arXiv subjects

Ila Fiete

Publications and source records attributed to Ila Fiete.

33 records · Page 2Linked to original sources

arXiv2024

Do Diffusion Models Learn Semantically Meaningful and Efficient Representations?

Diffusion models are capable of impressive feats of image generation with uncommon juxtapositions such as astronauts riding horses on the moon with properly placed shadows. These outputs indicate the ability to perform compositional generalization, but how do the models do so? We perform controlled experiments on conditional DDPMs learning to generate 2D spherical Gaussian bumps centered at specified $x$- and $y$-positions. Our results show that the emergence of semantically meaningful latent representations is key to achieving high performance. En route to successful performance over learning, the model traverses three distinct phases of latent representations: (phase A) no latent structure, (phase B) a 2D manifold of disordered states, and (phase C) a 2D ordered manifold. Corresponding to each of these phases, we identify qualitatively different generation behaviors: 1) multiple bumps are generated, 2) one bump is generated but at inaccurate $x$ and $y$ locations, 3) a bump is generated at the correct $x$ and y location. Furthermore, we show that even under imbalanced datasets where features ($x$- versus $y$-positions) are represented with skewed frequencies, the learning process for $x$ and $y$ is coupled rather than factorized, demonstrating that simple vanilla-flavored diffusion models cannot learn efficient representations in which localization in $x$ and $y$ are factorized into separate 1D tasks. These findings suggest the need for future work to find inductive biases that will push generative models to discover and exploit factorizable independent structures in their inputs, which will be required to vault these models into more data-efficient regimes.

cs.LG↗

arXiv2024

Resampling-free Particle Filters in High-dimensions

State estimation is crucial for the performance and safety of numerous robotic applications. Among the suite of estimation techniques, particle filters have been identified as a powerful solution due to their non-parametric nature. Yet, in high-dimensional state spaces, these filters face challenges such as 'particle deprivation' which hinders accurate representation of the true posterior distribution. This paper introduces a novel resampling-free particle filter designed to mitigate particle deprivation by forgoing the traditional resampling step. This ensures a broader and more diverse particle set, especially vital in high-dimensional scenarios. Theoretically, our proposed filter is shown to offer a near-accurate representation of the desired posterior distribution in high-dimensional contexts. Empirically, the effectiveness of our approach is underscored through a high-dimensional synthetic state estimation task and a 6D pose estimation derived from videos. We posit that as robotic systems evolve with greater degrees of freedom, particle filters tailored for high-dimensional state spaces will be indispensable.

cs.RO↗

arXiv2024

Improving Protein Optimization with Smoothed Fitness Landscapes

The ability to engineer novel proteins with higher fitness for a desired property would be revolutionary for biotechnology and medicine. Modeling the combinatorially large space of sequences is infeasible; prior methods often constrain optimization to a small mutational radius, but this drastically limits the design space. Instead of heuristics, we propose smoothing the fitness landscape to facilitate protein optimization. First, we formulate protein fitness as a graph signal then use Tikunov regularization to smooth the fitness landscape. We find optimizing in this smoothed landscape leads to improved performance across multiple methods in the GFP and AAV benchmarks. Second, we achieve state-of-the-art results utilizing discrete energy-based models and MCMC in the smoothed landscape. Our method, called Gibbs sampling with Graph-based Smoothing (GGS), demonstrates a unique ability to achieve 2.5 fold fitness improvement (with in-silico evaluation) over its training set. GGS demonstrates potential to optimize proteins in the limited data regime. Code: https://github.com/kirjner/GGS

q-bio.BM↗

arXiv2023

Beyond Geometry: Comparing the Temporal Structure of Computation in Neural Circuits with Dynamical Similarity Analysis

How can we tell whether two neural networks utilize the same internal processes for a particular computation? This question is pertinent for multiple subfields of neuroscience and machine learning, including neuroAI, mechanistic interpretability, and brain-machine interfaces. Standard approaches for comparing neural networks focus on the spatial geometry of latent states. Yet in recurrent networks, computations are implemented at the level of dynamics, and two networks performing the same computation with equivalent dynamics need not exhibit the same geometry. To bridge this gap, we introduce a novel similarity metric that compares two systems at the level of their dynamics, called Dynamical Similarity Analysis (DSA). Our method incorporates two components: Using recent advances in data-driven dynamical systems theory, we learn a high-dimensional linear system that accurately captures core features of the original nonlinear dynamics. Next, we compare different systems passed through this embedding using a novel extension of Procrustes Analysis that accounts for how vector fields change under orthogonal transformation. In four case studies, we demonstrate that our method disentangles conjugate and non-conjugate recurrent neural networks (RNNs), while geometric methods fall short. We additionally show that our method can distinguish learning rules in an unsupervised manner. Our method opens the door to comparative analyses of the essential temporal structure of computation in neural circuits.

q-bio.NC↗

arXiv2023

Neuro-Inspired Fragmentation and Recall to Overcome Catastrophic Forgetting in Curiosity

