Translation Invariant Representation Research Articles

COSMIC: Molecular Conformation Space Modeling in Internal Coordinates with an Adversarial Framework.

The fast and accurate conformation space modeling is an essential part of computational approaches for solving ligand and structure-based drug discovery problems. Recent state-of-the-art diffusion models for molecular conformation generation show promising distribution coverage and physical plausibility metrics but suffer from a slow sampling procedure. We propose a novel adversarial generative framework, COSMIC, that shows comparable generative performance but provides a time-efficient sampling and training procedure. Given a molecular graph and random noise, the generator produces a conformation in two stages. First, it constructs a conformation in a rotation and translation invariant representation─internal coordinates. In the second step, the model predicts the distances between neighboring atoms and performs a few fast optimization steps to refine the initial conformation. The proposed model considers conformation energy, achieving comparable space coverage, and diversity metrics results.

Probing Spatial Clues: Canonical Spatial Templates for Object Relationship Understanding

Humans often leverage spatial clues to categorize scenes in a fraction of a second. This form of intelligence is very relevant in time-critical situations (e.g., when driving a car) and valuable to transfer to automated systems. This work investigates the predictive power of solely processing spatial clues for scene understanding in 2D images and compares such an approach with the predictive power of visual appearance. To this end, we design the laboratory task of predicting the identity of two objects (e.g., “man” and “horse”) and their relationship or predicate (e.g., “riding”) given exclusively the ground truth bounding box coordinates of both objects. We also measure the performance attainable in Human Object Interaction (HOI) detection, a real-world spatial task, which includes a setting where ground truth boxes are not available at test time. An additional goal is to identify the principles necessary to effectively represent a spatial template, that is, the visual region in which two objects involved in a relationship expressed by a predicate occur. We propose a scale-, mirror-, and translation-invariant representation that captures the spatial essence of the relationship, i.e., a canonical spatial representation. Tests in two benchmarks reveal: (1) High performance is attainable by using exclusively spatial information in all tasks. (2) In HOI detection, the canonical template outperforms the rest of spatial, visual, and several state-of-the-art baselines. (3) Simple fusion of visual and spatial features substantially improves performance. (4) Our methods fare remarkably well with a small amount of data and rare categories. Our results obtained on the Visual Genome (VG) and the Humans Interacting with Common Objects - Detection (HICO-DET) datasets indicate that great predictive power can be obtained from spatial clues alone, opening up possibilities for performing fast scene understanding at a glance.

Complete set of translation invariant measurements with Lipschitz bounds

In image and audio signal classification, a major problem is to build stable representations that are invariant under rigid motions and, more generally, to small diffeomorphisms. Translation invariant representations of signals in C n are of particular importance. The existence of such representations is intimately related to classical invariant theory, inverse problems in compressed sensing and deep learning. Despite an impressive body of literature on the subject, most representations available are either not stable due to the presence of high frequencies or non discriminative. In the present paper, we construct low dimensional representations of signals in C n that are invariant under finite unitary group actions, as a special case we establish the existence of low-dimensional and complete Z m -invariant representations for any m ∈ N . Our construction yields a stable, discriminative transform with semi-explicit Lipschitz bounds on the dimension; this is particularly relevant for applications. Using some tools from Algebraic Geometry, we define a high dimensional homogeneous function that is injective. We then exploit the projective character of this embedding and see that the target space can be reduced significantly by using a generic linear transformation. Finally, we introduce the notion of non-parallel map, which is enjoyed by our function and employ this to construct a Lipschitz modification of it.

Multi-Resolution Dual-Tree Wavelet Scattering Network for Signal Classification

This paper introduces a Deep Scattering network that utilizes Dual-Tree complex wavelets to extract multi-scale translation invariant representations from an input signal. The computationally efficient Dual-Tree wavelets decompose the input signal into equally spaced representations over scales. Translation invariance is introduced in the representations by applying a non-linearity over a region followed by averaging. The discriminatory information from the equally spaced locally smooth signal representations aids the learning of the classi- fier. The proposed network is shown to outperform Mallat’s ScatterNet [1] on four datasets with different modalities, both for classification accuracy and computational efficiency.

