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In theory, oxidative modification of LDL-cholesterol promotes blockages in coronary arteries that lead to atherosclerosis and heart attacks , so vitamin E functioning as an antioxidant would reduce oxidized cholesterol and lower risk of cardiovascular disease. Vitamin E status has also been implicated in the maintenance of normal endothelial cell function of cells lining the inner surface of arteries, anti-inflammatory activity and inhibition of platelet adhesion and aggregation.

Diet higher in vitamin E may also be higher in other, unidentified components that promote heart health, or people choosing such diets may be making other healthy lifestyle choices. There is some supporting evidence from randomized clinical trials RCTs. For example, the Physicians’ Health Study II did not show any benefit after IU every other day for eight years, for heart attack, stroke, coronary mortality or all-cause mortality.

The effects of vitamin E supplementation on incidence of stroke were summarized in There were no significant benefits for vitamin E versus placebo. Subset analysis for ischaemic stroke , haemorrhagic stroke , fatal stroke, non-fatal stroke — all no significant difference in risk.

The authors concluded that there was a lack of clinically important benefit of vitamin E supplementation in the prevention of stroke. The beneficial effect was strongest is the subset of women who had a history of a prior thrombotic event or who were genetically coded for clot risk factor V Leiden or prothrombin mutation. In , the U. Food and Drug Administration rejected proposed health claims for vitamin E and cardiovascular health.

National Institutes of Health reviewed literature published up to and concluded “In general, clinical trials have not provided evidence that routine use of vitamin E supplements prevents cardiovascular disease or reduces its morbidity and mortality. In , the EFSA reviewed and rejected claims that a cause and effect relationship has been established between the dietary intake of vitamin E and maintenance of normal cardiac function or of normal blood circulation.

A meta-analysis reported that vitamin E significantly reduced elevated liver enzymes, steatosis, inflammation and fibrosis, suggesting that the vitamin may be useful for treatment of nonalcoholic fatty liver disease NAFLD and the more extreme subset known as nonalcoholic steatohepatitis NASH. There is an observed inverse correlation seen with dietary vitamin E, but no confirming evidence from placebo-controlled clinical trials.

A meta-analysis published in concluded that diets higher in vitamin E content lowered risk of developing Parkinson’s disease. Antioxidant vitamins as dietary supplements have been proposed as having benefits if consumed during pregnancy.

None of these trials reported any clinically meaningful information. Although there is widespread use of tocopheryl acetate as a topical medication , with claims for improved wound healing and reduced scar tissue, [] reviews have repeatedly concluded that there is insufficient evidence to support these claims. Incidence is low despite widespread use. These findings were based on fluid samples from the lungs of 29 patients with vaping-associated pulmonary injury , which provided direct evidence of vitamin E acetate at the primary site of injury in all the 29 lung fluid samples tested.

George M. Calhoun, Professor of Greek at the University of California, was credited with helping with the naming process. Nearly 50 years after the discovery of vitamin E an editorial in the Journal of the American Medical Association titled “Vitamin in search of a disease” read in part ” Evidence for vascular health was characterized as unconvincing.

The editorial closed with mention of some preliminary human evidence for protection against hemolytic anemia in young children. A role for vitamin E in coronary heart disease was first proposed in by Evan Shute and colleagues.

The role of vitamin E in infant nutrition has a long research history. From onward there were trials with premature infants suggesting that oral alpha-tocopherol was protective against edema , intracranial hemorrhage , hemolytic anemia and retrolental fibroplasia.

From Wikipedia, the free encyclopedia. Generic descriptor for all tocopherols and tocotrienols that exhibit alpha-tocopherol activity. Main article: Vitamin E deficiency.

Main article: Vaping-associated pulmonary injury. Present Knowledge in Nutrition, Eleventh Edition. ISBN Retrieved 3 August PMID Office of Dietary Supplements, U. National Institutes of Health. International Journal for Vitamin and Nutrition Research. Bibcode : PLoSO PMC January S2CID Archives of Dermatological Research.

Focus on Vitamin E Research. Nova Science Publishers. Bibcode : Sci JSTOR Journal of Biological Chemistry. A matter of stereochemistry”. Journal of Medicine and Life. European Journal of Biochemistry. Progress in Lipid Research. International Journal of Molecular Sciences. Molecular Aspects of Medicine. Journal of Experimental Botany. Retrieved 2 June EFSA Journal. Structure and function of alpha-tocopherol transfer protein: implications for vitamin E metabolism and AVED. Nutrition Research Reviews.

