Efficient transfer learning algorithms are key to the success of foundation models on diverse downstream tasks even with limited data. Recent works of Basu et al. (2023) and Kaba et al. (2022) propose group averaging (equitune) and optimizationbased methods, respectively, over features from group-transformed inputs to obtain equivariant outputs from non-equivariant neural networks. While Kaba et al. (2022) are only concerned with training from scratch, we find that equitune performs poorly on equivariant zero-shot tasks despite good finetuning results. We hypothesize that this is because pretrained models provide better quality features for certain transformations than others and simply averaging them is deleterious. Hence, we propose λ-equitune that averages the features using importance weights, λs. These weights are learned directly from the data using a small neural network, leading to excellent zero-shot and finetuned results that outperform equitune. Further, we prove that λ-equitune is equivariant and a universal approximator of equivariant functions. Additionally, we show that the method of Kaba et al. (2022) used with appropriate loss functions, which we call equizero, also gives excellent zero-shot and finetuned performance.

The simultaneous rise of machine learning as a service and concerns over user privacy have increasingly motivated the need for private inference (PI). While recent work demonstrates PI is possible using cryptographic primitives, the computational overheads render it impractical. State-of-art deep networks are inadequate in this context because the source of slowdown in PI stems from the ReLU operations whereas optimizations for plaintext inference focus on reducing FLOPs. In this paper we re-think ReLU computations and propose optimizations for PI tailored to properties of neural networks. Specifically, we reformulate ReLU as an approximate sign test and introduce a novel truncation method for the sign test that significantly reduces the cost per ReLU. These optimizations result in a specific type of stochastic ReLU. The key observation is that the stochastic fault behavior is well suited for the fault-tolerant properties of neural network inference. Thus, we provide significant savings without impacting accuracy. We collectively call the optimizations Circa and demonstrate improvements of up to 4.7 storage and 3 runtime over baseline implementations; we further show that Circa can be used on top of recent PI optimizations to obtain 1.8 additional speedup.

What spatial frequency information do humans and neural networks use to recognize objects? In neuroscience, critical band masking is an established tool that can reveal the frequency-selective filters used for object recognition. Critical band masking measures the sensitivity of recognition performance to noise added at each spatial frequency. Existing critical band masking studies show that humans recognize periodic patterns (gratings) and letters by means of a spatial-frequency filter (or "channel") that has a frequency bandwidth of one octave (doubling of frequency). Here, we introduce critical band masking as a task for network-human comparison and test 14 humans and 76 neural networks on 16-way ImageNet categorization in the presence of narrowband noise.

In this appendix, as a complementary to Theorems 1-2, we provide additional theorems, Theorems 3-4, which further illustrate the two advantages of the discretization process by considering an abstract model with the discretization bottleneck. For the advantage on the sensitivity, the error due to potential noise and perturbation without discretization -- the third term ξ(w,r0,M0,d) >0 in Theorem 4 -- is shown to be minimized to zero with discretization in Theorems 3. See Appendix C.1 for a simple comparison between the bound of Theorem 3 and that of Theorem 4 when the metric spaces (M,d) and (M0,d0) are chosen to be Euclidean spaces. We now introduce the notation used in Theorems 3-4. Here, ϕw represents a deep neural network with weight parameters w W RD, qe is the discretization process with the codebook e E RL m, and hθ represents a deep neural network with parameters θ Θ Rζ. Thus, the tuple of all learnable parameters are (w,e,θ).

Deep learning has advanced from fully connected architectures to structured models organized into components, e.g., the transformer composed of positional elements, modular architectures divided into slots, and graph neural nets made up of nodes. The nature of structured models is that communication among the components has a bottleneck, typically achieved by restricted connectivity and attention. In this work, we further tighten the bottleneck via discreteness of the representations transmitted between components. We hypothesize that this constraint serves as a useful form of inductive bias. Our hypothesis is motivated by past empirical work showing the benefits of discretization in non-structured architectures as well as our own theoretical results showing that discretization increases noise robustness and reduces the underlying dimensionality of the model.