σ-GPTs: A New Approach to Autoregressive Models

Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional encoding for the output, this order can be modulated on-the-fly per-sample which offers key advantageous properties. It allows for the sampling of and conditioning on arbitrary subsets of tokens, and it also allows sampling in one shot multiple tokens dynamically according to a rejection strategy, leading to a sub-linear number of model evaluations. We evaluate our method across various domains, including language modeling, path-solving, and aircraft vertical rate prediction, decreasing the number of steps required for generation by an order of magnitude.

Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flows

We consider the problem of sampling discrete field configurations $\phi$ from the Boltzmann distribution $[d\phi] Z^{-1} e^{-S[\phi]}$, where $S$ is the lattice-discretization of the continuous Euclidean action $\mathcal S$ of some quantum field theory. Since such densities arise as the approximation of the underlying functional density $[\mathcal D\phi(x)] \mathcal Z^{-1} e^{-\mathcal S[\phi(x)]}$, we frame the task as an instance of operator learning. In particular, we propose to approximate a time-dependent operator $\mathcal V_t$ whose time integral provides a mapping between the functional distributions of the free theory $[\mathcal D\phi(x)] \mathcal Z_0^{-1} e^{-\mathcal S_{0}[\phi(x)]}$ and of the target theory $[\mathcal D\phi(x)]\mathcal Z^{-1}e^{-\mathcal S[\phi(x)]}$. Whenever a particular lattice is chosen, the operator $\mathcal V_t$ can be discretized to a finite dimensional, time-dependent vector field $V_t$ which in turn induces a continuous normalizing flow between finite dimensional distributions over the chosen lattice. This flow can then be trained to be a diffeormorphism between the discretized free and target theories $[d\phi] Z_0^{-1} e^{-S_{0}[\phi]}$, $[d\phi] Z^{-1}e^{-S[\phi]}$. We run experiments on the $\phi^4$-theory to explore to what extent such operator-based flow architectures generalize to lattice sizes they were not trained on and show that pretraining on smaller lattices can lead to speedup over training only a target lattice size.

Multi-Lattice Sampling of Quantum Field Theories via Neural Operators

We consider the problem of sampling discrete field configurations $\phi$ from the Boltzmann distribution $[d\phi] Z^{-1} e^{-S[\phi]}$, where $S$ is the lattice-discretization of the continuous Euclidean action $\mathcal S$ of some quantum field theory. Since such densities arise as the approximation of the underlying functional density $[\mathcal D\phi(x)] \mathcal Z^{-1} e^{-\mathcal S[\phi(x)]}$, we frame the task as an instance of operator learning. In particular, we propose to approximate a time-dependent operator $\mathcal V_t$ whose time integral provides a mapping between the functional distributions of the free theory $[\mathcal D\phi(x)] \mathcal Z_0^{-1} e^{-\mathcal S_{0}[\phi(x)]}$ and of the target theory $[\mathcal D\phi(x)]\mathcal Z^{-1}e^{-\mathcal S[\phi(x)]}$. Whenever a particular lattice is chosen, the operator $\mathcal V_t$ can be discretized to a finite dimensional, time-dependent vector field $V_t$ which in turn induces a continuous normalizing flow between finite dimensional distributions over the chosen lattice. This flow can then be trained to be a diffeormorphism between the discretized free and target theories $[d\phi] Z_0^{-1} e^{-S_{0}[\phi]}$, $[d\phi] Z^{-1}e^{-S[\phi]}$. We run experiments on the $\phi^4$-theory to explore to what extent such operator-based flow architectures generalize to lattice sizes they were not trained on and show that pretraining on smaller lattices can lead to speedup over training only a target lattice size.

PAUMER: Patch Pausing Transformer for Semantic Segmentation

We study the problem of improving the efficiency of segmentation transformers by using disparate amounts of computation for different parts of the image. Our method, PAUMER, accomplishes this by pausing computation for patches that are deemed to not need any more computation before the final decoder. We use the entropy of predictions computed from intermediate activations as the pausing criterion, and find this aligns well with semantics of the image. Our method has a unique advantage that a single network trained with the proposed strategy can be effortlessly adapted at inference to various run-time requirements by modulating its pausing parameters. On two standard segmentation datasets, Cityscapes and ADE20K, we show that our method operates with about a $50\%$ higher throughput with an mIoU drop of about $0.65\%$ and $4.6\%$ respectively.