Journal of Nutritional Science and Vitaminology. Archived from the original PDF on June 15, Retrieved February 26, United Kingdom National Health Services.

The system relied on a NuBus card called Sound Accelerator, equipped with one Motorola processor. The card provided bit playback and Since audio streaming and non-destructive editing were performed on hard drives, the software was still limited by their performance; densely edited tracks could cause glitches. The core engine and much of the user interface of the first iteration of Pro Tools was based on Deck. The software, published in , was the first multi-track digital recorder based on a personal computer.

It was developed by OSC, a small San Francisco company founded the same year, in conjunction with Digidesign and ran on Digidesign’s hardware. The first Pro Tools system was launched on June 5, In , Josh Rosen, Mats Myrberg and John Dalton, the OSC’s engineers who developed Deck, split from Digidesign to focus on releasing lower-cost multi-track software that would run on computers with no additional hardware.

Peter Gotcher felt that the software needed a significant rewrite. Pro Tools II, the first software release fully developed by Digidesign, followed in the same year and addressed its predecessor’s weaknesses. In , Pro Tools 2. With TDM, up to four NuBus cards could be linked, obtaining a track system, while multiple DSP-based plug-ins could be run simultaneously and in real-time.

The operation was finalized in This change of architecture allowed the convergence of Macintosh computers with Intel -based PCs, for which PCI had become the standard internal communication bus. With the release of Pro Tools 24 in , Digidesign introduced a new bit interface the 24 and a new PCI card the d The d24 relied on Motorola processors, offering increased processing power and 24 tracks of bit audio [43] later increased to 32 tracks with a DAE software update.

A SCSI accelerator was required to keep up with the increased data throughput. Digidesign dropped its proprietary SCSI controller in favor of commercially available ones. Pro Tools 5 saw two substantial software developments: extended MIDI functionality and integration in an editable piano-roll view in the editor; MIDI automation, quantize and transpose [36] and the introduction of surround sound mixing and multichannel plug-ins—up to the 7. The migration from traditional, tape-based analog studio technology to the Pro Tools platform took place within the industry: [19] Ricky Martin ‘s ” Livin’ la Vida Loca ” was the first Billboard Hot number-one single to be recorded, edited, and mixed entirely within the Pro Tools environment, [46] allowing a more meticulous and effortless editing workflow especially on vocals.

While consolidating its presence in professional studios, Digidesign began to target the mid-range consumer market in by introducing the Digi bundle, consisting of a rack-mount audio interface with eight inputs and outputs with bit, Pro Tools, offering a solid and reliable alternative to analog recording and mixing, eventually became a standard in professional studios throughout the decade, while editing features such as Beat Detective introduced with Pro Tools 5.

Pro Tools LE, first introduced and distributed in with the Digi interface, [56] was a specific Pro Tools version in which the signal processing entirely relied on the host CPU. The software required a Digidesign interface to run, which acted as a copy-protection mechanism for the software.

Pro Tools LE shared the same interface of Pro Tools HD but had a smaller track count 24 tracks with Pro Tools 5, extended to 32 tracks with Pro Tools 6 [48] and 48 tracks with Pro Tools 8 [57] and supported a maximum sample rate of 96 kHz [58] depending on the interface used. Pro Tools 9, released in November , dropped the requirement of proprietary hardware to run the software. Core Audio allowed device aggregation, enabling using of more than one interface simultaneously.

In all other cases, it ran as Pro Tools 9 standard, with a smaller track count and some advanced features turned off. In response to Apple’s decision to include Emagic ‘s complete line of virtual instruments in Logic Pro in and following Avid ‘s acquisition of German virtual instruments developer Wizoo in , Pro Tools 8 was supplied with its first built-in virtual instruments library, the AIR Creative Collection, as well as with some new plug-ins, to make it more appealing for music production.

Each card mounted 18 DSP processors, manufactured by Texas Instruments, allowing an increased computational precision bit floating-point resolution for audio processing and bit floating-point summing, versus the previous bit and bit fixed-point resolution of the TDM engine , [4] thus improving dynamic range performance.

Signal processing could be run on the embedded DSP, providing additional computational power and enabling near zero-latency for DSP-reliant plug-ins. Two FPGA chips handled track playback, monitoring, and internal routing, providing a lower round trip latency. To maintain performance consistency, HDX products were specified with a fixed maximum number of voices each voice representing a monophonic channel.