Deep reinforcement learning methods exhibit impressive performance on a range of tasks but still struggle on hard exploration tasks in large environments with sparse rewards. To address this, intrinsic rewards can be generated using forward model prediction errors that decrease as the environment becomes known, and incentivize an agent to explore novel states. While prediction-based intrinsic rewards can help agents solve hard exploration tasks, they can suffer from catastrophic forgetting and actually increase at visited states. We first examine the conditions and causes of catastrophic forgetting in grid world environments. We then propose a new method FARCuriosity, inspired by how humans and animals learn. The method depends on fragmentation and recall: an agent fragments an environment based on surprisal, and uses different local curiosity modules (prediction-based intrinsic reward functions) for each fragment so that modules are not trained on the entire environment. At each fragmentation event, the agent stores the current module in long-term memory (LTM) and either initializes a new module or recalls a previously stored module based on its match with the current state. With fragmentation and recall, FARCuriosity achieves less forgetting and better overall performance in games with varied and heterogeneous environments in the Atari benchmark suite of tasks. Thus, this work highlights the problem of catastrophic forgetting in prediction-based curiosity methods and proposes a solution.

cs.AI↗

arXiv2023

Model-agnostic Measure of Generalization Difficulty

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images < few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

cs.LG↗

arXiv2023

Winning the lottery with neural connectivity constraints: faster learning across cognitive tasks with spatially constrained sparse RNNs

Recurrent neural networks (RNNs) are often used to model circuits in the brain, and can solve a variety of difficult computational problems requiring memory, error-correction, or selection [Hopfield, 1982, Maass et al., 2002, Maass, 2011]. However, fully-connected RNNs contrast structurally with their biological counterparts, which are extremely sparse (~0.1%). Motivated by the neocortex, where neural connectivity is constrained by physical distance along cortical sheets and other synaptic wiring costs, we introduce locality masked RNNs (LM-RNNs) that utilize task-agnostic predetermined graphs with sparsity as low as 4%. We study LM-RNNs in a multitask learning setting relevant to cognitive systems neuroscience with a commonly used set of tasks, 20-Cog-tasks [Yang et al., 2019]. We show through reductio ad absurdum that 20-Cog-tasks can be solved by a small pool of separated autapses that we can mechanistically analyze and understand. Thus, these tasks fall short of the goal of inducing complex recurrent dynamics and modular structure in RNNs. We next contribute a new cognitive multi-task battery, Mod-Cog, consisting of upto 132 tasks that expands by 7-fold the number of tasks and task-complexity of 20-Cog-tasks. Importantly, while autapses can solve the simple 20-Cog-tasks, the expanded task-set requires richer neural architectures and continuous attractor dynamics. On these tasks, we show that LM-RNNs with an optimal sparsity result in faster training and better data-efficiency than fully connected networks.

q-bio.NC↗

arXiv2022

See and Copy: Generation of complex compositional movements from modular and geometric RNN representations

A hallmark of biological intelligence and control is combinatorial generalization: animals are able to learn various things, then piece them together in new combinations to produce appropriate outputs for new tasks. Inspired by the ability of primates to readily imitate seen movement sequences, we present a model of motor control using a realistic model of arm dynamics, tasked with imitating a guide that makes arbitrary two-segment drawings. We hypothesize that modular organization is one of the keys to such flexible and generalizable control. We construct a modular control model consisting of separate encoding and motor RNNs and a scheduler, which we train end-to-end on the task. We show that the modular structure allows the model to generalize not only to unseen two-segment trajectories, but to new drawings consisting of many more segments than it was trained on, and also allows for rapid adaptation to perturbations. Finally, our model recapitulates experimental observations of the preparatory and execution-related processes unfolding during motor control, providing a normative explanation for functional segregation of preparatory and execution-related activity within the motor cortex.

q-bio.NC↗

arXiv2022

How to Train Your Wide Neural Network Without Backprop: An Input-Weight Alignment Perspective

Recent works have examined theoretical and empirical properties of wide neural networks trained in the Neural Tangent Kernel (NTK) regime. Given that biological neural networks are much wider than their artificial counterparts, we consider NTK regime wide neural networks as a possible model of biological neural networks. Leveraging NTK theory, we show theoretically that gradient descent drives layerwise weight updates that are aligned with their input activity correlations weighted by error, and demonstrate empirically that the result also holds in finite-width wide networks. The alignment result allows us to formulate a family of biologically-motivated, backpropagation-free learning rules that are theoretically equivalent to backpropagation in infinite-width networks. We test these learning rules on benchmark problems in feedforward and recurrent neural networks and demonstrate, in wide networks, comparable performance to backpropagation. The proposed rules are particularly effective in low data regimes, which are common in biological learning settings.

cs.LG↗

arXiv2022

Map Induction: Compositional spatial submap learning for efficient exploration in novel environments

Humans are expert explorers. Understanding the computational cognitive mechanisms that support this efficiency can advance the study of the human mind and enable more efficient exploration algorithms. We hypothesize that humans explore new environments efficiently by inferring the structure of unobserved spaces using spatial information collected from previously explored spaces. This cognitive process can be modeled computationally using program induction in a Hierarchical Bayesian framework that explicitly reasons about uncertainty with strong spatial priors. Using a new behavioral Map Induction Task, we demonstrate that this computational framework explains human exploration behavior better than non-inductive models and outperforms state-of-the-art planning algorithms when applied to a realistic spatial navigation domain.