Faster Causal Attention Over Large Sequences Through Sparse Flash Attention

Transformer-based language models have found many diverse applications requiring them to process sequences of increasing length. For these applications, the causal self-attention -- which is the only component scaling quadratically w.r.t. the sequence length -- becomes a central concern. While many works have proposed schemes to sparsify the attention patterns and reduce the computational overhead of self-attention, those are often limited by implementations concerns and end up imposing a simple and static structure over the attention matrix. Conversely, implementing more dynamic sparse attentions often results in runtimes significantly slower than computing the full attention using the Flash implementation from Dao et al. (2022). We extend FlashAttention to accommodate a large class of attention sparsity patterns that, in particular, encompass key/query dropping and hashing-based attention. This leads to implementations with no computational complexity overhead and a multi-fold runtime speedup on top of FlashAttention. Even with relatively low degrees of sparsity, our method improves visibly upon FlashAttention as the sequence length increases. Without sacrificing perplexity, we increase the training speed of a transformer language model by $2.0\times$ and $3.3\times$ for sequences of respectively $8k$ and $16k$ tokens.

Graph Neural Networks Go Forward-Forward

We present the Graph Forward-Forward (GFF) algorithm, an extension of the Forward-Forward procedure to graphs, able to handle features distributed over a graph's nodes. This allows training graph neural networks with forward passes only, without backpropagation. Our method is agnostic to the message-passing scheme, and provides a more biologically plausible learning scheme than backpropagation, while also carrying computational advantages. With GFF, graph neural networks are trained greedily layer by layer, using both positive and negative samples. We run experiments on 11 standard graph property prediction tasks, showing how GFF provides an effective alternative to backpropagation for training graph neural networks. This shows in particular that this procedure is remarkably efficient in spite of combining the per-layer training with the locality of the processing in a GNN.

Learning Deformation Trajectories of Boltzmann Densities

We introduce a training objective for continuous normalizing flows that can be used in the absence of samples but in the presence of an energy function. Our method relies on either a prescribed or a learnt interpolation $f_t$ of energy functions between the target energy $f_1$ and the energy function of a generalized Gaussian $f_0(x) = (|x|/\sigma)^p$. This then induces an interpolation of Boltzmann densities $p_t \propto e^{-f_t}$ and we aim to find a time-dependent vector field $V_t$ that transports samples along this family of densities. Concretely, this condition can be translated to a PDE between $V_t$ and $f_t$ and we minimize the amount by which this PDE fails to hold. We compare this objective to the reverse KL-divergence on Gaussian mixtures and on the $\phi^4$ lattice field theory on a circle.

ESLAM: Efficient Dense SLAM System Based on Hybrid Representation of Signed Distance Fields

We present ESLAM, an efficient implicit neural representation method for Simultaneous Localization and Mapping (SLAM). ESLAM reads RGB-D frames with unknown camera poses in a sequential manner and incrementally reconstructs the scene representation while estimating the current camera position in the scene. We incorporate the latest advances in Neural Radiance Fields (NeRF) into a SLAM system, resulting in an efficient and accurate dense visual SLAM method. Our scene representation consists of multi-scale axis-aligned perpendicular feature planes and shallow decoders that, for each point in the continuous space, decode the interpolated features into Truncated Signed Distance Field (TSDF) and RGB values. Our extensive experiments on two standard and recent datasets, Replica and ScanNet, show that ESLAM improves the accuracy of 3D reconstruction and camera localization of state-of-the-art dense visual SLAM methods by more than 50%, while it runs up to $\times$10 faster and does not require any pre-training.

Deformation Theory of Boltzmann Distributions

Consider a one-parameter family of Boltzmann distributions $p_t(x) = \tfrac{1}{Z_t}e^{-S_t(x)}$. We study the problem of sampling from $p_{t_0}$ by first sampling from $p_{t_1}$ and then applying a transformation $\Psi_{t_1}^{t_0}$ to the samples so that to they follow $p_{t_0}$. We derive an equation relating $\Psi$ and the corresponding family of unnormalized log-likelihoods $S_t$. We demonstrate the utility of this idea on the $\phi^4$ lattice field theory by extending its defining action $S_0$ to a family of actions $S_t$ and finding a $\tau$ such that normalizing flows perform better at learning the Boltzmann distribution $p_\tau$ than at learning $p_0$.

Accurate Extrinsic Prediction of Physical Systems Using Transformers

Accurate high-altitude wind forecasting is important for air traffic control. And the large volume of data available for this task makes deep neural network-based models a possibility. However, special methods are required because the data is measured only sparsely: along the main aircraft trajectories and arranged sparsely in space, namely along the main air corridors. Several deep learning approaches have been proposed, and in this work, we show that Transformers can fit this data efficiently and are able to extrapolate coherently from a context set. We show this by an extensive comparison of Transformers to numerous existing deep learning-based baselines in the literature. Besides high-altitude wind forecasting, we compare competing models on other dynamical physical systems, namely those modelled by partial differential equations, in particular the Poisson equation and Darcy Flow equation. For these experiments, in the case where the data is arranged non-regularly in space, Transformers outperform all the other evaluated methods. We also compared them in a more standard setup where the data is arranged on a grid and show that the Transformers are competitive with state-of-the-art methods, even though it does not require regular spacing. The code and datasets of the different experiments will be made publicly available at publication time.