Each HDX card enabled simultaneous voices at AAX was developed to provide the future implementation of bit plug-ins, although bit versions of AAX were still used in Pro Tools Notable software features introduced with Pro Tools 10 were editable clip-based gain automation Clip gain , the ability to load the session’s audio data into RAM to improve transport responsiveness Disk caching , quadrupled Automatic Delay Compensation length, audio fades processed in real-time, timeline length extended to 24 hours, support for bit float audio and mixed audio formats within the session, and the addition of Avid Channel Strip plug-in based on Euphonix System 5 console’s channel strip, following Avid’s acquisition of Euphonix in Pro Tools 11, released in June , switched from bit to bit software architecture with new audio and video engines, enabling the application and plug-ins to fully take advantage of system memory.

The new audio engine AAE introduced support of offline bouncing and simultaneous mixdowns multiple sources; dynamic plug-in processing allowed to reduce CPU usage when active native plug-ins don’t receive any input.

Two separate buffers were used for playback and for monitoring of record-enabled or input-monitored tracks. Pro Tools workflow is organized into two main windows: the timeline is shown in the Edit window, while the mixer is shown in the Mix window.

The timeline provides a graphical representation of all types of tracks: the audio envelope or waveform when zoomed in for audio tracks, a piano roll showing MIDI notes and controller values for MIDI and Instrument tracks, a sequence of frame thumbnails for video tracks, audio levels for auxiliary, master and VCA master tracks.

Time can be measured and displayed on the timeline in different scales: bars and beats, time or SMPTE timecode with selectable frame rates , audio samples, or film stock feet for audio-for-film referencing based on the 35 mm film format. Elastic Audio must be enabled to allow time stretching of audio clips. Audio and MIDI clips can be moved, cut, and duplicated non-destructively on the timeline edits change the clip organization on the timeline, but source files are not overwritten.

All other types of audio processing can be rendered on the timeline with the AudioSuite non-real-time version of AAX plug-ins. MIDI notes, velocities, and controllers can be edited directly on the timeline, each MIDI track showing an individual piano roll, or in a specific window, where several MIDI and Instrument tracks can be shown together in a single piano roll with color-coding.

Multiple MIDI controllers for each track can be viewed and edited on different lanes. Video files can be imported to one or more video tracks and organized in multiple playlists.

Multiple video files can be edited together and played back in real-time. Video output from one video track is provided in a separate window or can be viewed full screen. It also can show additional controls for the inserted virtual instrument , mic preamp gain, HEAT settings, and the EQ curve of supported plug-ins.

Audio can be routed to and from different outputs and inputs, both physical and internal. Internal routing is achieved using busses and auxiliary tracks; each track can have multiple output assignments.

Audio, auxiliary, and Instrument tracks or MIDI tracks routed to a virtual instrument plug-in can be committed to new tracks containing their rendered output. Virtual instruments can be committed to audio to prepare an arrangement project for mixing; track commit is also used to free up system resources during mixing or when the session is shared with systems not having some plug-ins installed.

Multiple tracks can be rendered at a time; it is also possible to render a specific timeline selection and define which range of inserts to render. Similarly, tracks can be frozen with their output rendered at the end of the plug-in chain or at a specific insert of their chain.

Editing is suspended on frozen tracks, but they can subsequently be unfrozen if further adjustments are needed. Whichever way you choose, you must also define which tensors are the inputs and outputs of the network. Tensors that are not marked as outputs are considered to be transient values that can be optimized away by the builder. Input and output tensors must be named, so that at runtime, TensorRT knows how to bind the input and output buffers to the model.

Since the builder can take minutes or more to run, you can also control how the builder searches for kernels, and cached search results for use in subsequent runs. After you have a network definition and a builder configuration, you can call the builder to create the engine. The builder eliminates dead computations, folds constants, and reorders and combines operations to run more efficiently on the GPU.

It can optionally reduce the precision of floating-point computations, either by simply running them in bit floating point, or by quantizing floating point values so that calculations can be performed using 8-bit integers.

It also times multiple implementations of each layer with varying data formats, then computes an optimal schedule to execute the model, minimizing the combined cost of kernel executions and format transforms. You can query an engine for information about the input and output tensors of the network – the expected dimensions, data type, data format, and so on.

The execution context contains all of the state associated with a particular invocation – thus you can have multiple contexts associated with a single engine, and run them in parallel.

When invoking inference, you must set up the input and output buffers in the appropriate locations. If not obvious based on your model, you can query the engine to determine in which memory space to provide the buffer. After the buffers are set up, inference can be invoked synchronously execute or asynchronously enqueue.

In the latter case, the required kernels are enqueued on a CUDA stream, and control is returned to the application as soon as possible. To wait for completion of asynchronous execution, synchronize on the stream using cudaStreamSynchronize. TensorRT ships with a library of plug-ins, and source for many of these and some additional plug-ins can be found here.