Deep Scattering Spectrum

A scattering transform defines a locally translation invariant representation which is stable to time-warping deformation. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades of wavelet convolutions and modulus operators. Second-order scattering coefficients characterize transient phenomena such as attacks and amplitude modulation. A frequency transposition invariant representation is obtained by applying a scattering transform along log-frequency. State-the-of-art classification results are obtained for musical genre and phone classification on GTZAN and TIMIT databases, respectively.

How Lateral Connections and Spiking Dynamics May Separate Multiple Objects Moving Together

Over successive stages, the ventral visual system of the primate brain develops neurons that respond selectively to particular objects or faces with translation, size and view invariance. The powerful neural representations found in Inferotemporal cortex form a remarkably rapid and robust basis for object recognition which belies the difficulties faced by the system when learning in natural visual environments. A central issue in understanding the process of biological object recognition is how these neurons learn to form separate representations of objects from complex visual scenes composed of multiple objects. We show how a one-layer competitive network comprised of ‘spiking’ neurons is able to learn separate transformation-invariant representations (exemplified by one-dimensional translations) of visual objects that are always seen together moving in lock-step, but separated in space. This is achieved by combining ‘Mexican hat’ functional lateral connectivity with cell firing-rate adaptation to temporally segment input representations of competing stimuli through anti-phase oscillations (perceptual cycles). These spiking dynamics are quickly and reliably generated, enabling selective modification of the feed-forward connections to neurons in the next layer through Spike-Time-Dependent Plasticity (STDP), resulting in separate translation-invariant representations of each stimulus. Variations in key properties of the model are investigated with respect to the network’s ability to develop appropriate input representations and subsequently output representations through STDP. Contrary to earlier rate-coded models of this learning process, this work shows how spiking neural networks may learn about more than one stimulus together without suffering from the ‘superposition catastrophe’. We take these results to suggest that spiking dynamics are key to understanding biological visual object recognition.

Double-gabor filters are independent components of small translation-invariant image patches.

The analysis of natural images with independent component analysis (ICA) yields localized bandpass Gabor-type filters similar to receptive fields of simple cells in visual cortex. We applied ICA on a subset of patches called position-centered patches, selected for forming a translation-invariant representation of small patches. The resulting filters were qualitatively different in two respects. One novel feature was the emergence of filters we call double-Gabor filters. In contrast to Gabor functions that are modulated in one direction, double-Gabor filters are sinusoidally modulated in two orthogonal directions. In addition the filters were more extended in space and frequency compared to standard ICA filters and better matched the distribution in experimental recordings from neurons in primary visual cortex. We further found a dual role for double-Gabor filters as edge and texture detectors, which could have engineering applications.

Continuous transformation learning of translation invariant representations

We show that spatial continuity can enable a network to learn translation invariant representations of objects by self-organization in a hierarchical model of cortical processing in the ventral visual system. During 'continuous transformation learning', the active synapses from each overlapping transform are associatively modified onto the set of postsynaptic neurons. Because other transforms of the same object overlap with previously learned exemplars, a common set of postsynaptic neurons is activated by the new transforms, and learning of the new active inputs onto the same postsynaptic neurons is facilitated. We show that the transforms must be close for this to occur; that the temporal order of presentation of each transformed image during training is not crucial for learning to occur; that relatively large numbers of transforms can be learned; and that such continuous transformation learning can be usefully combined with temporal trace training.

Invariant object recognition with trace learning and multiple stimuli present during training

Over successive stages, the ventral visual system develops neurons that respond with view, size and position invariance to objects including faces. A major challenge is to explain how invariant representations of individual objects could develop given visual input from environments containing multiple objects. Here we show that the neurons in a 1-layer competitive network learn to represent combinations of three objects simultaneously present during training if the number of objects in the training set is low (e.g. 4), to represent combinations of two objects as the number of objects is increased to for e.g. 10, and to represent individual objects as the number of objects in the training set is increased further to for e.g. 20. We next show that translation invariant representations can be formed even when multiple stimuli are always present during training, by including a temporal trace in the learning rule. Finally, we show that these concepts can be extended to a multi-layer hierarchical network model (VisNet) of the ventral visual system. This approach provides a way to understand how a visual system can, by self-organizing competitive learning, form separate invariant representations of each object even when each object is presented in a scene with multiple other objects present, as in natural visual scenes.

