a self-referential NN, however, can keep rapidly modifying all of itself during runtime. In principle, such NNs can meta-learn to learn, and meta-meta-learn to meta-learn to learn, and so on, in the sense of recursive self-improvement. While NN architectures potentially capable of implementing such behavior have been proposed since the '90s, there have been few if any practical studies. Here we revisit such NNs, building upon recent successes of fast weight programmers and closely related linear Transformers. We propose a scalable self-referential WM (SRWM) that uses outer products and the delta update rule to modify itself. We evaluate our SRWM in supervised few-shot learning and in multi-task reinforcement learning with procedurally generated game environments. Our experiments demonstrate both practical applicability and competitive performance of the proposed SRWM. Our code is public.

Improving Baselines in the Wild

We share our experience with the recently released WILDS benchmark, a collection of ten datasets dedicated to developing models and training strategies which are robust to domain shifts. Several experiments yield a couple of critical observations which we believe are of general interest for any future work on WILDS. Our study focuses on two datasets: iWildCam and FMoW. We show that (1) Conducting separate cross-validation for each evaluation metric is crucial for both datasets, (2) A weak correlation between validation and test performance might make model development difficult for iWildCam, (3) Minor changes in the training of hyper-parameters improve the baseline by a relatively large margin (mainly on FMoW), (4) There is a strong correlation between certain domains and certain target labels (mainly on iWildCam). To the best of our knowledge, no prior work on these datasets has reported these observations despite their obvious importance. Our code is public.

Training and Generating Neural Networks in Compressed Weight Space

The inputs and/or outputs of some neural nets are weight matrices of other neural nets. Indirect encodings or end-to-end compression of weight matrices could help to scale such approaches. Our goal is to open a discussion on this topic, starting with recurrent neural networks for character-level language modelling whose weight matrices are encoded by the discrete cosine transform. Our fast weight version thereof uses a recurrent neural network to parameterise the compressed weights. We present experimental results on the enwik8 dataset.