For regularized models whose input dynamic range is approximately one, this typically produces significant speedups with negligible change in accuracy. Refer to the Reduced Precision section for more details. Dynamic range information can be calculated by the builder this is called calibration based on representative input data. Or you can perform quantization-aware training in a framework and import the model to TensorRT with the necessary dynamic range information.

Refer to the Working with INT8 chapter for more details. In general, formats are chosen to optimize performance, and applications have no control over the choices.

TensorRT creates an optimized engine for each profile, choosing CUDA kernels that work for all shapes within the [minimum, maximum] range and are fastest for the optimization point – typically different kernels for each profile. You can then select among profiles at runtime. Refer to the Working with Dynamic Shapes chapter for more details. Refer to the Working with DLA chapter for more details.

Refer to the Refitting an Engine section for more details. Refer to the trtexec section for more details. For more details, refer to the Polygraphy repository. In order to illustrate object lifetimes, code in this chapter does not use smart pointers; however, their use is recommended with TensorRT interfaces. Refer to the Explicit Versus Implicit Batch section for more information. An important aspect of a TensorRT network definition is that it contains pointers to model weights, which are copied into the optimized engine by the builder.

Since the network was created using the parser, the parser owns the memory occupied by the weights, and so the parser object should not be deleted until after the builder has run.

An engine can have multiple execution contexts, allowing one set of weights to be used for multiple overlapping inference tasks. A current exception to this is when using dynamic shapes, when each optimization profile can only have one execution context.

It is common to enqueue cudaMemcpyAsync before and after the kernels to move data from the GPU if it is not already there. The final argument to enqueueV2 is an optional CUDA event that is signaled when the input buffers have been consumed, and their memory can be safely reused.

To determine when the kernels and possibly memcpy are complete, use standard CUDA synchronization mechanisms such as events or waiting on the stream.

If you prefer synchronous inference, use the executeV2 method instead of enqueueV2. Using these indices, set up GPU buffers for each input and output. First, create the CUDA stream. If you already have a CUDA stream, you can use a pointer to the existing stream.

It is common to enqueue asynchronous memcpy before and after the kernels to move data from the GPU if it is not already there. An important exception to this rule is creating an engine from a builder.

After you have created an engine, you may destroy the builder, network, parser, and build config and continue using the engine.

An API call to an object will use the logger associated with the corresponding top-level interface. For example, in a call to ExecutionContext::enqueue , the execution context was created from an engine, which was created from a runtime, so TensorRT will use the logger associated with that runtime.

You can implement this interface, and attach it to an API object to receive errors associated with that object. The recorder for an object will also be passed to any others it creates – for example, if you attach an error recorder to an engine, and create an execution context from that engine, it will use the same recorder. If you then attach a new error recorder to the execution context, it will receive only errors coming from that context.

If an error is generated but no error recorder is found, it will be emitted through the associated logger. Even with relatively little workspace however, timing requires creating buffers for input, output, and weights. TensorRT is robust against the operating system OS returning out-of-memory for such allocations. On some platforms the OS may successfully provide memory, which then the out-of-memory killer process observes that the system is low on memory, and kills TensorRT.

If this happens free up as much system memory as possible before retrying. During the build phase, there will typically be at least two copies of the weights in host memory: those from the original network, and those included as part of the engine as it is built.

In addition, when TensorRT combines weights for example convolution with batch normalization additional temporary weight tensors will be created. An engine, on deserialization, allocates device memory to store the model weights. Since the serialized engine is almost all weights, its size is a good approximation to the amount of device memory the weights require. You may optionally create an execution context without scratch memory using ICudaEngine::createExecutionContextWithoutDeviceMemory and provide that memory yourself for the duration of network execution.

This allows you to share it between multiple contexts that are not running concurrently, or for other uses while inference is not running.

Note that some layer implementations require these libraries, so that when they are excluded, the network may not compile. The amount of memory varies by platform, device, and TensorRT version.

You can use cudaGetMemInfo to determine the total amount of device memory in use. The expected runtime concurrency model is that different threads will operate on different execution contexts. The context contains the state of the network activation values, and so on during execution, so using a context concurrently in different threads results in undefined behavior.

There are no such issues using multiple threads to build with different GPUs. In general, different implementations will use a different order of floating point operations, resulting in small differences in the output. The impact of these differences on the final result is usually very small. However, when TensorRT is configured to optimize by tuning over multiple precisions, the difference between an FP16 and an FP32 kernel can be more significant, particularly if the network has not been well regularized or is otherwise sensitive to numerical drift.