Generalized Phase Shifting for $M$-Band Discrete Wavelet Packet Transforms

This correspondence presents a novel method for the construction of translation-invariant discrete wavelet packet (TIDWP) transforms for any decomposition level k, starting from any phase of a critically sampled discrete wavelet-packet representation of level k. The process is performed by phase shifting, i.e., the direct recovering of the wavelet coefficients omitted by the downsampling operations of each decomposition level without reconstructing the input signal. The proposed method enables tradeoffs between memory utilization and computational efficiency for the construction of translation-invariant representations. Hence, it is useful in resource-constrained TIDWP-based applications of digital signal compression, image segmentation and detection of transients

Selective Attention for Identification Model: Simulating visual neglect

Recently, we have introduced a computational model, termed Selective Attention Identification Model [SAIM; Heinke, Humphreys, Attention, spatial representation and visual neglect: simulating emergent attention and spatial memory in the Selective Attention for Identification Model (SAIM), Psychol. Rev. 110 (1) (2003) 29]. SAIM aims at translation-invariant object identification by selecting objects and mapping them into a focus of attention (FOA). With this architecture, SAIM can model a wide range of experimental evidence on normal attention and attentional disorders. Here, we demonstrate how SAIM can produce two specially striking forms of visual disorder, within- and between-object neglect. Patients with within-object neglect tend to ignore parts of objects and patients with between-object neglect might omit complete objects presented next to another object. Importantly, both deficits can occur irrespective of the objects’ positions in the visual field (translation invariant). To simulate neglect, the selection mechanism in SAIM was lesioned. Importantly, the selection mechanism selects objects and, at the same time, produces a translation-invariant representation of the objects in the FOA. Consequently, the lesion can have a translation-invariant effect, allowing SAIM to simulate within- and between-object neglect. This result gives additional credence to SAIM’s integral approach to attention and translation-invariant object identification.

A translation-invariant wavelet representation algorithm with applications

We address the time-varying problem of wavelet transforms, and a new translation-invariant wavelet representation algorithm is proposed. Using the algorithm introduced by Beylkin (see SIAM J. Numer. Anal., vol. 29, p.1716-1740, 1992), we compute the wavelet transform for all the circular time shifts of a length-N signal in O(N log N) operations. The wavelet coefficients of the time shift with minimal cost are selected as the best representation of the signal using a binary tree search algorithm with an appropriate cost function. We apply the translation-invariant representation algorithm to a geoacoustic data compression application. The results show that the new algorithm can reduce the distortion (the squared error in our case) substantially, if the input signals are transients that are sensitive to time shifts.

Symmetry Groups and Translation Invariant Representations of Markov Processes

The symmetry groups of the potential theory of a Markov process $X_t$ are used to introduce new algebraic and topological structures on the state space and the process. For example, let $G$ be the collection of bijections $\varphi$ on $E$ which preserve the collection of excessive functions. Assume there is a transitive subgroup $H$ of the symmetry group $G$ such that the only map $\varphi \in H$ fixing a point $e \in E$ is the identity map on $E$. There is a bijection $\Psi: E \rightarrow H$ so that the algebraic structure of $H$ can be carried to $E$, making $E$ into a group. If there is a left quasi-invariant measure on $E$, then there is a topology on $E$ making $E$ into a locally compact second countable metric group. There is also a time change $\tau(t)$ of $X_t$ such that $X_{\tau(t)}$ is a translation invariant process on $E$ and $X_{\tau(t)}$ is right-continuous with left limits in the new topology.

Representations of polytopes and polyhedral sets

In this paper we describe a variant of the diagram techniques, such as Gale diagrams for polytopes and positive diagrams for positive bases, which is appropriate for polyhedral sets. We obtain our new technique as a translation-invariant representation of polytopes or polyhedral sets. This approach leads naturally to simpler proofs of the familiar combinatorial diagram relationships. However, this method is more versatile than those previously employed, in that it can be used to investigate linear systems of polyhedral sets, and metrical properties such as volume. In particular, we give an easy proof of a result of Meyer on decomposability of polytopes, and a more perspicuous way of looking at the well-known theorem of Minkowski on the realizability of polytopes whose facets have given outer normal vectors and areas.