cs.LG↗

arXiv2020

Superlinear Precision and Memory in Simple Population Codes

The brain constructs population codes to represent stimuli through widely distributed patterns of activity across neurons. An important figure of merit of population codes is how much information about the original stimulus can be decoded from them. Fisher information is widely used to quantify coding precision and specify optimal codes, because of its relationship to mean squared error (MSE) under certain assumptions. When neural firing is sparse, however, optimizing Fisher information can result in codes that are highly sub-optimal in terms of MSE. We find that this discrepancy arises from the non-local component of error not accounted for by the Fisher information. Using this insight, we construct optimal population codes by directly minimizing the MSE. We study the scaling properties of MSE with coding parameters, focusing on the tuning curve width. We find that the optimal tuning curve width for coding no longer scales as the inverse population size, and the quadratic scaling of precision with system size predicted by Fisher information alone no longer holds. However, superlinearity is still preserved with only a logarithmic slowdown. We derive analogous results for networks storing the memory of a stimulus through continuous attractor dynamics, and show that similar scaling properties optimize memory and representation.

q-bio.NC↗

arXiv2017

Associative content-addressable networks with exponentially many robust stable states

The brain must robustly store a large number of memories, corresponding to the many events encountered over a lifetime. However, the number of memory states in existing neural network models either grows weakly with network size or recall fails catastrophically with vanishingly little noise. We construct an associative content-addressable memory with exponentially many stable states and robust error-correction. The network possesses expander graph connectivity on a restricted Boltzmann machine architecture. The expansion property allows simple neural network dynamics to perform at par with modern error-correcting codes. Appropriate networks can be constructed with sparse random connections, glomerular nodes, and associative learning using low dynamic-range weights. Thus, sparse quasi-random structures---characteristic of important error-correcting codes---may provide for high-performance computation in artificial neural networks and the brain.

q-bio.NC↗

arXiv2016

Training recurrent networks to generate hypotheses about how the brain solves hard navigation problems

Self-localization during navigation with noisy sensors in an ambiguous world is computationally challenging, yet animals and humans excel at it. In robotics, Simultaneous Location and Mapping (SLAM) algorithms solve this problem though joint sequential probabilistic inference of their own coordinates and those of external spatial landmarks. We generate the first neural solution to the SLAM problem by training recurrent LSTM networks to perform a set of hard 2D navigation tasks that include generalization to completely novel trajectories and environments. The hidden unit representations exhibit several key properties of hippocampal place cells, including stable tuning curves that remap between environments. Our result is also a proof of concept for end-to-end-learning of a SLAM algorithm using recurrent networks, and a demonstration of why this approach may have some advantages for robotic SLAM.

q-bio.NC↗

arXiv2014

A binary Hopfield network with $1/\log(n)$ information rate and applications to grid cell decoding

A Hopfield network is an auto-associative, distributive model of neural memory storage and retrieval. A form of error-correcting code, the Hopfield network can learn a set of patterns as stable points of the network dynamic, and retrieve them from noisy inputs -- thus Hopfield networks are their own decoders. Unlike in coding theory, where the information rate of a good code (in the Shannon sense) is finite but the cost of decoding does not play a role in the rate, the information rate of Hopfield networks trained with state-of-the-art learning algorithms is of the order ${\log(n)}/{n}$, a quantity that tends to zero asymptotically with $n$, the number of neurons in the network. For specially constructed networks, the best information rate currently achieved is of order ${1}/{\sqrt{n}}$. In this work, we design simple binary Hopfield networks that have asymptotically vanishing error rates at an information rate of ${1}/{\log(n)}$. These networks can be added as the decoders of any neural code with noisy neurons. As an example, we apply our network to a binary neural decoder of the grid cell code to attain information rate ${1}/{\log(n)}$.

q-bio.NC↗

arXiv2006

Triangular lattice neurons may implement an advanced numeral system to precisely encode rat position over large ranges

We argue by observation of the neural data that neurons in area dMEC of rats, which fire whenever the rat is on any vertex of a regular triangular lattice that tiles 2-d space, may be using an advanced numeral system to reversibly encode rat position. We interpret measured dMEC properties within the framework of a residue number system (RNS), and describe how RNS encoding -- which breaks the non-periodic variable of rat position into a set of narrowly distributed periodic variables -- allows a small set of cells to compactly represent and efficiently update rat position with high resolution over a large range. We show that the uniquely useful properties of RNS encoding still hold when the encoded and encoding quantities are relaxed to be real numbers with built-in uncertainties, and provide a numerical and functional estimate of the range and resolution of rat positions that can be uniquely encoded in dMEC. The use of a compact, `arithmetic-friendly' numeral system to encode a metric variable, as we propose is happening in dMEC, is qualitatively different from all previously identified examples of coding in the brain. We discuss the numerous neurobiological implications and predictions of our hypothesis.

q-bio.NC↗