Other configuration options that can result in a different kernel selection are different input sizes for example, batch size or a different optimization point for an input profile refer to the Working with Dynamic Shapes section.

You can use this to ensure that the same kernels are picked by the builder from run to run. For more information, refer to the Algorithm Selection and Reproducible Builds section. After an engine has been built, it is deterministic: providing the same input in the same runtime environment will produce the same output. If a timing query misses in the cache, the builder times the layer and updates the cache.

Setting the buffer size to 0 creates a new empty timing cache. If there is no timing cache attached to a builder, the builder creates its own temporary local cache and destroys it when it is done.

The new weights should have the same count as the original weights used to build the engine. Because of the way the engine is optimized, if you change some weights, you might have to supply some other weights too.

The interface can tell you what additional weights must be supplied. The set of missing weights returned is complete, in the sense that supplying only the missing weights does not generate a need for any more weights. If refit returns false, check the log for a diagnostic, perhaps about weights that are still missing. The updated engine behaves as if it had been built from a network updated with the new weights.

Sometimes it is important to have a deterministic build, or to recreate the algorithm choices of an earlier build. By providing an implementation of the IAlgorithmSelector interface and attaching it to a builder configuration with setAlgorithmSelector , you can guide algorithm selection manually. The method IAlgorithmSelector::selectAlgorithms receives an AlgorithmContext containing information about the algorithm requirements for a layer, and a set of Algorithm choices meeting those requirements.

It returns the set of algorithms which TensorRT should consider for the layer. The builder selects from these algorithms the one that minimizes the global runtime for the network. After TensorRT has finished optimizing the network for a given profile, it calls reportAlgorithms , which can be used to record the final choice made for each layer. To build a TensorRT engine deterministically, return a single choice from selectAlgorithms.

To replay choices from an earlier build, use reportAlgorithms to record the choices in that build, and return them in selectAlgorithms. Refer to sections Building an Engine and Deserializing a Plan for how to build an engine and run inference with this network. Refer to sections Building an Engine and Performing Inference for how to build an engine and run inference with this network. Note that TensorRT will still choose a higher-precision kernel if it results in overall lower runtime, or if no low-precision implementation exists.

When TensorRT chooses a precision for a layer, it automatically converts weights as necessary to run the layer. This provides a preferred type here, DataType::kFP16 for the inputs and outputs. The computation will use the same floating-point type as is preferred for the inputs. Most TensorRT implementations have the same floating-point types for input and output; however, Convolution, Deconvolution, and FullyConnected can support quantized INT8 input and unquantized FP16 or FP32 output, as sometimes working with higher-precision outputs from quantized inputs is necessary to preserve accuracy.

Setting the precision constraint hints to TensorRT that it should select a layer implementation whose inputs and outputs match the preferred types, inserting reformat operations if the outputs of the previous layer and the inputs to the next layer do not match the requested types. Note that TensorRT will only be able to select an implementation with these types if they are also enabled using the flags in the builder configuration. If the constraints are preferred, TensorRT obeys them unless there is no implementation with the preferred precision constraints, in which case it issues a warning and uses the fastest available implementation.

Output type constraints are similarly optional. A layer is free to choose from any precision or output types based on allowed builder precisions. The latter is mandatory defaulting to FP32 and specifies the type of a network output. If they are different, TensorRT will insert a cast to ensure that both specifications are respected. Thus if you are calling setOutputType for a layer that produces a network output, you should in general also configure the corresponding network output to have the same type.

It is more robust than FP16 for models that require an HDR high dynamic range for weights or activations. Note that for the vectorized formats, the channel dimension must be zero-padded to the multiple of the vector size. Refer to Data Format Descriptions for how the data are actually laid out in memory for these formats.

This ensures that kernels selected during the build phase are present and can run. The safety runtime is able to deserialize engines generated in an environment where the major, minor, patch, and build version of TensorRT does not match exactly in some cases.

If GPU clock speeds differ between engine serialization and runtime systems, the chosen tactics from the serialization system may not be optimal for the runtime system and may incur some performance degradation. If the device memory available during deserialization is smaller than the amount during serialization, deserialization may fail due to memory allocation failures.

When building small models on large devices, TensorRT may choose kernels that are less efficient but scale better across the available resources. Thus if optimizing a single TensorRT engine for use on multiple devices in the same architecture, the best approach is to run the builder on the smallest device. Alternatively, you can build the engine on the larger device with limited compute resources refer to the Limiting Compute Resources section.

In implicit batch mode, every tensor has an implicit batch dimension and all other dimensions must have constant length. This mode was used by early versions of TensorRT, and is now deprecated but continues to be supported for backwards compatibility. In explicit batch mode, all dimensions are explicit and can be dynamic, that is their length can change at execution time.

Many new features, such as dynamic shapes and loops, are available only in this mode. It is also required by the ONNX parser. The exception is that a tensor can be broadcast across the entire batch, through the ITensor::setBroadcastAcrossBatch method for network inputs, and implicit broadcasting for other tensors. Explicit batch mode erases the limitations – the batch axis is axis 0. A more accurate term for explicit batch would be “batch oblivious,” because in this mode, TensorRT attaches no special semantic meaning to the leading axis, except as required by specific operations.

Indeed in explicit batch mode there might not even be a batch dimension such as a network that handles only a single image or there might be multiple batch dimensions of unrelated lengths such as comparison of all possible pairs drawn from two batches. For implicit batch, use createNetwork or pass a 0 to createNetworkV2. Forcing kernel weights to have structured sparsity patterns can lead to accuracy loss. To measure inference performance with structured sparsity using trtexec , refer to the trtexec section.

Implicit broadcast rules remain unchanged since only unit-length dimensions are special for broadcast. For example, given two tensors with dimensions [1,y,z] and [x,1,z], their sum computed by IElementWiseLayer has dimensions [x,y,z], regardless of whether x, y, or z is zero.

If an engine binding is an empty tensor, it still needs a non-null memory address, and different tensors should have different addresses.. If using a memory allocator that might return a null pointer for zero bytes, ask for at least one byte instead. Refer to TensorRT Layers for any per-layer special handling of empty tensors. In addition, when the engine is built with dynamic shapes, the dynamic dimensions in the engine information will be shown as -1 and the tensor format information will not be shown because these fields depend on the actual shape at inference phase.

After the context is set, the inspector will print the engine information for the specific shape set in the context. The trtexec tool provides the –profilingVerbosity , –dumpLayerInfo , and –exportLayerInfo flags that can be used to get the engine information of a given engine. Currently, only binding information and layer information, including the dimensions of the intermediate tensors, precisions, formats, tactic indices, layer types, and layer parameters, are included in the engine information.

More specifications about the keys and the fields in the inspector output will also be provided. In addition, some subgraphs are handled by a next-generation graph optimizer that is not yet integrated with the engine inspector. Therefore, the layer information within these layers is not currently shown. This will be improved in a future TensorRT version. To enable the use of any quantized operations, the INT8 flag must be set in the builder configuration.

Post-training quantization PTQ derives scale factors after the network has been trained. TensorRT provides a workflow for PTQ, called calibration , where it measures the distribution of activations within each activation tensor as the network executes on representative input data, then uses that distribution to estimate a scale value for the tensor.

Quantization-aware training QAT computes scale factors during training. This allows the training process to compensate for the effects of the quantization and dequantization operations.

In implicitly quantized networks, each quantized tensor has an associated scale. When reading and writing the tensor, the scale is used to implicitly quantize and dequantize values. When processing implicitly quantized networks, TensorRT treats the model as a floating-point model when applying the graph optimizations, and uses INT8 opportunistically to optimize layer execution time.

Otherwise, FP32 or FP16 is used. In this mode, TensorRT is optimizing for performance only, and you have little control over where INT8 is used – even if you explicitly set the precision of a layer at the API level, TensorRT may fuse that layer with another during graph optimization, and lose the information that it must execute in INT8. Since TensorRT preserves the semantics of these layers, you can expect task accuracy very close to that seen in the framework. While optimizations preserve the placement of quantization and dequantization, they may change the order of floating-point operations in the model, so results will not be bitwise identical.

With explicit quantization, weights can be quantized using per-tensor quantization or they can be quantized using per-channel quantization. In either case, the scale precision is FP Activations can only be quantized using per-tensor quantization. The scale is a vector of coefficients and must have the same size as the quantization axis. The quantization scale must consist of all positive float coefficients.

The rounding method is rounding-to-nearest ties-to-even and clamping is in the range [, ]. TensorRT supports only per-tensor quantization for activation tensors, but supports per-channel weight quantization for convolution, deconvolution, fully connected layers, and MatMul where the second input is constant and both input matrices are 2D.

The API allows setting the dynamic range for a tensor using minimum and maximum values. Dynamic range is needed for all floating-point inputs and outputs of an operation that will execute in INT8. The amount of input data required is application-dependent, but experiments indicate that about images are sufficient for calibrating ImageNet classification networks.

Given the statistics for an activation tensor, deciding on the best scale value is not an exact science – it requires balancing two sources of error in the quantized representation: discretization error which increases as the range represented by each quantized value becomes larger and truncation error where values are clamped to the limits of the representable range. Thus, TensorRT provides multiple different calibrators that calculate the scale in different ways.

Older calibrators also performed layer fusion for GPU to optimize away unneeded Tensors before performing calibration. For example, calibrating using multiple small batches of calibration data may result in reduced histogram resolution and poor scale value. For each calibration step, TensorRT updates the histogram distribution for each activation tensor. If it encounters a value in the activation tensor, larger than the current histogram max, the histogram range is increased by a power of two to accommodate the new maximum value.

This approach works well unless histogram reallocation occurs in the last calibration step, resulting in a final histogram with half the bins empty. Such a histogram can produce poor calibration scales. This also makes calibration susceptible to the order of calibration batches, that is, a different order of calibration batches can result in the histogram size being increased at different points, producing slightly different calibration scales.

To avoid this issue, calibrate with as large a single batch as possible, and ensure that calibration batches are well randomized and have similar distribution. Calibration can be slow; therefore the output of step 2 the calibration table can be cached and reused. This is useful when building the same network multiple times on a given platform and is supported by all calibrators.

Before running calibration, TensorRT queries the calibrator implementation to see if it has access to a cached table. If so, it proceeds directly to step 3. Cached data is passed as a pointer and length. A sample calibration table can be found here. The calibration cache data is portable across different devices as long as the calibration happens before layer fusion.

This can simplify the workflow, for example by building the calibration table on a machine with a discrete GPU and then reusing it on an embedded platform. Fusions are not guaranteed to be the same across platforms or devices, so calibrating after layer fusion may not result in a portable calibration cache.

The calibration cache is in general not portable across TensorRT releases. To cache the calibration table, implement the writeCalibrationCache and readCalibrationCache methods.

The heuristic attempts to ensure that INT8 quantization is smoothed out by summation of multiple quantized values.

Layers considered to be “smoothing layers” are convolution, deconvolution, a fully connected layer, or matrix multiplication before reaching the network output. In explicit-quantization, network changes of representation to and from INT8 are explicit, therefore, INT8 must not be used as a type constraint.

PyTorch weights are therefore transposed by TensorRT. Quantizable-layers are deep-learning layers that can be converted to quantized layers by fusing with IQuantizeLayer and IDequantizeLayer instances. For the diagrams used in this chapter, green designates INT8 precision and blue designates floating-point precision. Arrows represent network activation tensors and squares represent network layers. The goal in propagation is to maximize the proportion of the graph that can be processed at low precision.

Thus, TensorRT propagates Q nodes backwards so that quantization happens as early as possible and DQ nodes forward so that dequantization happens as late as possible. Q-layers can swap places with layers that commute-with-Quantization and DQ-layers can swap places with layers that commute-with-Dequantization.

The following diagram illustrates DQ forward-propagation and Q backward-propagation. To understand Max Pooling commutation, let us look at the output of the maximum-pooling operation applied to some arbitrary input. Max Pooling is applied to groups of input coefficients and outputs the coefficient with the maximum value.

Function max commutes-with-quantization and so does Max Pooling. There is a distinction between how quantizable-layers and commuting-layers are processed. This is in contrast to how Max Pooling commuting is quantized. Quantization of the weights and activations reduces bandwidth requirements and also enables INT8 computation to accelerate bandwidth-limited and compute-limited layers.

SM75 and earlier devices may not have INT8 implementations for all layers. In this case, you will encounter a could not find any implementation error while building your engine. By default, do not quantize the outputs of weighted-operations.

It is sometimes useful to preserve the higher-precision dequantized output. For example, if the linear operation is followed by an activation function SiLU, in the following diagram that requires higher precision input to produce acceptable accuracy. Do not simulate batch-normalization and ReLU fusions in the training framework because TensorRT optimizations guarantee to preserve the arithmetic semantics of these operations.

TensorRT can fuse element-wise addition following weighted layers, which are useful for models with skip connections like ResNet and EfficientNet. The precision of the first input to the element-wise addition layer determines the precision of the output of the fusion. For example, in the following diagram, the precision of xf1 is floating point, so the output of the fused convolution is limited to floating-point, and the trailing Q-layer cannot be fused with the convolution.

In contrast, when x f 1 is quantized to INT8, as depicted in the following diagram, the output of the fused convolution is also INT8, and the trailing Q-layer is fused with the convolution. Contrast the following figure with Figure 7 , which shows a more performant configuration. The fusion of the element-wise addition is shown in Figure 8.

Use per-tensor quantization for activations; and per-channel quantization for weights. This configuration has been demonstrated empirically to lead to the best quantization accuracy. You can further optimize engine latency by enabling FP The following sections provide greater detail; however, here is an overview of the steps for building an engine with dynamic shapes:.

For example, one profile might specify a minimum size of [3,,] , a maximum size of [3,,] , and optimization dimensions of [3,,] while another profile might specify min, max and optimization dimensions of [3,,] , [3,,] , and [3,,]. At runtime, you must set an optimization profile before setting input dimensions.

Profiles are numbered in the order that they were added, starting at 0. Note that each execution context must use a separate optimization profile. If the associated CUDA engine has dynamic inputs, the optimization profile must be set at least once with a unique profile index that is not used by other execution contexts that are not destroyed. For the first execution context that is created for an engine, profile 0 is chosen implicitly. It must be called after any enqueue or enqueueV2 operations finish in the current context.

When multiple execution contexts run concurrently, it is allowed to switch to a profile that was formerly used but already released by another execution context with different dynamic input dimensions. The men could marry into some of the matrilineal tribes and be accepted, as their children were still considered to belong to the mother’s people. As European expansion increased in the Southeast, African and Native American marriages became more numerous.

Historically, interracial marriage in the United States was subject to great public opposition often a taboo , [53] especially among whites. It was only in when more than half of Americans approved of such marriages in general.

Attitudes towards interracial marriage can vary depending upon the race of the union and the person judging them – for example, black women expressed less approval for black men-white women marriages than the reverse, and Asian men less approval of white men-Asian women marriages than the reverse, seemingly due to concerns over mate competition.

A term has arisen to describe the social phenomenon of the so-called “marriage squeeze” for African American females. Historically, many American religions disapproved of interracial marriage. Biblical literalists are less likely to support interracial marriage to Asians and Latinos. Whites who attend multiracial congregations or engage in devotional religious practices are more likely to support interracial marriages. Children with a religious upbringing in non-Western states, particularly the South, were less likely to have interracially dated than those without religious upbringings.

According to a Baylor University study “people with no religious affiliation were not statistically more likely to be in intermarriages than evangelical or mainline Protestants or people from other religions” [64] with one exception, Catholics. Catholics were twice as likely to be in an interracial marriage than the general population. Some religions actively teach against interracial marriages.

For example, the Church of Jesus Christ of Latter-day Saints recommends against interracial marriages , but does not prohibit it. Even into the twentieth century, marriage between subcultures of Judaism was rare.

Eastern European Jews were the most analyzed subgroup due to having the largest presence in the U. During —, only 2. This figure only rose to 3. One of the greatest factors that swayed Jews away from intermarriage was a fear of assimilation and loss of identity.

Although the beginnings of a melting pot culture appeared to encourage diversity, it was also seen as a threat to the Jewish culture and religion. However, there was also fear of persecution due to racial tensions and frequent discrimination. Not all Jews were hesitant about assimilating into American culture. Some early Jewish authors such as Mary Antin were strong proponents of abandoning their Jewish heritage and encouraged interfaith marriage.

It was suggested as a way to make immigration easier and reflect positively on the Jews in a time of prevailing discrimination. They believed that intermarriage was beneficial to both the Jewish community and America as a whole. While intermarriage was relatively common among ethnic groups like the German and Italians, the practice of endogamy was still the domineering practice among the newer ethnic groups. It has been found that rates in Jewish intermarriage increase from the initial immigrant wave with each subsequent generation.

Racial endogamy is significantly stronger among recent immigrants. For instance, female immigrants of Chinese descent are more likely to marry U. In the United States, rates of interracial cohabitation are significantly higher than those of marriage. From Wikipedia, the free encyclopedia. No laws passed. Repealed before Repealed between to Overturned June 12, Further information: Black Indians. Main article: Marriage squeeze. Retrieved September 29, By Kim Parker and Amanda Barrasso.

By Justin McCarthy. Facing History. Retrieved February 23, The Complete Lincoln-Douglas Debates of University of Chicago Press. Loving Day”. Interracial dating attitudes among college students. Historical analysis of college campus interracial dating. College Student Journal, Mixing and matching: Assessing the concomitants of mixed ethnic relationships. Belinda; Mitchell-Kernan, Claudia Winter Journal of Marriage and Family.

JSTOR Slate magazine. Retrieved January 18, Newcastle University Press. Retrieved October 25, Family Relations. S2CID PMC PMID



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